Daily Papers

The ''pretraining-and-finetuning'' paradigm has become a norm for training domain-specific models in natural language processing and computer vision. In this work, we aim to examine this paradigm for symbolic music generation through leveraging the largest ever symbolic music dataset sourced from the MuseScore forum. We first pretrain a large unconditional transformer model using 1.5 million songs. We then propose a simple technique to equip this pretrained unconditional music transformer model with instrument and genre controls by finetuning the model with additional control tokens. Our proposed representation offers improved high-level controllability and expressiveness against two existing representations. The experimental results show that the proposed model can successfully generate music with user-specified instruments and genre. In a subjective listening test, the proposed model outperforms the pretrained baseline model in terms of coherence, harmony, arrangement and overall quality.

Diffusion Transformers (DiT) excel at image and video generation but face computational challenges due to self-attention's quadratic complexity. We propose DiTFastAttn, a novel post-training compression method to alleviate DiT's computational bottleneck. We identify three key redundancies in the attention computation during DiT inference: 1. spatial redundancy, where many attention heads focus on local information; 2. temporal redundancy, with high similarity between neighboring steps' attention outputs; 3. conditional redundancy, where conditional and unconditional inferences exhibit significant similarity. To tackle these redundancies, we propose three techniques: 1. Window Attention with Residual Caching to reduce spatial redundancy; 2. Temporal Similarity Reduction to exploit the similarity between steps; 3. Conditional Redundancy Elimination to skip redundant computations during conditional generation. To demonstrate the effectiveness of DiTFastAttn, we apply it to DiT, PixArt-Sigma for image generation tasks, and OpenSora for video generation tasks. Evaluation results show that for image generation, our method reduces up to 88\% of the FLOPs and achieves up to 1.6x speedup at high resolution generation.

Transformers have catalyzed advancements in computer vision and natural language processing (NLP) fields. However, substantial computational complexity poses limitations for their application in long-context tasks, such as high-resolution image generation. This paper introduces a series of architectures adapted from the RWKV model used in the NLP, with requisite modifications tailored for diffusion model applied to image generation tasks, referred to as Diffusion-RWKV. Similar to the diffusion with Transformers, our model is designed to efficiently handle patchnified inputs in a sequence with extra conditions, while also scaling up effectively, accommodating both large-scale parameters and extensive datasets. Its distinctive advantage manifests in its reduced spatial aggregation complexity, rendering it exceptionally adept at processing high-resolution images, thereby eliminating the necessity for windowing or group cached operations. Experimental results on both condition and unconditional image generation tasks demonstrate that Diffison-RWKV achieves performance on par with or surpasses existing CNN or Transformer-based diffusion models in FID and IS metrics while significantly reducing total computation FLOP usage.

Battery degradation remains a critical challenge in the pursuit of green technologies and sustainable energy solutions. Despite significant research efforts, predicting battery capacity loss accurately remains a formidable task due to its complex nature, influenced by both aging and cycling behaviors. To address this challenge, we introduce a novel general-purpose model for battery degradation prediction and synthesis, DiffBatt. Leveraging an innovative combination of conditional and unconditional diffusion models with classifier-free guidance and transformer architecture, DiffBatt achieves high expressivity and scalability. DiffBatt operates as a probabilistic model to capture uncertainty in aging behaviors and a generative model to simulate battery degradation. The performance of the model excels in prediction tasks while also enabling the generation of synthetic degradation curves, facilitating enhanced model training by data augmentation. In the remaining useful life prediction task, DiffBatt provides accurate results with a mean RMSE of 196 cycles across all datasets, outperforming all other models and demonstrating superior generalizability. This work represents an important step towards developing foundational models for battery degradation.

This paper presents a new exploration into a category of diffusion models built upon state space architecture. We endeavor to train diffusion models for image data, wherein the traditional U-Net backbone is supplanted by a state space backbone, functioning on raw patches or latent space. Given its notable efficacy in accommodating long-range dependencies, Diffusion State Space Models (DiS) are distinguished by treating all inputs including time, condition, and noisy image patches as tokens. Our assessment of DiS encompasses both unconditional and class-conditional image generation scenarios, revealing that DiS exhibits comparable, if not superior, performance to CNN-based or Transformer-based U-Net architectures of commensurate size. Furthermore, we analyze the scalability of DiS, gauged by the forward pass complexity quantified in Gflops. DiS models with higher Gflops, achieved through augmentation of depth/width or augmentation of input tokens, consistently demonstrate lower FID. In addition to demonstrating commendable scalability characteristics, DiS-H/2 models in latent space achieve performance levels akin to prior diffusion models on class-conditional ImageNet benchmarks at the resolution of 256times256 and 512times512, while significantly reducing the computational burden. The code and models are available at: https://github.com/feizc/DiS.

The creation of manufacturable and editable 3D shapes through Computer-Aided Design (CAD) remains a highly manual and time-consuming task, hampered by the complex topology of boundary representations of 3D solids and unintuitive design tools. While most work in the 3D shape generation literature focuses on representations like meshes, voxels, or point clouds, practical engineering applications demand the modifiability and manufacturability of CAD models and the ability for multi-modal conditional CAD model generation. This paper introduces GenCAD, a generative model that employs autoregressive transformers with a contrastive learning framework and latent diffusion models to transform image inputs into parametric CAD command sequences, resulting in editable 3D shape representations. Extensive evaluations demonstrate that GenCAD significantly outperforms existing state-of-the-art methods in terms of the unconditional and conditional generations of CAD models. Additionally, the contrastive learning framework of GenCAD facilitates the retrieval of CAD models using image queries from large CAD databases, which is a critical challenge within the CAD community. Our results provide a significant step forward in highlighting the potential of generative models to expedite the entire design-to-production pipeline and seamlessly integrate different design modalities.

This work introduces Video Diffusion Transformer (VDT), which pioneers the use of transformers in diffusion-based video generation. It features transformer blocks with modularized temporal and spatial attention modules to leverage the rich spatial-temporal representation inherited in transformers. We also propose a unified spatial-temporal mask modeling mechanism, seamlessly integrated with the model, to cater to diverse video generation scenarios. VDT offers several appealing benefits. 1) It excels at capturing temporal dependencies to produce temporally consistent video frames and even simulate the physics and dynamics of 3D objects over time. 2) It facilitates flexible conditioning information, \eg, simple concatenation in the token space, effectively unifying different token lengths and modalities. 3) Pairing with our proposed spatial-temporal mask modeling mechanism, it becomes a general-purpose video diffuser for harnessing a range of tasks, including unconditional generation, video prediction, interpolation, animation, and completion, etc. Extensive experiments on these tasks spanning various scenarios, including autonomous driving, natural weather, human action, and physics-based simulation, demonstrate the effectiveness of VDT. Additionally, we present comprehensive studies on how \model handles conditioning information with the mask modeling mechanism, which we believe will benefit future research and advance the field. Project page: https:VDT-2023.github.io

Transformers are powerful sequence models, but require time and memory that grows quadratically with the sequence length. In this paper we introduce sparse factorizations of the attention matrix which reduce this to O(n n). We also introduce a) a variation on architecture and initialization to train deeper networks, b) the recomputation of attention matrices to save memory, and c) fast attention kernels for training. We call networks with these changes Sparse Transformers, and show they can model sequences tens of thousands of timesteps long using hundreds of layers. We use the same architecture to model images, audio, and text from raw bytes, setting a new state of the art for density modeling of Enwik8, CIFAR-10, and ImageNet-64. We generate unconditional samples that demonstrate global coherence and great diversity, and show it is possible in principle to use self-attention to model sequences of length one million or more.

Inverse molecular design with diffusion models holds great potential for advancements in material and drug discovery. Despite success in unconditional molecular generation, integrating multiple properties such as synthetic score and gas permeability as condition constraints into diffusion models remains unexplored. We present the Graph Diffusion Transformer (Graph DiT) for multi-conditional molecular generation. Graph DiT integrates an encoder to learn numerical and categorical property representations with the Transformer-based denoiser. Unlike previous graph diffusion models that add noise separately on the atoms and bonds in the forward diffusion process, Graph DiT is trained with a novel graph-dependent noise model for accurate estimation of graph-related noise in molecules. We extensively validate Graph DiT for multi-conditional polymer and small molecule generation. Results demonstrate the superiority of Graph DiT across nine metrics from distribution learning to condition control for molecular properties. A polymer inverse design task for gas separation with feedback from domain experts further demonstrates its practical utility.

Recently, diffusion transformers have gained wide attention with its excellent performance in text-to-image and text-to-vidoe models, emphasizing the need for transformers as backbone for diffusion models. Transformer-based models have shown better generalization capability compared to CNN-based models for general vision tasks. However, much less has been explored in the existing literature regarding the capabilities of transformer-based diffusion backbones and expanding their generative prowess to other datasets. This paper focuses on enabling a single pre-trained diffusion transformer model to scale across multiple datasets swiftly, allowing for the completion of diverse generative tasks using just one model. To this end, we propose DiffScaler, an efficient scaling strategy for diffusion models where we train a minimal amount of parameters to adapt to different tasks. In particular, we learn task-specific transformations at each layer by incorporating the ability to utilize the learned subspaces of the pre-trained model, as well as the ability to learn additional task-specific subspaces, which may be absent in the pre-training dataset. As these parameters are independent, a single diffusion model with these task-specific parameters can be used to perform multiple tasks simultaneously. Moreover, we find that transformer-based diffusion models significantly outperform CNN-based diffusion models methods while performing fine-tuning over smaller datasets. We perform experiments on four unconditional image generation datasets. We show that using our proposed method, a single pre-trained model can scale up to perform these conditional and unconditional tasks, respectively, with minimal parameter tuning while performing as close as fine-tuning an entire diffusion model for that particular task.

We propose TR0N, a highly general framework to turn pre-trained unconditional generative models, such as GANs and VAEs, into conditional models. The conditioning can be highly arbitrary, and requires only a pre-trained auxiliary model. For example, we show how to turn unconditional models into class-conditional ones with the help of a classifier, and also into text-to-image models by leveraging CLIP. TR0N learns a lightweight stochastic mapping which "translates" between the space of conditions and the latent space of the generative model, in such a way that the generated latent corresponds to a data sample satisfying the desired condition. The translated latent samples are then further improved upon through Langevin dynamics, enabling us to obtain higher-quality data samples. TR0N requires no training data nor fine-tuning, yet can achieve a zero-shot FID of 10.9 on MS-COCO, outperforming competing alternatives not only on this metric, but also in sampling speed -- all while retaining a much higher level of generality. Our code is available at https://github.com/layer6ai-labs/tr0n.

Diffusion models have achieved remarkable success in text-to-image synthesis, largely attributed to the use of classifier-free guidance (CFG), which enables high-quality, condition-aligned image generation. CFG combines the conditional score (e.g., text-conditioned) with the unconditional score to control the output. However, the unconditional score is in charge of estimating the transition between manifolds of adjacent timesteps from x_t to x_{t-1}, which may inadvertently interfere with the trajectory toward the specific condition. In this work, we introduce a novel approach that leverages a geometric perspective on the unconditional score to enhance CFG performance when conditional scores are available. Specifically, we propose a method that filters the singular vectors of both conditional and unconditional scores using singular value decomposition. This filtering process aligns the unconditional score with the conditional score, thereby refining the sampling trajectory to stay closer to the manifold. Our approach improves image quality with negligible additional computation. We provide deeper insights into the score function behavior in diffusion models and present a practical technique for achieving more accurate and contextually coherent image synthesis.

Understanding the inner workings of machine learning models like Transformers is vital for their safe and ethical use. This paper provides a comprehensive analysis of a one-layer Transformer model trained to perform n-digit integer addition. Our findings suggest that the model dissects the task into parallel streams dedicated to individual digits, employing varied algorithms tailored to different positions within the digits. Furthermore, we identify a rare scenario characterized by high loss, which we explain. By thoroughly elucidating the model's algorithm, we provide new insights into its functioning. These findings are validated through rigorous testing and mathematical modeling, thereby contributing to the broader fields of model understanding and interpretability. Our approach opens the door for analyzing more complex tasks and multi-layer Transformer models.

Transformer training is notoriously difficult, requiring a careful design of optimizers and use of various heuristics. We make progress towards understanding the subtleties of training Transformers by carefully studying a simple yet canonical linearized shallow Transformer model. Specifically, we train linear Transformers to solve regression tasks, inspired by J.~von Oswald et al.~(ICML 2023), and K.~Ahn et al.~(NeurIPS 2023). Most importantly, we observe that our proposed linearized models can reproduce several prominent aspects of Transformer training dynamics. Consequently, the results obtained in this paper suggest that a simple linearized Transformer model could actually be a valuable, realistic abstraction for understanding Transformer optimization.

In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and classification, forecasting and missing value imputation. By evaluating our models on several benchmark datasets for multivariate time series regression and classification, we show that not only does our modeling approach represent the most successful method employing unsupervised learning of multivariate time series presented to date, but also that it exceeds the current state-of-the-art performance of supervised methods; it does so even when the number of training samples is very limited, while offering computational efficiency. Finally, we demonstrate that unsupervised pre-training of our transformer models offers a substantial performance benefit over fully supervised learning, even without leveraging additional unlabeled data, i.e., by reusing the same data samples through the unsupervised objective.

The Universal Transformer (UT) is a variant of the Transformer that shares parameters across its layers. Empirical evidence shows that UTs have better compositional generalization than Vanilla Transformers (VTs) in formal language tasks. The parameter-sharing also affords it better parameter efficiency than VTs. Despite its many advantages, scaling UT parameters is much more compute and memory intensive than scaling up a VT. This paper proposes the Sparse Universal Transformer (SUT), which leverages Sparse Mixture of Experts (SMoE) and a new stick-breaking-based dynamic halting mechanism to reduce UT's computation complexity while retaining its parameter efficiency and generalization ability. Experiments show that SUT achieves the same performance as strong baseline models while only using half computation and parameters on WMT'14 and strong generalization results on formal language tasks (Logical inference and CFQ). The new halting mechanism also enables around 50\% reduction in computation during inference with very little performance decrease on formal language tasks.

Transformers provide a class of expressive architectures that are extremely effective for sequence modeling. However, the key limitation of transformers is their quadratic memory and time complexity O(L^2) with respect to the sequence length in attention layers, which restricts application in extremely long sequences. Most existing approaches leverage sparsity or low-rank assumptions in the attention matrix to reduce cost, but sacrifice expressiveness. Instead, we propose Combiner, which provides full attention capability in each attention head while maintaining low computation and memory complexity. The key idea is to treat the self-attention mechanism as a conditional expectation over embeddings at each location, and approximate the conditional distribution with a structured factorization. Each location can attend to all other locations, either via direct attention, or through indirect attention to abstractions, which are again conditional expectations of embeddings from corresponding local regions. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention, resulting in the same sub-quadratic cost (O(Llog(L)) or O(LL)). Combiner is a drop-in replacement for attention layers in existing transformers and can be easily implemented in common frameworks. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach, yielding state-of-the-art results on several image and text modeling tasks.

Recurrent neural networks are effective models to process sequences. However, they are unable to learn long-term dependencies because of their inherent sequential nature. As a solution, Vaswani et al. introduced the Transformer, a model solely based on the attention mechanism that is able to relate any two positions of the input sequence, hence modelling arbitrary long dependencies. The Transformer has improved the state-of-the-art across numerous sequence modelling tasks. However, its effectiveness comes at the expense of a quadratic computational and memory complexity with respect to the sequence length, hindering its adoption. Fortunately, the deep learning community has always been interested in improving the models' efficiency, leading to a plethora of solutions such as parameter sharing, pruning, mixed-precision, and knowledge distillation. Recently, researchers have directly addressed the Transformer's limitation by designing lower-complexity alternatives such as the Longformer, Reformer, Linformer, and Performer. However, due to the wide range of solutions, it has become challenging for researchers and practitioners to determine which methods to apply in practice in order to meet the desired trade-off between capacity, computation, and memory. This survey addresses this issue by investigating popular approaches to make Transformers faster and lighter and by providing a comprehensive explanation of the methods' strengths, limitations, and underlying assumptions.

It is widely acknowledged that the performance of Transformer models is exponentially related to their number of parameters and computational complexity. While approaches like Mixture of Experts (MoE) decouple parameter count from computational complexity, they still face challenges in inference due to high memory access costs. This work introduces UltraMem, incorporating large-scale, ultra-sparse memory layer to address these limitations. Our approach significantly reduces inference latency while maintaining model performance. We also investigate the scaling laws of this new architecture, demonstrating that it not only exhibits favorable scaling properties but outperforms traditional models. In our experiments, we train networks with up to 20 million memory slots. The results show that our method achieves state-of-the-art inference speed and model performance within a given computational budget.

Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to represent real numbers. On all problems, transformers trained on sets of random matrices achieve high accuracies (over 90%). The models are robust to noise, and can generalize out of their training distribution. In particular, models trained to predict Laplace-distributed eigenvalues generalize to different classes of matrices: Wigner matrices or matrices with positive eigenvalues. The reverse is not true.

The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and spatio-temporal modelling. There are many introductions to transformers, but most do not contain precise mathematical descriptions of the architecture and the intuitions behind the design choices are often also missing. Moreover, as research takes a winding path, the explanations for the components of the transformer can be idiosyncratic. In this note we aim for a mathematically precise, intuitive, and clean description of the transformer architecture. We will not discuss training as this is rather standard. We assume that the reader is familiar with fundamental topics in machine learning including multi-layer perceptrons, linear transformations, softmax functions and basic probability.

Transformer-based architectures achieved breakthrough performance in natural language processing and computer vision, yet they remain inferior to simpler linear baselines in multivariate long-term forecasting. To better understand this phenomenon, we start by studying a toy linear forecasting problem for which we show that transformers are incapable of converging to their true solution despite their high expressive power. We further identify the attention of transformers as being responsible for this low generalization capacity. Building upon this insight, we propose a shallow lightweight transformer model that successfully escapes bad local minima when optimized with sharpness-aware optimization. We empirically demonstrate that this result extends to all commonly used real-world multivariate time series datasets. In particular, SAMformer surpasses current state-of-the-art methods and is on par with the biggest foundation model MOIRAI while having significantly fewer parameters. The code is available at https://github.com/romilbert/samformer.

Classifier-Free Guidance (CFG) is a fundamental technique in training conditional diffusion models. The common practice for CFG-based training is to use a single network to learn both conditional and unconditional noise prediction, with a small dropout rate for conditioning. However, we observe that the joint learning of unconditional noise with limited bandwidth in training results in poor priors for the unconditional case. More importantly, these poor unconditional noise predictions become a serious reason for degrading the quality of conditional generation. Inspired by the fact that most CFG-based conditional models are trained by fine-tuning a base model with better unconditional generation, we first show that simply replacing the unconditional noise in CFG with that predicted by the base model can significantly improve conditional generation. Furthermore, we show that a diffusion model other than the one the fine-tuned model was trained on can be used for unconditional noise replacement. We experimentally verify our claim with a range of CFG-based conditional models for both image and video generation, including Zero-1-to-3, Versatile Diffusion, DiT, DynamiCrafter, and InstructPix2Pix.

Attention-based transformers have become the standard architecture in many deep learning fields, primarily due to their ability to model long-range dependencies and handle variable-length input sequences. However, the attention mechanism with its quadratic complexity is a significant bottleneck in the transformer architecture. This algorithm is only uni-directional in the decoder and converges to a static pattern in over-parametrized decoder-only models. I address this issue by developing a generative function as attention or activation replacement. It still has the auto-regressive character by comparing each token with the previous one. In my test setting with nanoGPT this yields a smaller loss while having a smaller model. The loss further drops by incorporating an average context vector. This concept of attention replacement is distributed under the GNU AGPL v3 license at https://gitlab.com/Bachstelze/causal_generation.

Deep learning employs multi-layer neural networks trained via the backpropagation algorithm. This approach has achieved success across many domains and relies on adaptive gradient methods such as the Adam optimizer. Sequence modeling evolved from recurrent neural networks to attention-based models, culminating in the Transformer architecture. Transformers have achieved state-of-the-art performance in natural language processing (for example, BERT and GPT-3) and have been applied in computer vision and computational biology. However, theoretical understanding of these models remains limited. In this paper, we examine the mathematical foundations of deep learning and Transformers and present a novel theoretical result. We review key concepts from linear algebra, probability, and optimization that underpin deep learning, and we analyze the multi-head self-attention mechanism and the backpropagation algorithm in detail. Our main contribution is a universal approximation theorem for Transformers: we prove that a single-layer Transformer, comprising one self-attention layer followed by a position-wise feed-forward network with ReLU activation, can approximate any continuous sequence-to-sequence mapping on a compact domain to arbitrary precision. We provide a formal statement and a complete proof. Finally, we present case studies that demonstrate the practical implications of this result. Our findings advance the theoretical understanding of Transformer models and help bridge the gap between theory and practice.

Idempotence is the stability of image codec to re-compression. At the first glance, it is unrelated to perceptual image compression. However, we find that theoretically: 1) Conditional generative model-based perceptual codec satisfies idempotence; 2) Unconditional generative model with idempotence constraint is equivalent to conditional generative codec. Based on this newfound equivalence, we propose a new paradigm of perceptual image codec by inverting unconditional generative model with idempotence constraints. Our codec is theoretically equivalent to conditional generative codec, and it does not require training new models. Instead, it only requires a pre-trained mean-square-error codec and unconditional generative model. Empirically, we show that our proposed approach outperforms state-of-the-art methods such as HiFiC and ILLM, in terms of Fr\'echet Inception Distance (FID). The source code is provided in https://github.com/tongdaxu/Idempotence-and-Perceptual-Image-Compression.

Transformer-based models typically have a predefined bound to their input length, because of their need to potentially attend to every token in the input. In this work, we propose Unlimiformer: a general approach that can wrap any existing pretrained encoder-decoder transformer, and offload the attention computation across all layers to a single k-nearest-neighbor index; this index can be kept on either the GPU or CPU memory and queried in sub-linear time. This way, we can index extremely long input sequences, while every attention head in every decoder layer retrieves its top-k keys, instead of attending to every key. We demonstrate Unlimiformers's efficacy on several long-document and multi-document summarization benchmarks, showing that it can summarize even 350k token-long inputs from the BookSum dataset, without any input truncation at test time. Unlimiformer improves pretrained models such as BART and Longformer by extending them to unlimited inputs without additional learned weights and without modifying their code. We make our code and models publicly available at https://github.com/abertsch72/unlimiformer .

Since the success of GPT, large language models (LLMs) have been revolutionizing machine learning and have initiated the so-called LLM prompting paradigm. In the era of LLMs, people train a single general-purpose LLM and provide the LLM with different prompts to perform different tasks. However, such empirical success largely lacks theoretical understanding. Here, we present the first theoretical study on the LLM prompting paradigm to the best of our knowledge. In this work, we show that prompting is in fact Turing-complete: there exists a finite-size Transformer such that for any computable function, there exists a corresponding prompt following which the Transformer computes the function. Furthermore, we show that even though we use only a single finite-size Transformer, it can still achieve nearly the same complexity bounds as that of the class of all unbounded-size Transformers. Overall, our result reveals that prompting can enable a single finite-size Transformer to be efficiently universal, which establishes a theoretical underpinning for prompt engineering in practice.

In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the underlying technology employed in GPT-x as past work has focused on the more expressive, full auto-encoder transformer architecture. From this theoretical analysis, we show that the sparsity/compressibility of the word embedding is an important consideration for Turing completeness to hold. We also show that Transformers are are a variant of B machines studied by Hao Wang.

Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in handling more complex problems remains unexplored. In this paper, we prove that any linear transformer maintains an implicit linear model and can be interpreted as performing a variant of preconditioned gradient descent. We also investigate the use of linear transformers in a challenging scenario where the training data is corrupted with different levels of noise. Remarkably, we demonstrate that for this problem linear transformers discover an intricate and highly effective optimization algorithm, surpassing or matching in performance many reasonable baselines. We reverse-engineer this algorithm and show that it is a novel approach incorporating momentum and adaptive rescaling based on noise levels. Our findings show that even linear transformers possess the surprising ability to discover sophisticated optimization strategies.

In this paper, we take the advantage of previous pre-trained models (PTMs) and propose a novel Chinese Pre-trained Unbalanced Transformer (CPT). Different from previous Chinese PTMs, CPT is designed to utilize the shared knowledge between natural language understanding (NLU) and natural language generation (NLG) to boost the performance. CPT consists of three parts: a shared encoder, an understanding decoder, and a generation decoder. Two specific decoders with a shared encoder are pre-trained with masked language modeling (MLM) and denoising auto-encoding (DAE) tasks, respectively. With the partially shared architecture and multi-task pre-training, CPT can (1) learn specific knowledge of both NLU or NLG tasks with two decoders and (2) be fine-tuned flexibly that fully exploits the potential of the model. Moreover, the unbalanced Transformer saves the computational and storage cost, which makes CPT competitive and greatly accelerates the inference of text generation. Experimental results on a wide range of Chinese NLU and NLG tasks show the effectiveness of CPT.

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation ability of Transformers as sequence-to-sequence functions with infinite dimensional inputs. Although inputs and outputs are both infinite dimensional, we show that when the target function has anisotropic smoothness, Transformers can avoid the curse of dimensionality due to their feature extraction ability and parameter sharing property. In addition, we show that even if the smoothness changes depending on each input, Transformers can estimate the importance of features for each input and extract important features dynamically. Then, we proved that Transformers achieve similar convergence rate as in the case of the fixed smoothness. Our theoretical results support the practical success of Transformers for high dimensional data.

Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear regression tasks, and different from all the existing literature, we consider a bi-objective prediction task of predicting both the conditional expectation E[Y|X] and the conditional variance Var(Y|X). This additional uncertainty quantification objective provides a handle to (i) better design out-of-distribution experiments to distinguish ICL from in-weight learning (IWL) and (ii) make a better separation between the algorithms with and without using the prior information of the training distribution. Theoretically, we show that the trained Transformer reaches near Bayes-optimum, suggesting the usage of the information of the training distribution. Our method can be extended to other cases. Specifically, with the Transformer's context window S, we prove a generalization bound of mathcal{O}(min{S, T/(n T)}) on n tasks with sequences of length T, providing sharper analysis compared to previous results of mathcal{O}(1/n). Empirically, we illustrate that while the trained Transformer behaves as the Bayes-optimal solution as a natural consequence of supervised training in distribution, it does not necessarily perform a Bayesian inference when facing task shifts, in contrast to the equivalence between these two proposed in many existing literature. We also demonstrate the trained Transformer's ICL ability over covariates shift and prompt-length shift and interpret them as a generalization over a meta distribution.

Transformer models, notably large language models (LLMs), have the remarkable ability to perform in-context learning (ICL) -- to perform new tasks when prompted with unseen input-output examples without any explicit model training. In this work, we study how effectively transformers can bridge between their pretraining data mixture, comprised of multiple distinct task families, to identify and learn new tasks in-context which are both inside and outside the pretraining distribution. Building on previous work, we investigate this question in a controlled setting, where we study transformer models trained on sequences of (x, f(x)) pairs rather than natural language. Our empirical results show transformers demonstrate near-optimal unsupervised model selection capabilities, in their ability to first in-context identify different task families and in-context learn within them when the task families are well-represented in their pretraining data. However when presented with tasks or functions which are out-of-domain of their pretraining data, we demonstrate various failure modes of transformers and degradation of their generalization for even simple extrapolation tasks. Together our results highlight that the impressive ICL abilities of high-capacity sequence models may be more closely tied to the coverage of their pretraining data mixtures than inductive biases that create fundamental generalization capabilities.

The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction, directly generating diverse, novel protein structures from neural networks remains difficult. In this work, we present a new diffusion-based generative model that designs protein backbone structures via a procedure that mirrors the native folding process. We describe protein backbone structure as a series of consecutive angles capturing the relative orientation of the constituent amino acid residues, and generate new structures by denoising from a random, unfolded state towards a stable folded structure. Not only does this mirror how proteins biologically twist into energetically favorable conformations, the inherent shift and rotational invariance of this representation crucially alleviates the need for complex equivariant networks. We train a denoising diffusion probabilistic model with a simple transformer backbone and demonstrate that our resulting model unconditionally generates highly realistic protein structures with complexity and structural patterns akin to those of naturally-occurring proteins. As a useful resource, we release the first open-source codebase and trained models for protein structure diffusion.

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

Test-time adaptation (TTA) aims to enhance the performance of source-domain pretrained models when tested on unknown shifted target domains. Traditional TTA methods primarily adapt model weights based on target data streams, making model performance sensitive to the amount and order of target data. Recently, diffusion-driven TTA methods have demonstrated strong performance by using an unconditional diffusion model, which is also trained on the source domain to transform target data into synthetic data as a source domain projection. This allows the source model to make predictions without weight adaptation. In this paper, we argue that the domains of the source model and the synthetic data in diffusion-driven TTA methods are not aligned. To adapt the source model to the synthetic domain of the unconditional diffusion model, we introduce a Synthetic-Domain Alignment (SDA) framework to fine-tune the source model with synthetic data. Specifically, we first employ a conditional diffusion model to generate labeled samples, creating a synthetic dataset. Subsequently, we use the aforementioned unconditional diffusion model to add noise to and denoise each sample before fine-tuning. This process mitigates the potential domain gap between the conditional and unconditional models. Extensive experiments across various models and benchmarks demonstrate that SDA achieves superior domain alignment and consistently outperforms existing diffusion-driven TTA methods. Our code is available at https://github.com/SHI-Labs/Diffusion-Driven-Test-Time-Adaptation-via-Synthetic-Domain-Alignment.

As we show in this paper, the prediction for output token n+1 of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens 1, 2, ..., n-1. Usually, both mechanisms are employed and the symmetry with respect to the input tokens is broken. Recently, it has been shown that one can train Transformers without positional encodings. This must be enabled by the causal attention mechanism. In this paper, we elaborate on the argument that the causal connection mechanism must be responsible for the fact that Transformers are able to model input sequences where the order is important. Vertical "slices" of Transformers are all encouraged to represent the same location k in the input sequence. We hypothesize that residual connections contribute to this phenomenon, and demonstrate evidence for this.

Through considerable effort and intuition, several recent works have reverse-engineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a metric and dataset that elicit the desired model behavior. Then, they apply activation patching to find which abstract neural network units are involved in the behavior. By varying the dataset, metric, and units under investigation, researchers can understand the functionality of each component. We automate one of the process' steps: to identify the circuit that implements the specified behavior in the model's computational graph. We propose several algorithms and reproduce previous interpretability results to validate them. For example, the ACDC algorithm rediscovered 5/5 of the component types in a circuit in GPT-2 Small that computes the Greater-Than operation. ACDC selected 68 of the 32,000 edges in GPT-2 Small, all of which were manually found by previous work. Our code is available at https://github.com/ArthurConmy/Automatic-Circuit-Discovery.

Transformers often fail to learn generalizable algorithms, instead relying on brittle heuristics. Using graph connectivity as a testbed, we explain this phenomenon both theoretically and empirically. We consider a simplified Transformer architecture, the disentangled Transformer, and prove that an L-layer model has capacity to solve for graphs with diameters up to exactly 3^L, implementing an algorithm equivalent to computing powers of the adjacency matrix. We analyze the training-dynamics, and show that the learned strategy hinges on whether most training instances are within this model capacity. Within-capacity graphs (diameter leq 3^L) drive the learning of a correct algorithmic solution while beyond-capacity graphs drive the learning of a simple heuristic based on node degrees. Finally, we empirically demonstrate that restricting training data within a model's capacity leads to both standard and disentangled transformers learning the exact algorithm rather than the degree-based heuristic.

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair (x, y) with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture presents a challenge in emulating the iterative algorithms, which are commonly employed in traditional machine learning methods. To address this, we propose the utilization of looped transformer architecture and its associated training methodology, with the aim of incorporating iterative characteristics into the transformer architectures. Experimental results suggest that the looped transformer achieves performance comparable to the standard transformer in solving various data-fitting problems, while utilizing less than 10\% of the parameter count.

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the transformer model. Our framework can be used to understand and mitigate vanishing/exploding gradients, rank collapse, and instability associated with high attention scores. We also propose DeepScaleLM, an initialization and scaling scheme that conserves unit output/gradient moments throughout the model, enabling the training of very deep models with 100s of layers. We find that transformer models could be much deeper - our deep models with fewer parameters outperform shallow models in Language Modeling, Speech Translation, and Image Classification, across Encoder-only, Decoder-only and Encoder-Decoder variants, for both Pre-LN and Post-LN transformers, for multiple datasets and model sizes. These improvements also translate into improved performance on downstream Question Answering tasks and improved robustness for image classification.

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.

We perform an effective-theory analysis of forward-backward signal propagation in wide and deep Transformers, i.e., residual neural networks with multi-head self-attention blocks and multilayer perceptron blocks. This analysis suggests particular width scalings of initialization and training hyperparameters for these models. We then take up such suggestions, training Vision and Language Transformers in practical setups.

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer architecture is a critical component of LLMs, as it allows the model to selectively focus on specific input parts. The softmax unit, which is a key part of the attention mechanism, normalizes the attention scores. Hence, the performance of LLMs in various NLP tasks depends significantly on the crucial role played by the attention mechanism with the softmax unit. In-context learning, as one of the celebrated abilities of recent LLMs, is an important concept in querying LLMs such as ChatGPT. Without further parameter updates, Transformers can learn to predict based on few in-context examples. However, the reason why Transformers becomes in-context learners is not well understood. Recently, several works [ASA+22,GTLV22,ONR+22] have studied the in-context learning from a mathematical perspective based on a linear regression formulation min_x| Ax - b |_2, which show Transformers' capability of learning linear functions in context. In this work, we study the in-context learning based on a softmax regression formulation min_{x} | langle exp(Ax), {bf 1}_n rangle^{-1} exp(Ax) - b |_2 of Transformer's attention mechanism. We show the upper bounds of the data transformations induced by a single self-attention layer and by gradient-descent on a ell_2 regression loss for softmax prediction function, which imply that when training self-attention-only Transformers for fundamental regression tasks, the models learned by gradient-descent and Transformers show great similarity.

Transformer models are deployed in a wide range of settings, from multi-accelerator clusters to standalone mobile phones. The diverse inference constraints in these scenarios necessitate practitioners to train foundation models such as PaLM 2, Llama, & ViTs as a series of models of varying sizes. Due to significant training costs, only a select few model sizes are trained and supported, limiting more fine-grained control over relevant tradeoffs, including latency, cost, and accuracy. This work introduces MatFormer, a nested Transformer architecture designed to offer elasticity in a variety of deployment constraints. Each Feed Forward Network (FFN) block of a MatFormer model is jointly optimized with a few nested smaller FFN blocks. This training procedure allows for the Mix'n'Match of model granularities across layers -- i.e., a trained universal MatFormer model enables extraction of hundreds of accurate smaller models, which were never explicitly optimized. We empirically demonstrate MatFormer's effectiveness across different model classes (decoders & encoders), modalities (language & vision), and scales (up to 2.6B parameters). We find that a 2.6B decoder-only MatFormer language model (MatLM) allows us to extract smaller models spanning from 1.5B to 2.6B, each exhibiting comparable validation loss and one-shot downstream evaluations to their independently trained counterparts. Furthermore, we observe that smaller encoders extracted from a universal MatFormer-based ViT (MatViT) encoder preserve the metric-space structure for adaptive large-scale retrieval. Finally, we showcase that speculative decoding with the accurate and consistent submodels extracted from MatFormer can further reduce inference latency.

State of the art sequence-to-sequence models for large scale tasks perform a fixed number of computations for each input sequence regardless of whether it is easy or hard to process. In this paper, we train Transformer models which can make output predictions at different stages of the network and we investigate different ways to predict how much computation is required for a particular sequence. Unlike dynamic computation in Universal Transformers, which applies the same set of layers iteratively, we apply different layers at every step to adjust both the amount of computation as well as the model capacity. On IWSLT German-English translation our approach matches the accuracy of a well tuned baseline Transformer while using less than a quarter of the decoder layers.

We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for large-scale simulations to yield a more scalable and versatile general-purpose transformer architecture, which can be used as the backbone for building large-scale foundation models in physical sciences. We demonstrate that our proposed architecture outperforms state-of-the-art transformer architectures for computer vision on a large dataset of 16 different types of PDEs. We propose to embed different physical channels individually as spatio-temporal tokens, which interact via channel-wise self-attention. This helps to maintain a consistent information density of tokens when learning multiple types of PDEs simultaneously. We demonstrate that our pre-trained models achieve improved performance on several challenging downstream tasks compared to training from scratch and also beat other foundation model architectures for physics simulations.

We report a series of deep learning models to solve complex forward and inverse design problems in molecular modeling and design. Using both diffusion models inspired by nonequilibrium thermodynamics and attention-based transformer architectures, we demonstrate a flexible framework to capture complex chemical structures. First trained on the QM9 dataset and a series of quantum mechanical properties (e.g. homo, lumo, free energy, heat capacity, etc.), we then generalize the model to study and design key properties of deep eutectic solvents. In addition to separate forward and inverse models, we also report an integrated fully prompt-based multi-task generative pretrained transformer model that solves multiple forward, inverse design, and prediction tasks, flexibly and within one model. We show that the multi-task generative model has the overall best performance and allows for flexible integration of multiple objectives, within one model, and for distinct chemistries, suggesting that synergies emerge during training of this large language model. Trained jointly in tasks related to the QM9 dataset and deep eutectic solvents (DESs), the model can predict various quantum mechanical properties and critical properties to achieve deep eutectic solvent behavior. Several novel combinations of DESs are proposed based on this framework.

Solving Bayesian inverse problems efficiently remains a significant challenge due to the complexity of posterior distributions and the computational cost of traditional sampling methods. Given a series of observations and the forward model, we want to recover the distribution of the parameters, conditioned on observed experimental data. We show, that combining Conditional Flow Mathching (CFM) with transformer-based architecture, we can efficiently sample from such kind of distribution, conditioned on variable number of observations.

While there has been a large body of research attempting to circumvent tokenization for language modeling (Clark et al., 2022; Xue et al., 2022), the current consensus is that it is a necessary initial step for designing state-of-the-art performant language models. In this paper, we investigate tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. When trained on data drawn from certain simple k^{th}-order Markov processes for k > 1, transformers exhibit a surprising phenomenon - in the absence of tokenization, they empirically fail to learn the right distribution and predict characters according to a unigram model (Makkuva et al., 2024). With the addition of tokenization, however, we empirically observe that transformers break through this barrier and are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. With this observation as starting point, we study the end-to-end cross-entropy loss achieved by transformers with and without tokenization. With the appropriate tokenization, we show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from k^{th}-order Markov sources near optimally. Our analysis provides a justification for the use of tokenization in practice through studying the behavior of transformers on Markovian data.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of pre-conditioned GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of nonlinear functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

We investigate the transformer's capability for in-context learning (ICL) to simulate the training process of deep models. Our key contribution is providing a positive example of using a transformer to train a deep neural network by gradient descent in an implicit fashion via ICL. Specifically, we provide an explicit construction of a (2N+4)L-layer transformer capable of simulating L gradient descent steps of an N-layer ReLU network through ICL. We also give the theoretical guarantees for the approximation within any given error and the convergence of the ICL gradient descent. Additionally, we extend our analysis to the more practical setting using Softmax-based transformers. We validate our findings on synthetic datasets for 3-layer, 4-layer, and 6-layer neural networks. The results show that ICL performance matches that of direct training.

Recent research in mechanistic interpretability has attempted to reverse-engineer Transformer models by carefully inspecting network weights and activations. However, these approaches require considerable manual effort and still fall short of providing complete, faithful descriptions of the underlying algorithms. In this work, we introduce a procedure for training Transformers that are mechanistically interpretable by design. We build on RASP [Weiss et al., 2021], a programming language that can be compiled into Transformer weights. Instead of compiling human-written programs into Transformers, we design a modified Transformer that can be trained using gradient-based optimization and then automatically converted into a discrete, human-readable program. We refer to these models as Transformer Programs. To validate our approach, we learn Transformer Programs for a variety of problems, including an in-context learning task, a suite of algorithmic problems (e.g. sorting, recognizing Dyck languages), and NLP tasks including named entity recognition and text classification. The Transformer Programs can automatically find reasonable solutions, performing on par with standard Transformers of comparable size; and, more importantly, they are easy to interpret. To demonstrate these advantages, we convert Transformers into Python programs and use off-the-shelf code analysis tools to debug model errors and identify the "circuits" used to solve different sub-problems. We hope that Transformer Programs open a new path toward the goal of intrinsically interpretable machine learning.

One limitation of existing Transformer-based models is that they cannot handle very long sequences as input since their self-attention operations exhibit quadratic time and space complexity. This problem becomes especially acute when Transformers are deployed on hardware platforms equipped only with CPUs. To address this issue, we propose a novel method for accelerating self-attention at inference time that works with pretrained Transformer models out-of-the-box without requiring retraining. We experiment using our method to accelerate various long-sequence Transformers, including a leading LLaMA 2-based LLM, on various benchmarks and demonstrate a greater speedup of 2.73x - 7.63x while retaining 98.6% - 99.6% of the accuracy of the original pretrained models. The code is available on our project website at https://yuzhenmao.github.io/IceFormer/.

With the tremendous success of large transformer models in natural language understanding, down-sizing them for cost-effective deployments has become critical. Recent studies have explored the low-rank weight factorization techniques which are efficient to train, and apply out-of-the-box to any transformer architecture. Unfortunately, the low-rank assumption tends to be over-restrictive and hinders the expressiveness of the compressed model. This paper proposes, DSFormer, a simple alternative factorization scheme which expresses a target weight matrix as the product of a small dense and a semi-structured sparse matrix. The resulting approximation is more faithful to the weight distribution in transformers and therefore achieves a stronger efficiency-accuracy trade-off. Another concern with existing factorizers is their dependence on a task-unaware initialization step which degrades the accuracy of the resulting model. DSFormer addresses this issue through a novel Straight-Through Factorizer (STF) algorithm that jointly learns all the weight factorizations to directly maximize the final task accuracy. Extensive experiments on multiple natural language understanding benchmarks demonstrate that DSFormer obtains up to 40% better compression than the state-of-the-art low-rank factorizers, leading semi-structured sparsity baselines and popular knowledge distillation approaches. Our approach is also orthogonal to mainstream compressors and offers up to 50% additional compression when added to popular distilled, layer-shared and quantized transformers. We empirically evaluate the benefits of STF over conventional optimization practices.

The transformer model is known to be computationally demanding, and prohibitively costly for long sequences, as the self-attention module uses a quadratic time and space complexity with respect to sequence length. Many researchers have focused on designing new forms of self-attention or introducing new parameters to overcome this limitation, however a large portion of them prohibits the model to inherit weights from large pretrained models. In this work, the transformer's inefficiency has been taken care of from another perspective. We propose Fourier Transformer, a simple yet effective approach by progressively removing redundancies in hidden sequence using the ready-made Fast Fourier Transform (FFT) operator to perform Discrete Cosine Transformation (DCT). Fourier Transformer is able to significantly reduce computational costs while retain the ability to inherit from various large pretrained models. Experiments show that our model achieves state-of-the-art performances among all transformer-based models on the long-range modeling benchmark LRA with significant improvement in both speed and space. For generative seq-to-seq tasks including CNN/DailyMail and ELI5, by inheriting the BART weights our model outperforms the standard BART and other efficient models. Our code is publicly available at \url{https://github.com/LUMIA-Group/FourierTransformer}

Normalization layers are ubiquitous in modern neural networks and have long been considered essential. This work demonstrates that Transformers without normalization can achieve the same or better performance using a remarkably simple technique. We introduce Dynamic Tanh (DyT), an element-wise operation DyT(x) = tanh(alpha x), as a drop-in replacement for normalization layers in Transformers. DyT is inspired by the observation that layer normalization in Transformers often produces tanh-like, S-shaped input-output mappings. By incorporating DyT, Transformers without normalization can match or exceed the performance of their normalized counterparts, mostly without hyperparameter tuning. We validate the effectiveness of Transformers with DyT across diverse settings, ranging from recognition to generation, supervised to self-supervised learning, and computer vision to language models. These findings challenge the conventional understanding that normalization layers are indispensable in modern neural networks, and offer new insights into their role in deep networks.

Transformer-based models, exemplified by GPT-3, ChatGPT, and GPT-4, have recently garnered considerable attention in both academia and industry due to their promising performance in general language tasks. Nevertheless, these models typically involve computationally encoding processes, and in some cases, decoding processes as well, both of which are fundamentally large-scale matrix multiplication. These operations bring the inevitable challenges of massive computation resources and huge memory footprint, usually requiring at least 10^23 FLOPs and hundreds of gigabytes, respectively. A common method to address this issue is to reduce the computational and memory requirements by applying layerwise quantization to the transformer, replacing the usual fp32 data type with a low-bit equivalent. Unfortunately, this method often leads to decreased model accuracy and necessitates time-consuming retraining. Such retraining not only requires fine-tuning skills but also substantial computational resources, posing challenges for users. To specifically tackle these issues, we propose BCT, a framework of blockwise compression for transformers without retraining, aiming to facilitate model deployment. Unlike layerwise compression methods, BCT achieves finer compression of the entire transformer by operating blockwise. This method mitigates data distribution deviation caused by quantization, eliminating the requirement for retraining. BCT effectively compresses all components of the model, including but not limited to the embedding, matrix multiplication, GELU, Softmax, layer normalization, and intermediate results. In a case study, an efficient model is compressed by BCT achieving up to 7.988x compression. Subsequently, we also evaluate it on several General Language Understanding Evaluation (GLUE) datasets.

Large language models exhibit surprising emergent generalization properties, yet also struggle on many simple reasoning tasks such as arithmetic and parity. This raises the question of if and when Transformer models can learn the true algorithm for solving a task. We study the scope of Transformers' abilities in the specific setting of length generalization on algorithmic tasks. Here, we propose a unifying framework to understand when and how Transformers can exhibit strong length generalization on a given task. Specifically, we leverage RASP (Weiss et al., 2021) -- a programming language designed for the computational model of a Transformer -- and introduce the RASP-Generalization Conjecture: Transformers tend to length generalize on a task if the task can be solved by a short RASP program which works for all input lengths. This simple conjecture remarkably captures most known instances of length generalization on algorithmic tasks. Moreover, we leverage our insights to drastically improve generalization performance on traditionally hard tasks (such as parity and addition). On the theoretical side, we give a simple example where the "min-degree-interpolator" model of learning from Abbe et al. (2023) does not correctly predict Transformers' out-of-distribution behavior, but our conjecture does. Overall, our work provides a novel perspective on the mechanisms of compositional generalization and the algorithmic capabilities of Transformers.

There have been a lot of interest in the scaling properties of Transformer models. However, not much has been done on the front of investigating the effect of scaling properties of different inductive biases and model architectures. Do model architectures scale differently? If so, how does inductive bias affect scaling behaviour? How does this influence upstream (pretraining) and downstream (transfer)? This paper conducts a systematic study of scaling behaviour of ten diverse model architectures such as Transformers, Switch Transformers, Universal Transformers, Dynamic convolutions, Performers, and recently proposed MLP-Mixers. Via extensive experiments, we show that (1) architecture is an indeed an important consideration when performing scaling and (2) the best performing model can fluctuate at different scales. We believe that the findings outlined in this work has significant implications to how model architectures are currently evaluated in the community.

Transformers have emerged as the prevailing standard solution for various AI tasks, including computer vision and natural language processing. The widely adopted Query, Key, and Value formulation (QKV) has played a significant role in this. Nevertheless, no research has examined the essentiality of these three components for transformer performance. Therefore, we conducted an evaluation of the key-value formulation (KV), which generates symmetric attention maps, along with an asymmetric version that incorporates a 2D positional encoding into the attention matrix. Remarkably, this transformer requires fewer parameters and computation than the original one. Through experiments encompassing three task types -- synthetics (such as reversing or sorting a list), vision (mnist or cifar classification), and NLP (character generation and translation) -- we discovered that the KV transformer occasionally outperforms the QKV transformer. However, it also exhibits instances of underperformance compared to QKV, making it challenging to draw a definitive conclusion. Nonetheless, we consider the reported results to be encouraging and anticipate that they may pave the way for more efficient transformers in the future.

We propose an extension of the decoder Transformer that conditions its generative process on random latent variables which are learned without supervision thanks to a variational procedure. Experimental evaluations show that allowing such a conditioning translates into substantial improvements on downstream tasks.

Previous work on Universal Transformers (UTs) has demonstrated the importance of parameter sharing across layers. By allowing recurrence in depth, UTs have advantages over standard Transformers in learning compositional generalizations, but layer-sharing comes with a practical limitation of parameter-compute ratio: it drastically reduces the parameter count compared to the non-shared model with the same dimensionality. Naively scaling up the layer size to compensate for the loss of parameters makes its computational resource requirements prohibitive. In practice, no previous work has succeeded in proposing a shared-layer Transformer design that is competitive in parameter count-dominated tasks such as language modeling. Here we propose MoEUT (pronounced "moot"), an effective mixture-of-experts (MoE)-based shared-layer Transformer architecture, which combines several recent advances in MoEs for both feedforward and attention layers of standard Transformers together with novel layer-normalization and grouping schemes that are specific and crucial to UTs. The resulting UT model, for the first time, slightly outperforms standard Transformers on language modeling tasks such as BLiMP and PIQA, while using significantly less compute and memory.

Transformers have achieved great success in many artificial intelligence fields, such as natural language processing, computer vision, and audio processing. Therefore, it is natural to attract lots of interest from academic and industry researchers. Up to the present, a great variety of Transformer variants (a.k.a. X-formers) have been proposed, however, a systematic and comprehensive literature review on these Transformer variants is still missing. In this survey, we provide a comprehensive review of various X-formers. We first briefly introduce the vanilla Transformer and then propose a new taxonomy of X-formers. Next, we introduce the various X-formers from three perspectives: architectural modification, pre-training, and applications. Finally, we outline some potential directions for future research.

Neural sequence models, especially transformers, exhibit a remarkable capacity for in-context learning. They can construct new predictors from sequences of labeled examples (x, f(x)) presented in the input without further parameter updates. We investigate the hypothesis that transformer-based in-context learners implement standard learning algorithms implicitly, by encoding smaller models in their activations, and updating these implicit models as new examples appear in the context. Using linear regression as a prototypical problem, we offer three sources of evidence for this hypothesis. First, we prove by construction that transformers can implement learning algorithms for linear models based on gradient descent and closed-form ridge regression. Second, we show that trained in-context learners closely match the predictors computed by gradient descent, ridge regression, and exact least-squares regression, transitioning between different predictors as transformer depth and dataset noise vary, and converging to Bayesian estimators for large widths and depths. Third, we present preliminary evidence that in-context learners share algorithmic features with these predictors: learners' late layers non-linearly encode weight vectors and moment matrices. These results suggest that in-context learning is understandable in algorithmic terms, and that (at least in the linear case) learners may rediscover standard estimation algorithms. Code and reference implementations are released at https://github.com/ekinakyurek/google-research/blob/master/incontext.

Autoregressively trained transformers have brought a profound revolution to the world, especially with their in-context learning (ICL) ability to address downstream tasks. Recently, several studies suggest that transformers learn a mesa-optimizer during autoregressive (AR) pretraining to implement ICL. Namely, the forward pass of the trained transformer is equivalent to optimizing an inner objective function in-context. However, whether the practical non-convex training dynamics will converge to the ideal mesa-optimizer is still unclear. Towards filling this gap, we investigate the non-convex dynamics of a one-layer linear causal self-attention model autoregressively trained by gradient flow, where the sequences are generated by an AR process x_{t+1} = W x_t. First, under a certain condition of data distribution, we prove that an autoregressively trained transformer learns W by implementing one step of gradient descent to minimize an ordinary least squares (OLS) problem in-context. It then applies the learned W for next-token prediction, thereby verifying the mesa-optimization hypothesis. Next, under the same data conditions, we explore the capability limitations of the obtained mesa-optimizer. We show that a stronger assumption related to the moments of data is the sufficient and necessary condition that the learned mesa-optimizer recovers the distribution. Besides, we conduct exploratory analyses beyond the first data condition and prove that generally, the trained transformer will not perform vanilla gradient descent for the OLS problem. Finally, our simulation results verify the theoretical results.

Large language models demonstrate remarkable in-context learning capabilities, adapting to new tasks without parameter updates. While this phenomenon has been successfully modeled as implicit Bayesian inference, recent empirical findings reveal a fundamental contradiction: transformers systematically violate the martingale property, a cornerstone requirement of Bayesian updating on exchangeable data. This violation challenges the theoretical foundations underlying uncertainty quantification in critical applications. Our theoretical analysis establishes four key results: (1) positional encodings induce martingale violations of order Theta(log n / n); (2) transformers achieve information-theoretic optimality with excess risk O(n^{-1/2}) in expectation over orderings; (3) the implicit posterior representation converges to the true Bayesian posterior in the space of sufficient statistics; and (4) we derive the optimal chain-of-thought length as k^* = Theta(nlog(1/varepsilon)) with explicit constants, providing a principled approach to reduce inference costs while maintaining performance. Empirical validation on GPT-3 confirms predictions (1)-(3), with transformers reaching 99\% of theoretical entropy limits within 20 examples. Our framework provides practical methods for extracting calibrated uncertainty estimates from position-aware architectures and optimizing computational efficiency in deployment.

Although transformers are remarkably effective for many tasks, there are some surprisingly easy-looking regular languages that they struggle with. Hahn shows that for languages where acceptance depends on a single input symbol, a transformer's classification decisions become less and less confident (that is, with cross-entropy approaching 1 bit per string) as input strings get longer and longer. We examine this limitation using two languages: PARITY, the language of bit strings with an odd number of 1s, and FIRST, the language of bit strings starting with a 1. We demonstrate three ways of overcoming the limitation suggested by Hahn's lemma. First, we settle an open question by constructing a transformer that recognizes PARITY with perfect accuracy, and similarly for FIRST. Second, we use layer normalization to bring the cross-entropy of both models arbitrarily close to zero. Third, when transformers need to focus on a single position, as for FIRST, we find that they can fail to generalize to longer strings; we offer a simple remedy to this problem that also improves length generalization in machine translation.

Though Transformers have achieved promising results in many computer vision tasks, they tend to be over-confident in predictions, as the standard Dot Product Self-Attention (DPSA) can barely preserve distance for the unbounded input domain. In this work, we fill this gap by proposing a novel Lipschitz Regularized Transformer (LRFormer). Specifically, we present a new similarity function with the distance within Banach Space to ensure the Lipschitzness and also regularize the term by a contractive Lipschitz Bound. The proposed method is analyzed with a theoretical guarantee, providing a rigorous basis for its effectiveness and reliability. Extensive experiments conducted on standard vision benchmarks demonstrate that our method outperforms the state-of-the-art single forward pass approaches in prediction, calibration, and uncertainty estimation.

Transformers have achieved great success in machine learning applications. Normalization techniques, such as Layer Normalization (LayerNorm, LN) and Root Mean Square Normalization (RMSNorm), play a critical role in accelerating and stabilizing the training of Transformers. While LayerNorm recenters and rescales input vectors, RMSNorm only rescales the vectors by their RMS value. Despite being more computationally efficient, RMSNorm may compromise the representation ability of Transformers. There is currently no consensus regarding the preferred normalization technique, as some models employ LayerNorm while others utilize RMSNorm, especially in recent large language models. It is challenging to convert Transformers with one normalization to the other type. While there is an ongoing disagreement between the two normalization types, we propose a solution to unify two mainstream Transformer architectures, Pre-LN and Pre-RMSNorm Transformers. By removing the inherent redundant mean information in the main branch of Pre-LN Transformers, we can reduce LayerNorm to RMSNorm, achieving higher efficiency. We further propose the Compressed RMSNorm (CRMSNorm) and Pre-CRMSNorm Transformer based on a lossless compression of the zero-mean vectors. We formally establish the equivalence of Pre-LN, Pre-RMSNorm, and Pre-CRMSNorm Transformer variants in both training and inference. It implies that Pre-LN Transformers can be substituted with Pre-(C)RMSNorm counterparts at almost no cost, offering the same arithmetic functionality along with free efficiency improvement. Experiments demonstrate that we can reduce the training and inference time of Pre-LN Transformers by 1% - 10%.

Large pre-trained models have achieved outstanding results in sequence modeling. The Transformer block and its attention mechanism have been the main drivers of the success of these models. Recently, alternative architectures, such as Selective Structured State Space Models (SSMs), have been proposed to address the inefficiencies of Transformers. This paper explores the compression of SSM-based models, particularly Mamba and its hybrids. We study the sensitivity of these models to the removal of selected components at different granularities to reduce the model size and computational overhead, thus improving their efficiency while maintaining accuracy. The proposed solutions, collectively referred to as Mamba-Shedder, achieve a speedup of up to 1.4x during inference, demonstrating that model efficiency can be improved by eliminating several redundancies with minimal impact on the overall model performance. The code is available at https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning.

Transformers are considered conceptually different compared to the previous generation of state-of-the-art NLP models - recurrent neural networks (RNNs). In this work, we demonstrate that decoder-only transformers can in fact be conceptualized as infinite multi-state RNNs - an RNN variant with unlimited hidden state size. We further show that pretrained transformers can be converted into finite multi-state RNNs by fixing the size of their hidden state. We observe that several existing transformers cache compression techniques can be framed as such conversion policies, and introduce a novel policy, TOVA, which is simpler compared to these policies. Our experiments with several long range tasks indicate that TOVA outperforms all other baseline policies, while being nearly on par with the full (infinite) model, and using in some cases only 1{8} of the original cache size. Our results indicate that transformer decoder LLMs often behave in practice as RNNs. They also lay out the option of mitigating one of their most painful computational bottlenecks - the size of their cache memory. We publicly release our code at https://github.com/schwartz-lab-NLP/TOVA.

Transformer has shown state-of-the-art performance on various applications and has recently emerged as a promising tool for surrogate modeling of partial differential equations (PDEs). Despite the introduction of linear-complexity variant, applying attention to a large number of grid points can result in instability and is still expensive to compute. In this work, we propose Factorized Transformer(FactFormer), which is based on an axial factorized kernel integral. Concretely, we introduce a learnable projection operator that decomposes the input function into multiple sub-functions with one-dimensional domain. These sub-functions are then evaluated and used to compute the instance-based kernel with an axial factorized scheme. We showcase that the proposed model is able to simulate 2D Kolmogorov flow on a 256 by 256 grid and 3D smoke buoyancy on a 64 by 64 by 64 grid with good accuracy and efficiency. In addition, we find out that with the factorization scheme, the attention matrices enjoy a more compact spectrum than full softmax-free attention matrices.

Relative Positional Encoding (RPE), which encodes the relative distance between any pair of tokens, is one of the most successful modifications to the original Transformer. As far as we know, theoretical understanding of the RPE-based Transformers is largely unexplored. In this work, we mathematically analyze the power of RPE-based Transformers regarding whether the model is capable of approximating any continuous sequence-to-sequence functions. One may naturally assume the answer is in the affirmative -- RPE-based Transformers are universal function approximators. However, we present a negative result by showing there exist continuous sequence-to-sequence functions that RPE-based Transformers cannot approximate no matter how deep and wide the neural network is. One key reason lies in that most RPEs are placed in the softmax attention that always generates a right stochastic matrix. This restricts the network from capturing positional information in the RPEs and limits its capacity. To overcome the problem and make the model more powerful, we first present sufficient conditions for RPE-based Transformers to achieve universal function approximation. With the theoretical guidance, we develop a novel attention module, called Universal RPE-based (URPE) Attention, which satisfies the conditions. Therefore, the corresponding URPE-based Transformers become universal function approximators. Extensive experiments covering typical architectures and tasks demonstrate that our model is parameter-efficient and can achieve superior performance to strong baselines in a wide range of applications. The code will be made publicly available at https://github.com/lsj2408/URPE.

Large artificial neural networks have become a mainstay of language, vision, and audio processing and synthesis, yet their initializations and learning rates are often set in an unsophisticated fashion, due to the high cost of hyperparameter sweeps at scale. The mu-Parameterization (muP) offers a potential solution to this challenge, yielding scaling rules for model initialization and learning rates while reportedly enabling zero-shot hyperparameter transfer from small to large models. Despite its evident promise, the muP method is not yet widely adopted, perhaps due to higher implementation complexity, many variations, or complex theoretical background. This work investigates muP empirically, focusing on the ubiquitous transformer architecture, and aims to answer a simple question: does mu-Transfer yield optimal learning rates in practice? Studying models of up to 10B parameters and training budgets of up to 190B tokens, we find mu-Transfer works as intended for the majority of important cases, yet also identify a few cases where it may not.

Large models based on the Transformer architecture play increasingly vital roles in artificial intelligence, particularly within the realms of natural language processing (NLP) and computer vision (CV). Model compression methods reduce their memory and computational cost, which is a necessary step to implement the transformer models on practical devices. Given the unique architecture of transformer, featuring alternative attention and Feedforward Neural Network (FFN) modules, specific compression techniques are required. The efficiency of these compression methods is also paramount, as it is usually impractical to retrain large models on the entire training dataset.This survey provides a comprehensive review of recent compression methods, with a specific focus on their application to transformer models. The compression methods are primarily categorized into pruning, quantization, knowledge distillation, and efficient architecture design. In each category, we discuss compression methods for both CV and NLP tasks, highlighting common underlying principles. At last, we delve into the relation between various compression methods, and discuss the further directions in this domain.

Transformers do not scale very well to long sequence lengths largely because of quadratic self-attention complexity. In the recent months, a wide spectrum of efficient, fast Transformers have been proposed to tackle this problem, more often than not claiming superior or comparable model quality to vanilla Transformer models. To this date, there is no well-established consensus on how to evaluate this class of models. Moreover, inconsistent benchmarking on a wide spectrum of tasks and datasets makes it difficult to assess relative model quality amongst many models. This paper proposes a systematic and unified benchmark, LRA, specifically focused on evaluating model quality under long-context scenarios. Our benchmark is a suite of tasks consisting of sequences ranging from 1K to 16K tokens, encompassing a wide range of data types and modalities such as text, natural, synthetic images, and mathematical expressions requiring similarity, structural, and visual-spatial reasoning. We systematically evaluate ten well-established long-range Transformer models (Reformers, Linformers, Linear Transformers, Sinkhorn Transformers, Performers, Synthesizers, Sparse Transformers, and Longformers) on our newly proposed benchmark suite. LRA paves the way towards better understanding this class of efficient Transformer models, facilitates more research in this direction, and presents new challenging tasks to tackle. Our benchmark code will be released at https://github.com/google-research/long-range-arena.

Traditional transformer models often allocate a fixed amount of computational resources to every input token, leading to inefficient and unnecessary computation. To address this, the Mixture of Depths (MoD) was introduced to dynamically adjust the computational depth by skipping less important layers. Despite its promise, current MoD approaches remain under-explored and face two main challenges: (1) high training costs due to the need to train the entire model along with the routers that determine which layers to skip, and (2) the risk of performance degradation when important layers are bypassed. In response to the first issue, we propose Router-Tuning, a method that fine-tunes only the router on a small dataset, drastically reducing the computational overhead associated with full model training. For the second challenge, we propose MindSkip, which deploys Attention with Dynamic Depths. This method preserves the model's performance while significantly enhancing computational and memory efficiency. Extensive experiments demonstrate that our approach delivers competitive results while dramatically improving the computation efficiency, e.g., 21\% speedup and only a 0.2\% performance drop. The code is released at https://github.com/CASE-Lab-UMD/Router-Tuning.

Our understanding of the generalization capabilities of neural networks (NNs) is still incomplete. Prevailing explanations are based on implicit biases of gradient descent (GD) but they cannot account for the capabilities of models from gradient-free methods nor the simplicity bias recently observed in untrained networks. This paper seeks other sources of generalization in NNs. Findings. To understand the inductive biases provided by architectures independently from GD, we examine untrained, random-weight networks. Even simple MLPs show strong inductive biases: uniform sampling in weight space yields a very biased distribution of functions in terms of complexity. But unlike common wisdom, NNs do not have an inherent "simplicity bias". This property depends on components such as ReLUs, residual connections, and layer normalizations. Alternative architectures can be built with a bias for any level of complexity. Transformers also inherit all these properties from their building blocks. Implications. We provide a fresh explanation for the success of deep learning independent from gradient-based training. It points at promising avenues for controlling the solutions implemented by trained models.

Multiplications are responsible for most of the computational cost involved in neural network training and inference. Recent research has thus looked for ways to reduce the cost associated with them. Inspired by Mogami (2020), we replace multiplication with a cheap piecewise affine approximation that is achieved by adding the bit representation of the floating point numbers together as integers. We show that transformers can be trained with the resulting modified matrix multiplications on both vision and language tasks with little to no performance impact, and without changes to the training hyperparameters. We further replace all non-linearities in the networks making them fully and jointly piecewise affine in both inputs and weights. Finally, we show that we can eliminate all multiplications in the entire training process, including operations in the forward pass, backward pass and optimizer update, demonstrating the first successful training of modern neural network architectures in a fully multiplication-free fashion.

Understanding Transformer-based models has attracted significant attention, as they lie at the heart of recent technological advances across machine learning. While most interpretability methods rely on running models over inputs, recent work has shown that a zero-pass approach, where parameters are interpreted directly without a forward/backward pass is feasible for some Transformer parameters, and for two-layer attention networks. In this work, we present a theoretical analysis where all parameters of a trained Transformer are interpreted by projecting them into the embedding space, that is, the space of vocabulary items they operate on. We derive a simple theoretical framework to support our arguments and provide ample evidence for its validity. First, an empirical analysis showing that parameters of both pretrained and fine-tuned models can be interpreted in embedding space. Second, we present two applications of our framework: (a) aligning the parameters of different models that share a vocabulary, and (b) constructing a classifier without training by ``translating'' the parameters of a fine-tuned classifier to parameters of a different model that was only pretrained. Overall, our findings open the door to interpretation methods that, at least in part, abstract away from model specifics and operate in the embedding space only.

An emerging solution for explaining Transformer-based models is to use vector-based analysis on how the representations are formed. However, providing a faithful vector-based explanation for a multi-layer model could be challenging in three aspects: (1) Incorporating all components into the analysis, (2) Aggregating the layer dynamics to determine the information flow and mixture throughout the entire model, and (3) Identifying the connection between the vector-based analysis and the model's predictions. In this paper, we present DecompX to tackle these challenges. DecompX is based on the construction of decomposed token representations and their successive propagation throughout the model without mixing them in between layers. Additionally, our proposal provides multiple advantages over existing solutions for its inclusion of all encoder components (especially nonlinear feed-forward networks) and the classification head. The former allows acquiring precise vectors while the latter transforms the decomposition into meaningful prediction-based values, eliminating the need for norm- or summation-based vector aggregation. According to the standard faithfulness evaluations, DecompX consistently outperforms existing gradient-based and vector-based approaches on various datasets. Our code is available at https://github.com/mohsenfayyaz/DecompX.

The Transformer is widely used in natural language processing tasks. To train a Transformer however, one usually needs a carefully designed learning rate warm-up stage, which is shown to be crucial to the final performance but will slow down the optimization and bring more hyper-parameter tunings. In this paper, we first study theoretically why the learning rate warm-up stage is essential and show that the location of layer normalization matters. Specifically, we prove with mean field theory that at initialization, for the original-designed Post-LN Transformer, which places the layer normalization between the residual blocks, the expected gradients of the parameters near the output layer are large. Therefore, using a large learning rate on those gradients makes the training unstable. The warm-up stage is practically helpful for avoiding this problem. On the other hand, our theory also shows that if the layer normalization is put inside the residual blocks (recently proposed as Pre-LN Transformer), the gradients are well-behaved at initialization. This motivates us to remove the warm-up stage for the training of Pre-LN Transformers. We show in our experiments that Pre-LN Transformers without the warm-up stage can reach comparable results with baselines while requiring significantly less training time and hyper-parameter tuning on a wide range of applications.

By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called muP, for *widthwise hyperparameter transfer*, i.e., predicting optimal hyperparameters of wide neural networks from narrow ones. Here we investigate the analogous classification for *depthwise parametrizations* of deep residual networks (resnets). We classify depthwise parametrizations of block multiplier and learning rate by their infinite-width-then-depth limits. In resnets where each block has only one layer, we identify a unique optimal parametrization, called Depth-muP that extends muP and show empirically it admits depthwise hyperparameter transfer. We identify *feature diversity* as a crucial factor in deep networks, and Depth-muP can be characterized as maximizing both feature learning and feature diversity. Exploiting this, we find that absolute value, among all homogeneous nonlinearities, maximizes feature diversity and indeed empirically leads to significantly better performance. However, if each block is deeper (such as modern transformers), then we find fundamental limitations in all possible infinite-depth limits of such parametrizations, which we illustrate both theoretically and empirically on simple networks as well as Megatron transformer trained on Common Crawl.

Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert continuous signals into segments. Yet, time series data are uniquely challenging due to significant distribution shifts and intrinsic noise levels. To address these two challenges,we introduce the Sparse Vector Quantized FFN-Free Transformer (Sparse-VQ). Our methodology capitalizes on a sparse vector quantization technique coupled with Reverse Instance Normalization (RevIN) to reduce noise impact and capture sufficient statistics for forecasting, serving as an alternative to the Feed-Forward layer (FFN) in the transformer architecture. Our FFN-free approach trims the parameter count, enhancing computational efficiency and reducing overfitting. Through evaluations across ten benchmark datasets, including the newly introduced CAISO dataset, Sparse-VQ surpasses leading models with a 7.84% and 4.17% decrease in MAE for univariate and multivariate time series forecasting, respectively. Moreover, it can be seamlessly integrated with existing transformer-based models to elevate their performance.

Incorporating modular designs into neural networks demonstrates superior out-of-generalization, learning efficiency, etc. Existing modular neural networks are generally explicit because their modular architectures are pre-defined, and individual modules are expected to implement distinct functions. Conversely, recent works reveal that there exist implicit modular structures in standard pre-trained transformers, namely Emergent Modularity. They indicate that such modular structures exhibit during the early pre-training phase and are totally spontaneous. However, most transformers are still treated as monolithic models with their modular natures underutilized. Therefore, given the excellent properties of explicit modular architecture, we explore whether and how dense pre-trained transformers can benefit from emergent modular structures. To study this question, we construct Emergent Mixture-of-Experts (EMoE). Without introducing additional parameters, EMoE can be seen as the modular counterpart of the original model and can be effortlessly incorporated into downstream tuning. Extensive experiments (we tune 1785 models) on various downstream tasks (vision and language) and models (22M to1.5B) demonstrate that EMoE effectively boosts in-domain and out-of-domain generalization abilities. Further analysis and ablation study suggest that EMoE mitigates negative knowledge transfer and is robust to various configurations. Code is available at https://github.com/qiuzh20/EMoE

We explore a data-driven approach for learning to optimize neural networks. We construct a dataset of neural network checkpoints and train a generative model on the parameters. In particular, our model is a conditional diffusion transformer that, given an initial input parameter vector and a prompted loss, error, or return, predicts the distribution over parameter updates that achieve the desired metric. At test time, it can optimize neural networks with unseen parameters for downstream tasks in just one update. We find that our approach successfully generates parameters for a wide range of loss prompts. Moreover, it can sample multimodal parameter solutions and has favorable scaling properties. We apply our method to different neural network architectures and tasks in supervised and reinforcement learning.

Transformers, with their attention mechanisms, have emerged as the state-of-the-art architectures of sequential modeling and empirically outperform feed-forward neural networks (FFNNs) across many fields, such as natural language processing and computer vision. However, their generalization ability, particularly for low-sensitivity functions, remains less studied. We bridge this gap by analyzing transformers on the k-parity problem. Daniely and Malach (NeurIPS 2020) show that FFNNs with one hidden layer and O(nk^7 log k) parameters can learn k-parity, where the input length n is typically much larger than k. In this paper, we prove that FFNNs require at least Omega(n) parameters to learn k-parity, while transformers require only O(k) parameters, surpassing the theoretical lower bound needed by FFNNs. We further prove that this parameter efficiency cannot be achieved with fixed attention heads. Our work establishes transformers as theoretically superior to FFNNs in learning parity function, showing how their attention mechanisms enable parameter-efficient generalization in functions with low sensitivity.

Increasing the size of a Transformer model does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, improved generalization ability occurs as the model memorizes the training samples. We present a theoretical framework that sheds light on the memorization process and performance dynamics of transformer-based language models. We model the behavior of Transformers with associative memories using Hopfield networks, such that each transformer block effectively conducts an approximate nearest-neighbor search. Based on this, we design an energy function analogous to that in the modern continuous Hopfield network which provides an insightful explanation for the attention mechanism. Using the majorization-minimization technique, we construct a global energy function that captures the layered architecture of the Transformer. Under specific conditions, we show that the minimum achievable cross-entropy loss is bounded from below by a constant approximately equal to 1. We substantiate our theoretical results by conducting experiments with GPT-2 on various data sizes, as well as training vanilla Transformers on a dataset of 2M tokens.

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal imageleftrightarrowtext models, and mathematical problem solving. In all cases autoregressive Transformers smoothly improve in performance as model size and compute budgets increase, following a power-law plus constant scaling law. The optimal model size also depends on the compute budget through a power-law, with exponents that are nearly universal across all data domains. The cross-entropy loss has an information theoretic interpretation as S(True) + D_{KL}(True||Model), and the empirical scaling laws suggest a prediction for both the true data distribution's entropy and the KL divergence between the true and model distributions. With this interpretation, billion-parameter Transformers are nearly perfect models of the YFCC100M image distribution downsampled to an 8times 8 resolution, and we can forecast the model size needed to achieve any given reducible loss (ie D_{KL}) in nats/image for other resolutions. We find a number of additional scaling laws in specific domains: (a) we identify a scaling relation for the mutual information between captions and images in multimodal models, and show how to answer the question "Is a picture worth a thousand words?"; (b) in the case of mathematical problem solving, we identify scaling laws for model performance when extrapolating beyond the training distribution; (c) we finetune generative image models for ImageNet classification and find smooth scaling of the classification loss and error rate, even as the generative loss levels off. Taken together, these results strengthen the case that scaling laws have important implications for neural network performance, including on downstream tasks.

In this paper, we apply the self-attention from the state-of-the-art Transformer in Attention Is All You Need for the first time to a data-driven operator learning problem related to partial differential equations. An effort is put together to explain the heuristics of, and to improve the efficacy of the attention mechanism. By employing the operator approximation theory in Hilbert spaces, it is demonstrated for the first time that the softmax normalization in the scaled dot-product attention is sufficient but not necessary. Without softmax, the approximation capacity of a linearized Transformer variant can be proved to be comparable to a Petrov-Galerkin projection layer-wise, and the estimate is independent with respect to the sequence length. A new layer normalization scheme mimicking the Petrov-Galerkin projection is proposed to allow a scaling to propagate through attention layers, which helps the model achieve remarkable accuracy in operator learning tasks with unnormalized data. Finally, we present three operator learning experiments, including the viscid Burgers' equation, an interface Darcy flow, and an inverse interface coefficient identification problem. The newly proposed simple attention-based operator learner, Galerkin Transformer, shows significant improvements in both training cost and evaluation accuracy over its softmax-normalized counterparts.

Large transformer models pretrained on offline reinforcement learning datasets have demonstrated remarkable in-context reinforcement learning (ICRL) capabilities, where they can make good decisions when prompted with interaction trajectories from unseen environments. However, when and how transformers can be trained to perform ICRL have not been theoretically well-understood. In particular, it is unclear which reinforcement-learning algorithms transformers can perform in context, and how distribution mismatch in offline training data affects the learned algorithms. This paper provides a theoretical framework that analyzes supervised pretraining for ICRL. This includes two recently proposed training methods -- algorithm distillation and decision-pretrained transformers. First, assuming model realizability, we prove the supervised-pretrained transformer will imitate the conditional expectation of the expert algorithm given the observed trajectory. The generalization error will scale with model capacity and a distribution divergence factor between the expert and offline algorithms. Second, we show transformers with ReLU attention can efficiently approximate near-optimal online reinforcement learning algorithms like LinUCB and Thompson sampling for stochastic linear bandits, and UCB-VI for tabular Markov decision processes. This provides the first quantitative analysis of the ICRL capabilities of transformers pretrained from offline trajectories.

Transformer neural networks can exhibit a surprising capacity for in-context learning (ICL) despite not being explicitly trained for it. Prior work has provided a deeper understanding of how ICL emerges in transformers, e.g. through the lens of mechanistic interpretability, Bayesian inference, or by examining the distributional properties of training data. However, in each of these cases, ICL is treated largely as a persistent phenomenon; namely, once ICL emerges, it is assumed to persist asymptotically. Here, we show that the emergence of ICL during transformer training is, in fact, often transient. We train transformers on synthetic data designed so that both ICL and in-weights learning (IWL) strategies can lead to correct predictions. We find that ICL first emerges, then disappears and gives way to IWL, all while the training loss decreases, indicating an asymptotic preference for IWL. The transient nature of ICL is observed in transformers across a range of model sizes and datasets, raising the question of how much to "overtrain" transformers when seeking compact, cheaper-to-run models. We find that L2 regularization may offer a path to more persistent ICL that removes the need for early stopping based on ICL-style validation tasks. Finally, we present initial evidence that ICL transience may be caused by competition between ICL and IWL circuits.

Transformers pretrained on diverse tasks exhibit remarkable in-context learning (ICL) capabilities, enabling them to solve unseen tasks solely based on input contexts without adjusting model parameters. In this paper, we study ICL in one of its simplest setups: pretraining a linearly parameterized single-layer linear attention model for linear regression with a Gaussian prior. We establish a statistical task complexity bound for the attention model pretraining, showing that effective pretraining only requires a small number of independent tasks. Furthermore, we prove that the pretrained model closely matches the Bayes optimal algorithm, i.e., optimally tuned ridge regression, by achieving nearly Bayes optimal risk on unseen tasks under a fixed context length. These theoretical findings complement prior experimental research and shed light on the statistical foundations of ICL.

Despite their nearly universal adoption for large language models, the internal workings of transformers are not well understood. We aim to better understand the impact of removing or reorganizing information throughout the layers of a pretrained transformer. Such an understanding could both yield better usage of existing models as well as to make architectural improvements to produce new variants. We present a series of empirical studies on frozen models that show that the lower and final layers of pretrained transformers differ from middle layers, but that middle layers have a surprising amount of uniformity. We further show that some classes of problems have robustness to skipping layers, running the layers in an order different from how they were trained, or running the layers in parallel. Our observations suggest that even frozen pretrained models may gracefully trade accuracy for latency by skipping layers or running layers in parallel.

The Transformer architecture deeply changed the natural language processing, outperforming all previous state-of-the-art models. However, well-known Transformer models like BERT, RoBERTa, and GPT-2 require a huge compute budget to create a high quality contextualised representation. In this paper, we study several efficient pre-training objectives for Transformers-based models. By testing these objectives on different tasks, we determine which of the ELECTRA model's new features is the most relevant. We confirm that Transformers pre-training is improved when the input does not contain masked tokens and that the usage of the whole output to compute the loss reduces training time. Moreover, inspired by ELECTRA, we study a model composed of two blocks; a discriminator and a simple generator based on a statistical model with no impact on the computational performances. Besides, we prove that eliminating the MASK token and considering the whole output during the loss computation are essential choices to improve performance. Furthermore, we show that it is possible to efficiently train BERT-like models using a discriminative approach as in ELECTRA but without a complex generator, which is expensive. Finally, we show that ELECTRA benefits heavily from a state-of-the-art hyper-parameters search.

Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling problem by means of energy potentials (unnormalized likelihood functions). In contrast, the realm of Optimal Transport (OT) and, in particular, neural OT solvers is much less explored and limited by few recent works (excluding WGAN-based approaches which utilize OT as a loss function and do not model OT maps themselves). In our work, we bridge the gap between EBMs and Entropy-regularized OT. We present a novel methodology which allows utilizing the recent developments and technical improvements of the former in order to enrich the latter. From the theoretical perspective, we prove generalization bounds for our technique. In practice, we validate its applicability in toy 2D and image domains. To showcase the scalability, we empower our method with a pre-trained StyleGAN and apply it to high-res AFHQ 512times 512 unpaired I2I translation. For simplicity, we choose simple short- and long-run EBMs as a backbone of our Energy-guided Entropic OT approach, leaving the application of more sophisticated EBMs for future research. Our code is available at: https://github.com/PetrMokrov/Energy-guided-Entropic-OT

In-context learning is one of the surprising and useful features of large language models. How it works is an active area of research. Recently, stylized meta-learning-like setups have been devised that train these models on a sequence of input-output pairs (x, f(x)) from a function class using the language modeling loss and observe generalization to unseen functions from the same class. One of the main discoveries in this line of research has been that for several problems such as linear regression, trained transformers learn algorithms for learning functions in context. However, the inductive biases of these models resulting in this behavior are not clearly understood. A model with unlimited training data and compute is a Bayesian predictor: it learns the pretraining distribution. It has been shown that high-capacity transformers mimic the Bayesian predictor for linear regression. In this paper, we show empirical evidence of transformers exhibiting the behavior of this ideal learner across different linear and non-linear function classes. We also extend the previous setups to work in the multitask setting and verify that transformers can do in-context learning in this setup as well and the Bayesian perspective sheds light on this setting also. Finally, via the example of learning Fourier series, we study the inductive bias for in-context learning. We find that in-context learning may or may not have simplicity bias depending on the pretraining data distribution.

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

Progress in the realisation of reliable large-scale quantum computers has motivated research into the design of quantum machine learning models. We present Quixer: a novel quantum transformer model which utilises the Linear Combination of Unitaries and Quantum Singular Value Transform primitives as building blocks. Quixer operates by preparing a superposition of tokens and applying a trainable non-linear transformation to this mix. We present the first results for a quantum transformer model applied to a practical language modelling task, obtaining results competitive with an equivalent classical baseline. In addition, we include resource estimates for evaluating the model on quantum hardware, and provide an open-source implementation for classical simulation. We conclude by highlighting the generality of Quixer, showing that its parameterised components can be substituted with fixed structures to yield new classes of quantum transformers.

Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review Transformer schemes for time series modeling by highlighting their strengths as well as limitations. In particular, we examine the development of time series Transformers in two perspectives. From the perspective of network structure, we summarize the adaptations and modifications that have been made to Transformers in order to accommodate the challenges in time series analysis. From the perspective of applications, we categorize time series Transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.

This paper reveals a novel linear characteristic exclusive to transformer decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We analyze embedding transformations between sequential layers, uncovering a near-perfect linear relationship (Procrustes similarity score of 0.99). However, linearity decreases when the residual component is removed due to a consistently low output norm of the transformer layer. Our experiments show that removing or linearly approximating some of the most linear blocks of transformers does not affect significantly the loss or model performance. Moreover, in our pretraining experiments on smaller models we introduce a cosine-similarity-based regularization, aimed at reducing layer linearity. This regularization improves performance metrics on benchmarks like Tiny Stories and SuperGLUE and as well successfully decreases the linearity of the models. This study challenges the existing understanding of transformer architectures, suggesting that their operation may be more linear than previously assumed.

We introduce LMCodec, a causal neural speech codec that provides high quality audio at very low bitrates. The backbone of the system is a causal convolutional codec that encodes audio into a hierarchy of coarse-to-fine tokens using residual vector quantization. LMCodec trains a Transformer language model to predict the fine tokens from the coarse ones in a generative fashion, allowing for the transmission of fewer codes. A second Transformer predicts the uncertainty of the next codes given the past transmitted codes, and is used to perform conditional entropy coding. A MUSHRA subjective test was conducted and shows that the quality is comparable to reference codecs at higher bitrates. Example audio is available at https://mjenrungrot.github.io/chrome-media-audio-papers/publications/lmcodec.

Transformers, currently the state-of-the-art in natural language understanding (NLU) tasks, are prone to generate uncalibrated predictions or extreme probabilities, making the process of taking different decisions based on their output relatively difficult. In this paper we propose to build several inductive Venn--ABERS predictors (IVAP), which are guaranteed to be well calibrated under minimal assumptions, based on a selection of pre-trained transformers. We test their performance over a set of diverse NLU tasks and show that they are capable of producing well-calibrated probabilistic predictions that are uniformly spread over the [0,1] interval -- all while retaining the original model's predictive accuracy.

Transformer neural operators have recently become an effective approach for surrogate modeling of systems governed by partial differential equations (PDEs). In this paper, we introduce a modified implicit factorized transformer (IFactFormer-m) model which replaces the original chained factorized attention with parallel factorized attention. The IFactFormer-m model successfully performs long-term predictions for turbulent channel flow, whereas the original IFactFormer (IFactFormer-o), Fourier neural operator (FNO), and implicit Fourier neural operator (IFNO) exhibit a poor performance. Turbulent channel flows are simulated by direct numerical simulation using fine grids at friction Reynolds numbers Re_{tau}approx 180,395,590, and filtered to coarse grids for training neural operator. The neural operator takes the current flow field as input and predicts the flow field at the next time step, and long-term prediction is achieved in the posterior through an autoregressive approach. The results show that IFactFormer-m, compared to other neural operators and the traditional large eddy simulation (LES) methods including dynamic Smagorinsky model (DSM) and the wall-adapted local eddy-viscosity (WALE) model, reduces prediction errors in the short term, and achieves stable and accurate long-term prediction of various statistical properties and flow structures, including the energy spectrum, mean streamwise velocity, root mean square (rms) values of fluctuating velocities, Reynolds shear stress, and spatial structures of instantaneous velocity. Moreover, the trained IFactFormer-m is much faster than traditional LES methods. By analyzing the attention kernels, we elucidate the reasons why IFactFormer-m converges faster and achieves a stable and accurate long-term prediction compared to IFactFormer-o. Code and data are available at: https://github.com/huiyu-2002/IFactFormer-m.

This paper presents Representation-Conditioned image Generation (RCG), a simple yet effective image generation framework which sets a new benchmark in class-unconditional image generation. RCG does not condition on any human annotations. Instead, it conditions on a self-supervised representation distribution which is mapped from the image distribution using a pre-trained encoder. During generation, RCG samples from such representation distribution using a representation diffusion model (RDM), and employs a pixel generator to craft image pixels conditioned on the sampled representation. Such a design provides substantial guidance during the generative process, resulting in high-quality image generation. Tested on ImageNet 256times256, RCG achieves a Frechet Inception Distance (FID) of 3.31 and an Inception Score (IS) of 253.4. These results not only significantly improve the state-of-the-art of class-unconditional image generation but also rival the current leading methods in class-conditional image generation, bridging the long-standing performance gap between these two tasks. Code is available at https://github.com/LTH14/rcg.

Sequence modeling plays a vital role across various domains, with recurrent neural networks being historically the predominant method of performing these tasks. However, the emergence of transformers has altered this paradigm due to their superior performance. Built upon these advances, transformers have conjoined CNNs as two leading foundational models for learning visual representations. However, transformers are hindered by the O(N^2) complexity of their attention mechanisms, while CNNs lack global receptive fields and dynamic weight allocation. State Space Models (SSMs), specifically the \textbf{Mamba} model with selection mechanisms and hardware-aware architecture, have garnered immense interest lately in sequential modeling and visual representation learning, challenging the dominance of transformers by providing infinite context lengths and offering substantial efficiency maintaining linear complexity in the input sequence. Capitalizing on the advances in computer vision, medical imaging has heralded a new epoch with Mamba models. Intending to help researchers navigate the surge, this survey seeks to offer an encyclopedic review of Mamba models in medical imaging. Specifically, we start with a comprehensive theoretical review forming the basis of SSMs, including Mamba architecture and its alternatives for sequence modeling paradigms in this context. Next, we offer a structured classification of Mamba models in the medical field and introduce a diverse categorization scheme based on their application, imaging modalities, and targeted organs. Finally, we summarize key challenges, discuss different future research directions of the SSMs in the medical domain, and propose several directions to fulfill the demands of this field. In addition, we have compiled the studies discussed in this paper along with their open-source implementations on our GitHub repository.

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.

This document aims to be a self-contained, mathematically precise overview of transformer architectures and algorithms (*not* results). It covers what transformers are, how they are trained, what they are used for, their key architectural components, and a preview of the most prominent models. The reader is assumed to be familiar with basic ML terminology and simpler neural network architectures such as MLPs.

Recent advancements in text-to-speech (TTS) powered by language models have showcased remarkable capabilities in achieving naturalness and zero-shot voice cloning. Notably, the decoder-only transformer is the prominent architecture in this domain. However, transformers face challenges stemming from their quadratic complexity in sequence length, impeding training on lengthy sequences and resource-constrained hardware. Moreover they lack specific inductive bias with regards to the monotonic nature of TTS alignments. In response, we propose to replace transformers with emerging recurrent architectures and introduce specialized cross-attention mechanisms for reducing repeating and skipping issues. Consequently our architecture can be efficiently trained on long samples and achieve state-of-the-art zero-shot voice cloning against baselines of comparable size. Our implementation and demos are available at https://github.com/theodorblackbird/lina-speech.

While the Transformer architecture has achieved remarkable success across various domains, a thorough theoretical foundation explaining its optimization dynamics is yet to be fully developed. In this study, we aim to bridge this understanding gap by answering the following two core questions: (1) Which types of Transformer architectures allow Gradient Descent (GD) to achieve guaranteed convergence? and (2) Under what initial conditions and architectural specifics does the Transformer achieve rapid convergence during training? By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions. Our findings demonstrate that, with appropriate weight initialization, GD can train a Transformer model (with either kernel type) to achieve a global optimal solution, especially when the input embedding dimension is large. Nonetheless, certain scenarios highlight potential pitfalls: training a Transformer using the Softmax attention kernel may sometimes lead to suboptimal local solutions. In contrast, the Gaussian attention kernel exhibits a much favorable behavior. Our empirical study further validate the theoretical findings.

Transformer model architectures have garnered immense interest lately due to their effectiveness across a range of domains like language, vision and reinforcement learning. In the field of natural language processing for example, Transformers have become an indispensable staple in the modern deep learning stack. Recently, a dizzying number of "X-former" models have been proposed - Reformer, Linformer, Performer, Longformer, to name a few - which improve upon the original Transformer architecture, many of which make improvements around computational and memory efficiency. With the aim of helping the avid researcher navigate this flurry, this paper characterizes a large and thoughtful selection of recent efficiency-flavored "X-former" models, providing an organized and comprehensive overview of existing work and models across multiple domains.

Negative binomial regression is essential for analyzing over-dispersed count data in in comparative studies, but parameter estimation becomes computationally challenging in large screens requiring millions of comparisons. We investigate using a pre-trained transformer to produce estimates of negative binomial regression parameters from observed count data, trained through synthetic data generation to learn to invert the process of generating counts from parameters. The transformer method achieved better parameter accuracy than maximum likelihood optimization while being 20 times faster. However, comparisons unexpectedly revealed that method of moment estimates performed as well as maximum likelihood optimization in accuracy, while being 1,000 times faster and producing better-calibrated and more powerful tests, making it the most efficient solution for this application.

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

A big convergence of model architectures across language, vision, speech, and multimodal is emerging. However, under the same name "Transformers", the above areas use different implementations for better performance, e.g., Post-LayerNorm for BERT, and Pre-LayerNorm for GPT and vision Transformers. We call for the development of Foundation Transformer for true general-purpose modeling, which serves as a go-to architecture for various tasks and modalities with guaranteed training stability. In this work, we introduce a Transformer variant, named Magneto, to fulfill the goal. Specifically, we propose Sub-LayerNorm for good expressivity, and the initialization strategy theoretically derived from DeepNet for stable scaling up. Extensive experiments demonstrate its superior performance and better stability than the de facto Transformer variants designed for various applications, including language modeling (i.e., BERT, and GPT), machine translation, vision pretraining (i.e., BEiT), speech recognition, and multimodal pretraining (i.e., BEiT-3).

Transformers have been established as the most popular backbones in sequence modeling, mainly due to their effectiveness in in-context retrieval tasks and the ability to learn at scale. Their quadratic memory and time complexity, however, bound their applicability in longer sequences and so has motivated researchers to explore effective alternative architectures such as modern recurrent neural networks (a.k.a long-term recurrent memory module). Despite their recent success in diverse downstream tasks, they struggle in tasks that requires long context understanding and extrapolation to longer sequences. We observe that these shortcomings come from three disjoint aspects in their design: (1) limited memory capacity that is bounded by the architecture of memory and feature mapping of the input; (2) online nature of update, i.e., optimizing the memory only with respect to the last input; and (3) less expressive management of their fixed-size memory. To enhance all these three aspects, we present ATLAS, a long-term memory module with high capacity that learns to memorize the context by optimizing the memory based on the current and past tokens, overcoming the online nature of long-term memory models. Building on this insight, we present a new family of Transformer-like architectures, called DeepTransformers, that are strict generalizations of the original Transformer architecture. Our experimental results on language modeling, common-sense reasoning, recall-intensive, and long-context understanding tasks show that ATLAS surpasses the performance of Transformers and recent linear recurrent models. ATLAS further improves the long context performance of Titans, achieving +80\% accuracy in 10M context length of BABILong benchmark.

Transformer models (TMs) have exhibited remarkable in-context reinforcement learning (ICRL) capabilities, allowing them to generalize to and improve in previously unseen environments without re-training or fine-tuning. This is typically accomplished by imitating the complete learning histories of a source RL algorithm over a substantial amount of pretraining environments, which, however, may transfer suboptimal behaviors inherited from the source algorithm/dataset. Therefore, in this work, we address the issue of inheriting suboptimality from the perspective of dataset preprocessing. Motivated by the success of the weighted empirical risk minimization, we propose a simple yet effective approach, learning history filtering (LHF), to enhance ICRL by reweighting and filtering the learning histories based on their improvement and stability characteristics. To the best of our knowledge, LHF is the first approach to avoid source suboptimality by dataset preprocessing, and can be combined with the current state-of-the-art (SOTA) ICRL algorithms. We substantiate the effectiveness of LHF through a series of experiments conducted on the well-known ICRL benchmarks, encompassing both discrete environments and continuous robotic manipulation tasks, with three SOTA ICRL algorithms (AD, DPT, DICP) as the backbones. LHF exhibits robust performance across a variety of suboptimal scenarios, as well as under varying hyperparameters and sampling strategies. Notably, the superior performance of LHF becomes more pronounced in the presence of noisy data, indicating the significance of filtering learning histories.

Pretrained transformer models have demonstrated remarkable performance across various natural language processing tasks. These models leverage the attention mechanism to capture long- and short-range dependencies in the sequence. However, the (full) attention mechanism incurs high computational cost - quadratic in the sequence length, which is not affordable in tasks with long sequences, e.g., inputs with 8k tokens. Although sparse attention can be used to improve computational efficiency, as suggested in existing work, it has limited modeling capacity and often fails to capture complicated dependencies in long sequences. To tackle this challenge, we propose MASFormer, an easy-to-implement transformer variant with Mixed Attention Spans. Specifically, MASFormer is equipped with full attention to capture long-range dependencies, but only at a small number of layers. For the remaining layers, MASformer only employs sparse attention to capture short-range dependencies. Our experiments on natural language modeling and generation tasks show that a decoder-only MASFormer model of 1.3B parameters can achieve competitive performance to vanilla transformers with full attention while significantly reducing computational cost (up to 75%). Additionally, we investigate the effectiveness of continual training with long sequence data and how sequence length impacts downstream generation performance, which may be of independent interest.

Pretrained transformers exhibit the remarkable ability of in-context learning (ICL): they can learn tasks from just a few examples provided in the prompt without updating any weights. This raises a foundational question: can ICL solve fundamentally new tasks that are very different from those seen during pretraining? To probe this question, we examine ICL's performance on linear regression while varying the diversity of tasks in the pretraining dataset. We empirically demonstrate a task diversity threshold for the emergence of ICL. Below this threshold, the pretrained transformer cannot solve unseen regression tasks, instead behaving like a Bayesian estimator with the non-diverse pretraining task distribution as the prior. Beyond this threshold, the transformer significantly outperforms this estimator; its behavior aligns with that of ridge regression, corresponding to a Gaussian prior over all tasks, including those not seen during pretraining. Thus, when pretrained on data with task diversity greater than the threshold, transformers can optimally solve fundamentally new tasks in-context. Importantly, this capability hinges on it deviating from the Bayes optimal estimator with the pretraining distribution as the prior. This study also explores the effect of regularization, model capacity and task structure and underscores, in a concrete example, the critical role of task diversity, alongside data and model scale, in the emergence of ICL. Code is available at https://github.com/mansheej/icl-task-diversity.

Recent years have seen a phenomenal rise in performance and applications of transformer neural networks. The family of transformer networks, including Bidirectional Encoder Representations from Transformer (BERT), Generative Pretrained Transformer (GPT) and Vision Transformer (ViT), have shown their effectiveness across Natural Language Processing (NLP) and Computer Vision (CV) domains. Transformer-based networks such as ChatGPT have impacted the lives of common men. However, the quest for high predictive performance has led to an exponential increase in transformers' memory and compute footprint. Researchers have proposed techniques to optimize transformer inference at all levels of abstraction. This paper presents a comprehensive survey of techniques for optimizing the inference phase of transformer networks. We survey techniques such as knowledge distillation, pruning, quantization, neural architecture search and lightweight network design at the algorithmic level. We further review hardware-level optimization techniques and the design of novel hardware accelerators for transformers. We summarize the quantitative results on the number of parameters/FLOPs and accuracy of several models/techniques to showcase the tradeoff exercised by them. We also outline future directions in this rapidly evolving field of research. We believe that this survey will educate both novice and seasoned researchers and also spark a plethora of research efforts in this field.

In this thesis, we introduce Greenformers, a collection of model efficiency methods to improve the model efficiency of the recently renowned transformer models with a low-rank approximation approach. The development trend of deep learning models tends to results in a more complex and larger model. Although it leads to a better and more accurate prediction, the resulting model becomes even more costly, as it requires weeks of training with a huge amount of GPU resources. Particularly, the size and computational cost of transformer-based models have increased tremendously since its first debut in 2017 from ~100 million parameters up to ~1.6 trillion parameters in early 2021. This computationally hungry model also incurs a substantial cost to the environment and even reaches an alarming level of carbon footprint. Some of these models are so massive that it is even impossible to run the model without a GPU cluster. Greenformers improve the model efficiency of transformer models by applying low-rank approximation approaches. Specifically, we propose a low-rank factorization approach to improve the efficiency of the transformer model called Low-Rank Transformer. We further compare our model with an existing low-rank factorization approach called Linformer. Based on our analysis, the Low-Rank Transformer model is suitable for improving both the time and memory efficiency in processing short-sequence (<= 512) input data, while the Linformer model is suitable for improving the efficiency in processing long-sequence input data (>= 512). We also show that Low-Rank Transformer is more suitable for on-device deployment, as it significantly reduces the model size. Additionally, we estimate that applying LRT to the existing BERT-base model can significantly reduce the computational, economical, and environmental costs for developing such models by more than 30% of its original costs.

Recently, sequence learning methods have been applied to the problem of off-policy Reinforcement Learning, including the seminal work on Decision Transformers, which employs transformers for this task. Since transformers are parameter-heavy, cannot benefit from history longer than a fixed window size, and are not computed using recurrence, we set out to investigate the suitability of the S4 family of models, which are based on state-space layers and have been shown to outperform transformers, especially in modeling long-range dependencies. In this work we present two main algorithms: (i) an off-policy training procedure that works with trajectories, while still maintaining the training efficiency of the S4 model. (ii) An on-policy training procedure that is trained in a recurrent manner, benefits from long-range dependencies, and is based on a novel stable actor-critic mechanism. Our results indicate that our method outperforms multiple variants of decision transformers, as well as the other baseline methods on most tasks, while reducing the latency, number of parameters, and training time by several orders of magnitude, making our approach more suitable for real-world RL.

Generative Pre-trained Transformers (GPTs) have demonstrated remarkable performance across diverse domains through the extensive scaling of model parameters. Recent works observe the redundancy across the transformer blocks and develop compression methods by structured pruning of the unimportant blocks. However, such straightforward elimination will always provide irreversible performance degradation. In this paper, we propose FuseGPT, a novel methodology to recycle the pruned transformer blocks to further recover the model performance. Firstly we introduce a new importance detection metric, Macro Influence (MI), to detect the long-term influence of each transformer block by calculating their loss of information after removal. Then we propose group-level layers fusion, which adopts the parameters in layers of the unimportant blocks and injects them into the corresponding layers inside the neighboring blocks. The fusion is not one-off but through iterative parameter updates by lightweight group-level fine-tuning. Specifically, these injected parameters are frozen but weighted with learnable rank decomposition matrices to reduce the overhead during fine-tuning. Our approach not only works well on large language models but also on large multimodal models. The experiments have shown that, by using modest amounts of data, FuseGPT can outperform previous works in both perplexity and zero-shot task performance.

Model compression offers a promising path to reducing the cost and inaccessibility of large pre-trained models, without significantly compromising their impressive performance. Large Transformer models, including large language models (LLMs), often contain computational redundancy, which can serve as a target for new model compression methods. In this work, we specifically target neuron-level redundancies in model layers by combining groups of similar neurons into fewer neurons. We frame this width reduction as a Discrete Optimal Transport problem, and propose DOTResize, a novel Transformer compression method that uses optimal transport theory to transform and compress model weights. To ensure applicability within the Transformer architecture, we motivate and incorporate entropic regularization and matrix factorization into the transportation maps produced by our method. Unlike pruning-based approaches which discard neurons based on importance measures, DOTResize re-projects the entire neuron width, allowing the retention and redistribution of useful signal across the reduced layer. Empirical results show that compared to simple or state-of-the-art neuron width-pruning techniques, DOTResize can outperform these methods across multiple LLM families and sizes, while achieving measurable reductions in real-world computational cost.

Deep learning, as a vital technique, has sparked a notable revolution in artificial intelligence. As the most representative architecture, Transformers have empowered numerous advanced models, especially the large language models that comprise billions of parameters, becoming a cornerstone in deep learning. Despite the impressive achievements, Transformers still face inherent limitations, particularly the time-consuming inference resulting from the quadratic computation complexity of attention calculation. Recently, a novel architecture named Mamba, drawing inspiration from classical state space models, has emerged as a promising alternative for building foundation models, delivering comparable modeling abilities to Transformers while preserving near-linear scalability concerning sequence length. This has sparked an increasing number of studies actively exploring Mamba's potential to achieve impressive performance across diverse domains. Given such rapid evolution, there is a critical need for a systematic review that consolidates existing Mamba-empowered models, offering a comprehensive understanding of this emerging model architecture. In this survey, we therefore conduct an in-depth investigation of recent Mamba-associated studies, covering from three main aspects: the advancements of Mamba-based models, the techniques of adapting Mamba to diverse data, and the applications where Mamba can excel. Specifically, we first recall the foundational knowledge of various representative deep learning models and the details of Mamba as preliminaries. Then, to showcase the significance of Mamba, we comprehensively review the related studies focusing on Mamba models' architecture design, data adaptability, and applications. Finally, we present an discussion of current limitations and explore various promising research directions to provide deeper insights for future investigations.

The search for a general model that can operate seamlessly across multiple domains remains a key goal in machine learning research. The prevailing methodology in Reinforcement Learning (RL) typically limits models to a single task within a unimodal framework, a limitation that contrasts with the broader vision of a versatile, multi-domain model. In this paper, we present Jack of All Trades (JAT), a transformer-based model with a unique design optimized for handling sequential decision-making tasks and multimodal data types. The JAT model demonstrates its robust capabilities and versatility by achieving strong performance on very different RL benchmarks, along with promising results on Computer Vision (CV) and Natural Language Processing (NLP) tasks, all using a single set of weights. The JAT model marks a significant step towards more general, cross-domain AI model design, and notably, it is the first model of its kind to be fully open-sourced (see https://huggingface.co/jat-project/jat), including a pioneering general-purpose dataset.

Recent theoretical work has identified surprisingly simple reasoning problems, such as checking if two nodes in a graph are connected or simulating finite-state machines, that are provably unsolvable by standard transformers that answer immediately after reading their input. However, in practice, transformers' reasoning can be improved by allowing them to use a "chain of thought" or "scratchpad", i.e., generate and condition on a sequence of intermediate tokens before answering. Motivated by this, we ask: Does such intermediate generation fundamentally extend the computational power of a decoder-only transformer? We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. For instance, we find that transformer decoders with a logarithmic number of decoding steps (w.r.t. the input length) push the limits of standard transformers only slightly, while a linear number of decoding steps, assuming a slight generalization to standard pre-norm, adds a clear new ability (under standard complexity conjectures): recognizing all regular languages. Our results also imply that linear steps keep transformer decoders within context-sensitive languages, and polynomial steps with generalized pre-norm make them recognize exactly the class of polynomial-time solvable problems -- the first exact characterization of a type of transformers in terms of standard complexity classes. Together, our results provide a nuanced framework for understanding how the length of a transformer's chain of thought or scratchpad impacts its reasoning power.

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard multilayer perceptrons (MLPs) with elementwise activation functions. In this note, I examine bilinear layers, which are a type of MLP layer that are mathematically much easier to analyze while simultaneously performing better than standard MLPs. Although they are nonlinear functions of their input, I demonstrate that bilinear layers can be expressed using only linear operations and third order tensors. We can integrate this expression for bilinear layers into a mathematical framework for transformer circuits, which was previously limited to attention-only transformers. These results suggest that bilinear layers are easier to analyze mathematically than current architectures and thus may lend themselves to deeper safety insights by allowing us to talk more formally about circuits in neural networks. Additionally, bilinear layers may offer an alternative path for mechanistic interpretability through understanding the mechanisms of feature construction instead of enumerating a (potentially exponentially) large number of features in large models.

We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enable continuous-in-time evaluations. A novel training strategy leveraging the semi-group property of time-dependent PDEs to allow for significant scaling-up of the training data is also proposed. Poseidon is pretrained on a diverse, large scale dataset for the governing equations of fluid dynamics. It is then evaluated on a suite of 15 challenging downstream tasks that include a wide variety of PDE types and operators. We show that Poseidon exhibits excellent performance across the board by outperforming baselines significantly, both in terms of sample efficiency and accuracy. Poseidon also generalizes very well to new physics that is not seen during pretraining. Moreover, Poseidon scales with respect to model and data size, both for pretraining and for downstream tasks. Taken together, our results showcase the surprising ability of Poseidon to learn effective representations from a very small set of PDEs during pretraining in order to generalize well to unseen and unrelated PDEs downstream, demonstrating its potential as an effective, general purpose PDE foundation model. Finally, the Poseidon model as well as underlying pretraining and downstream datasets are open sourced, with code being available at https://github.com/camlab-ethz/poseidon and pretrained models and datasets at https://huggingface.co/camlab-ethz.

Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically, due to their massive size, even inference for large, highly-accurate GPT models may require multiple performant GPUs, which limits the usability of such models. While there is emerging work on relieving this pressure via model compression, the applicability and performance of existing compression techniques is limited by the scale and complexity of GPT models. In this paper, we address this challenge, and propose GPTQ, a new one-shot weight quantization method based on approximate second-order information, that is both highly-accurate and highly-efficient. Specifically, GPTQ can quantize GPT models with 175 billion parameters in approximately four GPU hours, reducing the bitwidth down to 3 or 4 bits per weight, with negligible accuracy degradation relative to the uncompressed baseline. Our method more than doubles the compression gains relative to previously-proposed one-shot quantization methods, preserving accuracy, allowing us for the first time to execute an 175 billion-parameter model inside a single GPU for generative inference. Moreover, we also show that our method can still provide reasonable accuracy in the extreme quantization regime, in which weights are quantized to 2-bit or even ternary quantization levels. We show experimentally that these improvements can be leveraged for end-to-end inference speedups over FP16, of around 3.25x when using high-end GPUs (NVIDIA A100) and 4.5x when using more cost-effective ones (NVIDIA A6000). The implementation is available at https://github.com/IST-DASLab/gptq.

Transformers have greatly advanced the state-of-the-art in Natural Language Processing (NLP) in recent years, but present very large computation and storage requirements. We observe that the design process of Transformers (pre-train a foundation model on a large dataset in a self-supervised manner, and subsequently fine-tune it for different downstream tasks) leads to task-specific models that are highly over-parameterized, adversely impacting both accuracy and inference efficiency. We propose AxFormer, a systematic framework that applies accuracy-driven approximations to create optimized transformer models for a given downstream task. AxFormer combines two key optimizations -- accuracy-driven pruning and selective hard attention. Accuracy-driven pruning identifies and removes parts of the fine-tuned transformer that hinder performance on the given downstream task. Sparse hard-attention optimizes attention blocks in selected layers by eliminating irrelevant word aggregations, thereby helping the model focus only on the relevant parts of the input. In effect, AxFormer leads to models that are more accurate, while also being faster and smaller. Our experiments on GLUE and SQUAD tasks show that AxFormer models are up to 4.5% more accurate, while also being up to 2.5X faster and up to 3.2X smaller than conventional fine-tuned models. In addition, we demonstrate that AxFormer can be combined with previous efforts such as distillation or quantization to achieve further efficiency gains.

The LayerNorm (LN) layer in GPT-style transformer models has long been a hindrance to mechanistic interpretability. LN is a crucial component required to stabilize the training of large language models, and LN or the similar RMSNorm have been used in practically all large language models based on the transformer architecture. The non-linear nature of the LN layers is a hindrance for mechanistic interpretability as it hinders interpretation of the residual stream, and makes it difficult to decompose the model into circuits. Some research have gone so far as to name "reasons interpretability researchers hate layer norm". In this paper we show that it is possible to remove the LN layers from a pre-trained GPT2-small model by fine-tuning on a fraction (500M tokens) of the training data. We demonstrate that this LN-free model achieves similar performance to the original model on the OpenWebText and ThePile datasets (-0.05 cross-entropy loss), and the Hellaswag benchmark (-0.5% accuracy). We provide the fine-tuning procedure and a Hugging Face repository with the fine-tuned GPT2-small models. Our work not only provides a simplified model for mechanistic interpretability research, but also provides evidence that the LN layers, at inference time, do not play a crucial role in transformer models.

In deep learning, models typically reuse the same parameters for all inputs. Mixture of Experts (MoE) defies this and instead selects different parameters for each incoming example. The result is a sparsely-activated model -- with outrageous numbers of parameters -- but a constant computational cost. However, despite several notable successes of MoE, widespread adoption has been hindered by complexity, communication costs and training instability -- we address these with the Switch Transformer. We simplify the MoE routing algorithm and design intuitive improved models with reduced communication and computational costs. Our proposed training techniques help wrangle the instabilities and we show large sparse models may be trained, for the first time, with lower precision (bfloat16) formats. We design models based off T5-Base and T5-Large to obtain up to 7x increases in pre-training speed with the same computational resources. These improvements extend into multilingual settings where we measure gains over the mT5-Base version across all 101 languages. Finally, we advance the current scale of language models by pre-training up to trillion parameter models on the "Colossal Clean Crawled Corpus" and achieve a 4x speedup over the T5-XXL model.

We propose expanding the shared Transformer module to produce and initialize Transformers of varying depths, enabling adaptation to diverse resource constraints. Drawing an analogy to genetic expansibility, we term such module as learngene. To identify the expansion mechanism, we delve into the relationship between the layer's position and its corresponding weight value, and find that linear function appropriately approximates this relationship. Building on this insight, we present Transformer as Linear Expansion of learnGene (TLEG), a novel approach for flexibly producing and initializing Transformers of diverse depths. Specifically, to learn learngene, we firstly construct an auxiliary Transformer linearly expanded from learngene, after which we train it through employing soft distillation. Subsequently, we can produce and initialize Transformers of varying depths via linearly expanding the well-trained learngene, thereby supporting diverse downstream scenarios. Extensive experiments on ImageNet-1K demonstrate that TLEG achieves comparable or better performance in contrast to many individual models trained from scratch, while reducing around 2x training cost. When transferring to several downstream classification datasets, TLEG surpasses existing initialization methods by a large margin (e.g., +6.87% on iNat 2019 and +7.66% on CIFAR-100). Under the situation where we need to produce models of varying depths adapting for different resource constraints, TLEG achieves comparable results while reducing around 19x parameters stored to initialize these models and around 5x pre-training costs, in contrast to the pre-training and fine-tuning approach. When transferring a fixed set of parameters to initialize different models, TLEG presents better flexibility and competitive performance while reducing around 2.9x parameters stored to initialize, compared to the pre-training approach.

Transformer models have revolutionized natural language processing with their unparalleled ability to grasp complex contextual relationships. However, the vast number of parameters in these models has raised concerns regarding computational efficiency, environmental impact, and deployability on resource-limited platforms. To address these challenges, this paper investigates the application of weight pruning-a strategic reduction of model parameters based on their significance-as an optimization strategy for Transformer architectures. Through extensive experimentation, we explore various pruning methodologies, highlighting their impact on model performance, size, and computational demands. Our findings suggest that with judicious selection of pruning hyperparameters, significant reductions in model size are attainable without considerable compromise on performance. Moreover, when coupled with post-pruning fine-tuning strategies, some pruned models even exhibit enhanced generalization capabilities. This work seeks to bridge the gap between model efficiency and performance, paving the way for more scalable and environmentally responsible deep learning applications.

Recent legislation has led to interest in machine unlearning, i.e., removing specific training samples from a predictive model as if they never existed in the training dataset. Unlearning may also be required due to corrupted/adversarial data or simply a user's updated privacy requirement. For models which require no training (k-NN), simply deleting the closest original sample can be effective. But this idea is inapplicable to models which learn richer representations. Recent ideas leveraging optimization-based updates scale poorly with the model dimension d, due to inverting the Hessian of the loss function. We use a variant of a new conditional independence coefficient, L-CODEC, to identify a subset of the model parameters with the most semantic overlap on an individual sample level. Our approach completely avoids the need to invert a (possibly) huge matrix. By utilizing a Markov blanket selection, we premise that L-CODEC is also suitable for deep unlearning, as well as other applications in vision. Compared to alternatives, L-CODEC makes approximate unlearning possible in settings that would otherwise be infeasible, including vision models used for face recognition, person re-identification and NLP models that may require unlearning samples identified for exclusion. Code can be found at https://github.com/vsingh-group/LCODEC-deep-unlearning/

Linear Transformers and State Space Models have emerged as efficient alternatives to softmax Transformers for causal sequence modeling, enabling parallel training via matrix multiplication and efficient RNN-style inference. However, despite their success in causal tasks, no unified framework exists for applying Linear Transformers to bidirectional sequence modeling. We introduce LION, the first framework to systematically extend Linear Transformers to the bidirectional setting. LION generalizes three core representations commonly used in the causal case - full Linear Attention , bidirectional RNN, and chunkwise parallel form - to the bidirectional setting. These forms are theoretically equivalent and enable models to exploit the strengths of each during training and inference. We prove that a broad class of Linear Transformers can be extended using LION and validate our framework via three core examples based on the choice of decay type: LION-LIT, the bidirectional extension of arXiv:2006.16236; LION-D, based on arXiv:2307.08621; and LION-S, a variant using selective decay arXiv:2103.02143, arXiv:2312.0075. Across standard bidirectional tasks, LION enables models to match or exceed the performance of softmax Transformers, while offering significantly faster training and more efficient inference than existing State Space Models.

In the classical transformer attention scheme, we are given three n times d size matrices Q, K, V (the query, key, and value tokens), and the goal is to compute a new n times d size matrix D^{-1} exp(QK^top) V where D = diag( exp(QK^top) {bf 1}_n ). In this work, we study a generalization of attention which captures triple-wise correlations. This generalization is able to solve problems about detecting triple-wise connections that were shown to be impossible for transformers. The potential downside of this generalization is that it appears as though computations are even more difficult, since the straightforward algorithm requires cubic time in n. However, we show that in the bounded-entry setting (which arises in practice, and which is well-studied in both theory and practice), there is actually a near-linear time algorithm. More precisely, we show that bounded entries are both necessary and sufficient for quickly performing generalized computations: bullet On the positive side, if all entries of the input matrices are bounded above by o(sqrt[3]{log n}) then we show how to approximate the ``tensor-type'' attention matrix in n^{1+o(1)} time. bullet On the negative side, we show that if the entries of the input matrices may be as large as Omega(sqrt[3]{log n}), then there is no algorithm that runs faster than n^{3-o(1)} (assuming the Strong Exponential Time Hypothesis from fine-grained complexity theory). We also show that our construction, algorithms, and lower bounds naturally generalize to higher-order tensors and correlations. Interestingly, the higher the order of the tensors, the lower the bound on the entries needs to be for an efficient algorithm. Our results thus yield a natural tradeoff between the boundedness of the entries, and order of the tensor one may use for more expressive, efficient attention computation.

Transformers have become the de-facto standard model in artificial intelligence since 2017 despite numerous shortcomings ranging from energy inefficiency to hallucinations. Research has made a lot of progress in improving elements of transformers, and, more generally, deep learning manifesting in many proposals for architectures, layers, optimization objectives, and optimization techniques. For researchers it is difficult to keep track of such developments on a broader level. We provide a comprehensive overview of the many important, recent works in these areas to those who already have a basic understanding of deep learning. Our focus differs from other works, as we target specifically novel, alternative potentially disruptive approaches to transformers as well as successful ideas of recent deep learning. We hope that such a holistic and unified treatment of influential, recent works and novel ideas helps researchers to form new connections between diverse areas of deep learning. We identify and discuss multiple patterns that summarize the key strategies for successful innovations over the last decade as well as works that can be seen as rising stars. Especially, we discuss attempts on how to improve on transformers covering (partially) proven methods such as state space models but also including far-out ideas in deep learning that seem promising despite not achieving state-of-the-art results. We also cover a discussion on recent state-of-the-art models such as OpenAI's GPT series and Meta's LLama models and, Google's Gemini model family.

Pretrained transformer models have achieved state-of-the-art results in many tasks and benchmarks recently. Many state-of-the-art Language Models (LMs), however, do not scale well above the threshold of 512 input tokens. In specialized domains though (such as legal, scientific or biomedical), models often need to process very long text (sometimes well above 10000 tokens). Even though many efficient transformers have been proposed (such as Longformer, BigBird or FNet), so far, only very few such efficient models are available for specialized domains. Additionally, since the pretraining process is extremely costly in general - but even more so as the sequence length increases - it is often only in reach of large research labs. One way of making pretraining cheaper is the Replaced Token Detection (RTD) task, by providing more signal during training, since the loss can be computed over all tokens. In this work, we train Longformer models with the efficient RTD task on legal data to showcase that pretraining efficient LMs is possible using much less compute. We evaluate the trained models on challenging summarization tasks requiring the model to summarize long texts to show to what extent the models can achieve good performance on downstream tasks. We find that both the small and base models outperform their baselines on the in-domain BillSum and out-of-domain PubMed tasks in their respective parameter range. We publish our code and models for research purposes.

There remain many open questions pertaining to the scaling behaviour of Transformer architectures. These scaling decisions and findings can be critical, as training runs often come with an associated computational cost which have both financial and/or environmental impact. The goal of this paper is to present scaling insights from pretraining and finetuning Transformers. While Kaplan et al. presents a comprehensive study of the scaling behaviour of Transformer language models, the scope is only on the upstream (pretraining) loss. Therefore, it is still unclear if these set of findings transfer to downstream task within the context of the pretrain-finetune paradigm. The key findings of this paper are as follows: (1) we show that aside from only the model size, model shape matters for downstream fine-tuning, (2) scaling protocols operate differently at different compute regions, (3) widely adopted T5-base and T5-large sizes are Pareto-inefficient. To this end, we present improved scaling protocols whereby our redesigned models achieve similar downstream fine-tuning quality while having 50\% fewer parameters and training 40\% faster compared to the widely adopted T5-base model. We publicly release over 100 pretrained checkpoints of different T5 configurations to facilitate future research and analysis.

The crystallization of modeling methods around the Transformer architecture has been a boon for practitioners. Simple, well-motivated architectural variations can transfer across tasks and scale, increasing the impact of modeling research. However, with the emergence of state-of-the-art 100B+ parameters models, large language models are increasingly expensive to accurately design and train. Notably, it can be difficult to evaluate how modeling decisions may impact emergent capabilities, given that these capabilities arise mainly from sheer scale alone. In the process of building BLOOM--the Big Science Large Open-science Open-access Multilingual language model--our goal is to identify an architecture and training setup that makes the best use of our 1,000,000 A100-GPU-hours budget. Specifically, we perform an ablation study at the billion-parameter scale comparing different modeling practices and their impact on zero-shot generalization. In addition, we study the impact of various popular pre-training corpora on zero-shot generalization. We also study the performance of a multilingual model and how it compares to the English-only one. Finally, we consider the scaling behaviour of Transformers to choose the target model size, shape, and training setup. All our models and code are open-sourced at https://huggingface.co/bigscience .

Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill composition in a collection of modular arithmetic tasks. Specifically, we consider a finite collection of linear modular functions z = a , x + b , y ;mod; p labeled by the vector (a, b) in Z_p^2. We use some of these tasks for pre-training and the rest for out-of-distribution testing. We empirically show that a GPT-style transformer exhibits a transition from in-distribution to out-of-distribution generalization as the number of pre-training tasks increases. We find that the smallest model capable of out-of-distribution generalization requires two transformer blocks, while for deeper models, the out-of-distribution generalization phase is transient, necessitating early stopping. Finally, we perform an interpretability study of the pre-trained models, revealing the highly structured representations in both phases; and discuss the learnt algorithm.

Recent progress in natural language processing has been driven by advances in both model architecture and model pretraining. Transformer architectures have facilitated building higher-capacity models and pretraining has made it possible to effectively utilize this capacity for a wide variety of tasks. Transformers is an open-source library with the goal of opening up these advances to the wider machine learning community. The library consists of carefully engineered state-of-the art Transformer architectures under a unified API. Backing this library is a curated collection of pretrained models made by and available for the community. Transformers is designed to be extensible by researchers, simple for practitioners, and fast and robust in industrial deployments. The library is available at https://github.com/huggingface/transformers.

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The new method achieves superior accuracy over its predecessors and contemporary operator learners and shows robustness to noises in benchmarks. This research shall strengthen the insights that, despite being invented for natural language processing tasks, the attention mechanism offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.

Current machine learning systems are brittle in the face of distribution shifts (DS), where the target distribution that the system is tested on differs from the source distribution used to train the system. This problem of robustness to DS has been studied extensively in the field of domain adaptation. For deep neural networks, a popular framework for unsupervised domain adaptation (UDA) is domain matching, in which algorithms try to align the marginal distributions in the feature or output space. The current theoretical understanding of these methods, however, is limited and existing theoretical results are not precise enough to characterize their performance in practice. In this paper, we derive new bounds based on optimal transport that analyze the UDA problem. Our new bounds include a term which we dub as entanglement, consisting of an expectation of Wasserstein distance between conditionals with respect to changing data distributions. Analysis of the entanglement term provides a novel perspective on the unoptimizable aspects of UDA. In various experiments with multiple models across several DS scenarios, we show that this term can be used to explain the varying performance of UDA algorithms.

Research on Large Language Models (LLMs) has recently seen exponential growth, largely focused on transformer-based architectures, as introduced by [1] and further advanced by the decoder-only variations in [2]. Contemporary studies typically aim to improve model capabilities by increasing both the architecture's complexity and the volume of training data. However, research exploring how to reduce model sizes while maintaining performance is limited. This study introduces three modifications to the decoder-only transformer architecture: ParallelGPT (p-gpt), LinearlyCompressedGPT (lc-gpt), and ConvCompressedGPT (cc-gpt). These variants achieve comparable performance to conventional architectures in code generation tasks while benefiting from reduced model sizes and faster training times. We open-source the model weights and codebase to support future research and development in this domain.

Modern cryptographic methods for implementing privacy-preserving LLMs such as Homomorphic Encryption (HE) require the LLMs to have a polynomial form. Forming such a representation is challenging because Transformers include non-polynomial components, such as Softmax and layer normalization. Previous approaches have either directly approximated pre-trained models with large-degree polynomials, which are less efficient over HE, or replaced non-polynomial components with easier-to-approximate primitives before training, e.g., Softmax with pointwise attention. The latter approach might introduce scalability challenges. We present a new HE-friendly variant of self-attention that offers a stable form for training and is easy to approximate with polynomials for secure inference. Our work introduces the first polynomial LLMs with 32 layers and over a billion parameters, exceeding the size of previous models by more than tenfold. The resulting models demonstrate reasoning and in-context learning (ICL) capabilities comparable to standard transformers of the same size, representing a breakthrough in the field. Finally, we provide a detailed latency breakdown for each computation over encrypted data, paving the way for further optimization, and explore the differences in inductive bias between transformers relying on our HE-friendly variant and standard transformers. Our code is attached as a supplement.

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired image-to-image (I2I) translation tasks due to the Gaussian prior assumption. Schr\"{o}dinger Bridge (SB), which learns an SDE to translate between two arbitrary distributions, have risen as an attractive solution to this problem. Yet, to our best knowledge, none of SB models so far have been successful at unpaired translation between high-resolution images. In this work, we propose Unpaired Neural Schr\"{o}dinger Bridge (UNSB), which expresses the SB problem as a sequence of adversarial learning problems. This allows us to incorporate advanced discriminators and regularization to learn a SB between unpaired data. We show that UNSB is scalable and successfully solves various unpaired I2I translation tasks. Code: https://github.com/cyclomon/UNSB

Mixture-of-Experts (MoE), a conditional computation architecture, achieved promising performance by scaling local module (i.e. feed-forward network) of transformer. However, scaling the cross-token module (i.e. self-attention) is challenging due to the unstable training. This work proposes Sparse-MLP, an all-MLP model which applies sparsely-activated MLPs to cross-token modeling. Specifically, in each Sparse block of our all-MLP model, we apply two stages of MoE layers: one with MLP experts mixing information within channels along image patch dimension, the other with MLP experts mixing information within patches along the channel dimension. In addition, by proposing importance-score routing strategy for MoE and redesigning the image representation shape, we further improve our model's computational efficiency. Experimentally, we are more computation-efficient than Vision Transformers with comparable accuracy. Also, our models can outperform MLP-Mixer by 2.5\% on ImageNet Top-1 accuracy with fewer parameters and computational cost. On downstream tasks, i.e. Cifar10 and Cifar100, our models can still achieve better performance than baselines.

Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This stark disparity raise human's concerns about their safe and ethical use, hinder their widespread adoption.In this paper, we focus on a typical arithmetic task, integer multiplication, to explore and explain the imperfection of transformers in this domain. We provide comprehensive analysis of a vanilla transformer trained to perform n-digit integer multiplication. Our observations indicate that the model decomposes multiplication task into multiple parallel subtasks, sequentially optimizing each subtask for each digit to complete the final multiplication. Based on observation and analysis, we infer the reasons of transformers deficiencies in multiplication tasks lies in their difficulty in calculating successive carryovers and caching intermediate results, and confirmed this inference through experiments. Guided by these findings, we propose improvements to enhance transformers performance on multiplication tasks. These enhancements are validated through rigorous testing and mathematical modeling, not only enhance transformer's interpretability, but also improve its performance, e.g., we achieve over 99.9% accuracy on 5-digit integer multiplication with a tiny transformer, outperform LLMs GPT-4. Our method contributes to the broader fields of model understanding and interpretability, paving the way for analyzing more complex tasks and Transformer models. This work underscores the importance of explainable AI, helping to build trust in large language models and promoting their adoption in critical applications.

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps and learns the kernel by learning the spectral distribution. This not only helps in learning a generic kernel end-to-end, but also reduces the time and space complexity of Transformers from quadratic to linear. We show that KERNELIZED TRANSFORMERS achieve performance comparable to existing efficient Transformer architectures, both in terms of accuracy as well as computational efficiency. Our study also demonstrates that the choice of the kernel has a substantial impact on performance, and kernel learning variants are competitive alternatives to fixed kernel Transformers, both in long as well as short sequence tasks.

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem of extracting relevant context information from long sequences in NLP and realistic scenes in CV. A classical neural network component, a Multi-Layer Perceptron (MLP), complements the attention mechanism. Its necessity is frequently justified by its capability of modeling nonlinear relationships. However, the attention mechanism itself is nonlinear through its internal use of similarity measures. A possible hypothesis is that this nonlinearity is sufficient for modeling typical application problems. As the MLPs usually contain the most trainable parameters of the whole model, their omission would substantially reduce the parameter set size. Further components can also be reorganized to reduce the number of parameters. Under some conditions, query and key matrices can be collapsed into a single matrix of the same size. The same is true about value and projection matrices, which can also be omitted without eliminating the substance of the attention mechanism. Initially, the similarity measure was defined asymmetrically, with peculiar properties such as that a token is possibly dissimilar to itself. A possible symmetric definition requires only half of the parameters. We have laid the groundwork by testing widespread CV benchmarks: MNIST and CIFAR-10. The tests have shown that simplified transformer architectures (a) without MLP, (b) with collapsed matrices, and (c) symmetric similarity matrices exhibit similar performance as the original architecture, saving up to 90% of parameters without hurting the classification performance.

In deep learning theory, the covariance matrix of the representations serves as a proxy to examine the network's trainability. Motivated by the success of Transformers, we study the covariance matrix of a modified Softmax-based attention model with skip connections in the proportional limit of infinite-depth-and-width. We show that at initialization the limiting distribution can be described by a stochastic differential equation (SDE) indexed by the depth-to-width ratio. To achieve a well-defined stochastic limit, the Transformer's attention mechanism is modified by centering the Softmax output at identity, and scaling the Softmax logits by a width-dependent temperature parameter. We examine the stability of the network through the corresponding SDE, showing how the scale of both the drift and diffusion can be elegantly controlled with the aid of residual connections. The existence of a stable SDE implies that the covariance structure is well-behaved, even for very large depth and width, thus preventing the notorious issues of rank degeneracy in deep attention models. Finally, we show, through simulations, that the SDE provides a surprisingly good description of the corresponding finite-size model. We coin the name shaped Transformer for these architectural modifications.

As the rapid progression of practical applications based on Large Language Models continues, the importance of extrapolating performance has grown exponentially in the research domain. In our study, we identified an anomalous behavior in Transformer models that had been previously overlooked, leading to a chaos around closest tokens which carried the most important information. We've coined this discovery the "headache of Transformers". To address this at its core, we introduced a novel self-attention structure named Collinear Constrained Attention (CoCA). This structure can be seamlessly integrated with existing extrapolation, interpolation methods, and other optimization strategies designed for traditional Transformer models. We have achieved excellent extrapolating performance even for 16 times to 24 times of sequence lengths during inference without any fine-tuning on our model. We have also enhanced CoCA's computational and spatial efficiency to ensure its practicality. We plan to open-source CoCA shortly. In the meantime, we've made our code available in the appendix for reappearing experiments.

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of Transformers. For one, we replace dot-product attention by one that uses locality-sensitive hashing, changing its complexity from O(L^2) to O(Llog L), where L is the length of the sequence. Furthermore, we use reversible residual layers instead of the standard residuals, which allows storing activations only once in the training process instead of N times, where N is the number of layers. The resulting model, the Reformer, performs on par with Transformer models while being much more memory-efficient and much faster on long sequences.

Inference-time computation techniques, analogous to human System 2 Thinking, have recently become popular for improving model performances. However, most existing approaches suffer from several limitations: they are modality-specific (e.g., working only in text), problem-specific (e.g., verifiable domains like math and coding), or require additional supervision/training on top of unsupervised pretraining (e.g., verifiers or verifiable rewards). In this paper, we ask the question "Is it possible to generalize these System 2 Thinking approaches, and develop models that learn to think solely from unsupervised learning?" Interestingly, we find the answer is yes, by learning to explicitly verify the compatibility between inputs and candidate-predictions, and then re-framing prediction problems as optimization with respect to this verifier. Specifically, we train Energy-Based Transformers (EBTs) -- a new class of Energy-Based Models (EBMs) -- to assign an energy value to every input and candidate-prediction pair, enabling predictions through gradient descent-based energy minimization until convergence. Across both discrete (text) and continuous (visual) modalities, we find EBTs scale faster than the dominant Transformer++ approach during training, achieving an up to 35% higher scaling rate with respect to data, batch size, parameters, FLOPs, and depth. During inference, EBTs improve performance with System 2 Thinking by 29% more than the Transformer++ on language tasks, and EBTs outperform Diffusion Transformers on image denoising while using fewer forward passes. Further, we find that EBTs achieve better results than existing models on most downstream tasks given the same or worse pretraining performance, suggesting that EBTs generalize better than existing approaches. Consequently, EBTs are a promising new paradigm for scaling both the learning and thinking capabilities of models.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Transformers have found extensive applications across various domains due to the powerful fitting capabilities. This success can be partially attributed to their inherent nonlinearity. Thus, in addition to the ReLU function employed in the original transformer architecture, researchers have explored alternative modules such as GeLU and SwishGLU to enhance nonlinearity and thereby augment representational capacity. In this paper, we propose a novel category of polynomial composition activations (PolyCom), designed to optimize the dynamics of transformers. Theoretically, we provide a comprehensive mathematical analysis of PolyCom, highlighting its enhanced expressivity and efficacy relative to other activation functions. Notably, we demonstrate that networks incorporating PolyCom achieve the optimal approximation rate, indicating that PolyCom networks require minimal parameters to approximate general smooth functions in Sobolev spaces. We conduct empirical experiments on the pre-training configurations of large language models (LLMs), including both dense and sparse architectures. By substituting conventional activation functions with PolyCom, we enable LLMs to capture higher-order interactions within the data, thus improving performance metrics in terms of accuracy and convergence rates. Extensive experimental results demonstrate the effectiveness of our method, showing substantial improvements over other activation functions. Code is available at https://github.com/BryceZhuo/PolyCom.

Foundation models have revolutionized natural language processing through a ``train once, deploy anywhere'' paradigm, where a single pre-trained model adapts to countless downstream tasks without retraining. Access to a Physics Foundation Model (PFM) would be transformative -- democratizing access to high-fidelity simulations, accelerating scientific discovery, and eliminating the need for specialized solver development. Yet current physics-aware machine learning approaches remain fundamentally limited to single, narrow domains and require retraining for each new system. We present the General Physics Transformer (GPhyT), trained on 1.8 TB of diverse simulation data, that demonstrates foundation model capabilities are achievable for physics. Our key insight is that transformers can learn to infer governing dynamics from context, enabling a single model to simulate fluid-solid interactions, shock waves, thermal convection, and multi-phase dynamics without being told the underlying equations. GPhyT achieves three critical breakthroughs: (1) superior performance across multiple physics domains, outperforming specialized architectures by up to 29x, (2) zero-shot generalization to entirely unseen physical systems through in-context learning, and (3) stable long-term predictions through 50-timestep rollouts. By establishing that a single model can learn generalizable physical principles from data alone, this work opens the path toward a universal PFM that could transform computational science and engineering.

Transformer-based pre-trained models with millions of parameters require large storage. Recent approaches tackle this shortcoming by training adapters, but these approaches still require a relatively large number of parameters. In this study, AdapterBias, a surprisingly simple yet effective adapter architecture, is proposed. AdapterBias adds a token-dependent shift to the hidden output of transformer layers to adapt to downstream tasks with only a vector and a linear layer. Extensive experiments are conducted to demonstrate the effectiveness of AdapterBias. The experiments show that our proposed method can dramatically reduce the trainable parameters compared to the previous works with a minimal decrease in task performances compared with fine-tuned pre-trained models. We further find that AdapterBias automatically learns to assign more significant representation shifts to the tokens related to the task in consideration.

Large Transformer models are capable of implementing a plethora of so-called in-context learning algorithms. These include gradient descent, classification, sequence completion, transformation, and improvement. In this work, we investigate whether large language models (LLMs), which never explicitly encountered the task of black-box optimization, are in principle capable of implementing evolutionary optimization algorithms. While previous works have solely focused on language-based task specification, we move forward and focus on the zero-shot application of LLMs to black-box optimization. We introduce a novel prompting strategy, consisting of least-to-most sorting of discretized population members and querying the LLM to propose an improvement to the mean statistic, i.e. perform a type of black-box recombination operation. Empirically, we find that our setup allows the user to obtain an LLM-based evolution strategy, which we call `EvoLLM', that robustly outperforms baseline algorithms such as random search and Gaussian Hill Climbing on synthetic BBOB functions as well as small neuroevolution tasks. Hence, LLMs can act as `plug-in' in-context recombination operators. We provide several comparative studies of the LLM's model size, prompt strategy, and context construction. Finally, we show that one can flexibly improve EvoLLM's performance by providing teacher algorithm information via instruction fine-tuning on previously collected teacher optimization trajectories.

Equivariant Transformers such as Equiformer have demonstrated the efficacy of applying Transformers to the domain of 3D atomistic systems. However, they are still limited to small degrees of equivariant representations due to their computational complexity. In this paper, we investigate whether these architectures can scale well to higher degrees. Starting from Equiformer, we first replace SO(3) convolutions with eSCN convolutions to efficiently incorporate higher-degree tensors. Then, to better leverage the power of higher degrees, we propose three architectural improvements -- attention re-normalization, separable S^2 activation and separable layer normalization. Putting this all together, we propose EquiformerV2, which outperforms previous state-of-the-art methods on the large-scale OC20 dataset by up to 12% on forces, 4% on energies, offers better speed-accuracy trade-offs, and 2times reduction in DFT calculations needed for computing adsorption energies.

Transformer models are foundational to natural language processing (NLP) and computer vision. Despite various recent works devoted to reducing the quadratic cost of such models (as a function of the sequence length n), dealing with ultra long sequences efficiently (e.g., with more than 16K tokens) remains challenging. Applications such as answering questions based on an entire book or summarizing a scientific article are inefficient or infeasible. In this paper, we propose to significantly reduce the dependency of a Transformer model's complexity on n, by compressing the input into a representation whose size r is independent of n at each layer. Specifically, by exploiting the fact that in many tasks, only a small subset of special tokens (we call VIP-tokens) are most relevant to the final prediction, we propose a VIP-token centric compression (Vcc) scheme which selectively compresses the input sequence based on their impact on approximating the representation of these VIP-tokens. Compared with competitive baselines, the proposed algorithm not only is efficient (achieving more than 3times efficiency improvement compared to baselines on 4K and 16K lengths), but also achieves competitive or better performance on a large number of tasks. Further, we show that our algorithm can be scaled to 128K tokens (or more) while consistently offering accuracy improvement.

We study how information propagates in decoder-only Transformers, which are the architectural backbone of most existing frontier large language models (LLMs). We rely on a theoretical signal propagation analysis -- specifically, we analyse the representations of the last token in the final layer of the Transformer, as this is the representation used for next-token prediction. Our analysis reveals a representational collapse phenomenon: we prove that certain distinct sequences of inputs to the Transformer can yield arbitrarily close representations in the final token. This effect is exacerbated by the low-precision floating-point formats frequently used in modern LLMs. As a result, the model is provably unable to respond to these sequences in different ways -- leading to errors in, e.g., tasks involving counting or copying. Further, we show that decoder-only Transformer language models can lose sensitivity to specific tokens in the input, which relates to the well-known phenomenon of over-squashing in graph neural networks. We provide empirical evidence supporting our claims on contemporary LLMs. Our theory also points to simple solutions towards ameliorating these issues.

Transformer models have demonstrated high accuracy in numerous applications but have high complexity and lack sequential processing capability making them ill-suited for many streaming applications at the edge where devices are heavily resource-constrained. Thus motivated, many researchers have proposed reformulating the transformer models as RNN modules which modify the self-attention computation with explicit states. However, these approaches often incur significant performance degradation. The ultimate goal is to develop a model that has the following properties: parallel training, streaming and low-cost inference, and SOTA performance. In this paper, we propose a new direction to achieve this goal. We show how architectural modifications to a recurrent model can help push its performance toward Transformer models while retaining its sequential processing capability. Specifically, inspired by the recent success of Legendre Memory Units (LMU) in sequence learning tasks, we propose LMUFormer, which augments the LMU with convolutional patch embedding and convolutional channel mixer. Moreover, we present a spiking version of this architecture, which introduces the benefit of states within the patch embedding and channel mixer modules while simultaneously reducing the computing complexity. We evaluated our architectures on multiple sequence datasets. In comparison to SOTA transformer-based models within the ANN domain on the SCv2 dataset, our LMUFormer demonstrates comparable performance while necessitating a remarkable 53 times reduction in parameters and a substantial 65 times decrement in FLOPs. Additionally, owing to our model's proficiency in real-time data processing, we can achieve a 32.03% reduction in sequence length, all while incurring an inconsequential decline in performance. Our code is publicly available at https://github.com/zeyuliu1037/LMUFormer.git.

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Large transformer-based models are able to perform in-context few-shot learning, without being explicitly trained for it. This observation raises the question: what aspects of the training regime lead to this emergent behavior? Here, we show that this behavior is driven by the distributions of the training data itself. In-context learning emerges when the training data exhibits particular distributional properties such as burstiness (items appear in clusters rather than being uniformly distributed over time) and having large numbers of rarely occurring classes. In-context learning also emerges more strongly when item meanings or interpretations are dynamic rather than fixed. These properties are exemplified by natural language, but are also inherent to naturalistic data in a wide range of other domains. They also depart significantly from the uniform, i.i.d. training distributions typically used for standard supervised learning. In our initial experiments, we found that in-context learning traded off against more conventional weight-based learning, and models were unable to achieve both simultaneously. However, our later experiments uncovered that the two modes of learning could co-exist in a single model when it was trained on data following a skewed Zipfian distribution -- another common property of naturalistic data, including language. In further experiments, we found that naturalistic data distributions were only able to elicit in-context learning in transformers, and not in recurrent models. In sum, our findings indicate how the transformer architecture works together with particular properties of the training data to drive the intriguing emergent in-context learning behaviour of large language models, and how future work might encourage both in-context and in-weights learning in domains beyond language.

Transformers have been actively studied for time-series forecasting in recent years. While often showing promising results in various scenarios, traditional Transformers are not designed to fully exploit the characteristics of time-series data and thus suffer some fundamental limitations, e.g., they generally lack of decomposition capability and interpretability, and are neither effective nor efficient for long-term forecasting. In this paper, we propose ETSFormer, a novel time-series Transformer architecture, which exploits the principle of exponential smoothing in improving Transformers for time-series forecasting. In particular, inspired by the classical exponential smoothing methods in time-series forecasting, we propose the novel exponential smoothing attention (ESA) and frequency attention (FA) to replace the self-attention mechanism in vanilla Transformers, thus improving both accuracy and efficiency. Based on these, we redesign the Transformer architecture with modular decomposition blocks such that it can learn to decompose the time-series data into interpretable time-series components such as level, growth and seasonality. Extensive experiments on various time-series benchmarks validate the efficacy and advantages of the proposed method. Code is available at https://github.com/salesforce/ETSformer.

Conditional computation is a popular strategy to make Transformers more efficient. Existing methods often target individual modules (e.g., mixture-of-experts layers) or skip layers independently of one another. However, interpretability research has demonstrated that the middle layers of Transformers exhibit greater redundancy, and that early layers aggregate information into token positions. Guided by these insights, we propose a novel architecture that dynamically skips a variable number of layers from the middle outward. In particular, a learned gating mechanism determines whether to bypass a symmetric span of central blocks based on the input, and a gated attention mechanism prevents subsequent tokens from attending to skipped token positions. Residual norms are controlled with a 'sandwich' or 'perilayernorm' scheme and gate sparsity with an adaptive regularization loss. We had aimed to reduce compute requirements for 'simpler' tokens and potentially foster an emergent multi-level representational hierarchy but, at the scales investigated, our approach does not achieve improvements in the trade-off between validation cross-entropy and estimated FLOPs compared to dense baselines with fewer layers. We release our code at https://github.com/tim-lawson/skip-middle.

This paper introduces a novel modification of the transformer architecture, tailored for the data-efficient pretraining of language models. This aspect is evaluated by participating in the BabyLM challenge, where our solution won both the strict and strict-small tracks. Our approach allows each transformer layer to select which outputs of previous layers to process. The empirical results verify the potential of this simple modification and show that not all layers are equally as important.

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features -- such as those found by sparse autoencoders (SAEs) -- are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior. To address this we explore transcoders, which seek to faithfully approximate a densely activating MLP layer with a wider, sparsely-activating MLP layer. We successfully train transcoders on language models with 120M, 410M, and 1.4B parameters, and find them to perform at least on par with SAEs in terms of sparsity, faithfulness, and human-interpretability. We then introduce a novel method for using transcoders to perform weights-based circuit analysis through MLP sublayers. The resulting circuits neatly factorize into input-dependent and input-invariant terms. Finally, we apply transcoders to reverse-engineer unknown circuits in the model, and we obtain novel insights regarding the greater-than circuit in GPT2-small. Our results suggest that transcoders can prove effective in decomposing model computations involving MLPs into interpretable circuits. Code is available at https://github.com/jacobdunefsky/transcoder_circuits.

All-MLP architectures have attracted increasing interest as an alternative to attention-based models. In NLP, recent work like gMLP shows that all-MLPs can match Transformers in language modeling, but still lag behind in downstream tasks. In this work, we analyze the limitations of MLPs in expressiveness, and propose sparsely activated MLPs with mixture-of-experts (MoEs) in both feature and input (token) dimensions. Such sparse all-MLPs significantly increase model capacity and expressiveness while keeping the compute constant. We address critical challenges in incorporating conditional computation with two routing strategies. The proposed sparse all-MLP improves language modeling perplexity and obtains up to 2times improvement in training efficiency compared to both Transformer-based MoEs (GShard, Switch Transformer, Base Layers and HASH Layers) as well as dense Transformers and all-MLPs. Finally, we evaluate its zero-shot in-context learning performance on six downstream tasks, and find that it surpasses Transformer-based MoEs and dense Transformers.

Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor h in R^{C times T times d}. Given embedding vector h_{c,t} in R^d at sequence position t le T in a sequence (or context) c le C, extracting the mean effects yields the decomposition \[ h_{c,t} = \mu + pos_t + ctx_c + resid_{c,t} \] where mu is the global mean vector, pos_t and ctx_c are the mean vectors across contexts and across positions respectively, and resid_{c,t} is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) (pos_t)_{t} forms a low-dimensional, continuous, and often spiral shape across layers, (2) (ctx_c)_c shows clear cluster structure that falls into context topics, and (3) (pos_t)_{t} and (ctx_c)_c are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.

Massive activations are scalar values in transformer hidden states that achieve values orders of magnitude larger than typical activations and have been shown to be critical for model functionality. While prior work has characterized these phenomena in fully trained models, the temporal dynamics of their emergence during training remain poorly understood. We present the first comprehensive analysis of massive activation development throughout transformer training, using the Pythia model family as our testbed. Through systematic analysis of various model sizes across multiple training checkpoints, we demonstrate that massive activation emergence follows predictable mathematical patterns that can be accurately modeled using an exponentially-modulated logarithmic function with five key parameters. We develop a machine learning framework to predict these mathematical parameters from architectural specifications alone, achieving high accuracy for steady-state behavior and moderate accuracy for emergence timing and magnitude. These findings enable architects to predict and potentially control key aspects of massive activation emergence through design choices, with significant implications for model stability, training cycle length, interpretability, and optimization. Our findings demonstrate that the emergence of massive activations is governed by model design and can be anticipated, and potentially controlled, before training begins.

AdamW has been the default optimizer for transformer pretraining. For many years, our community searches for faster and more stable optimizers with only constraint positive outcomes. In this work, we propose a single-line modification in Pytorch to any momentum-based optimizer, which we rename Cautious Optimizer, e.g. C-AdamW and C-Lion. Our theoretical result shows that this modification preserves Adam's Hamiltonian function and it does not break the convergence guarantee under the Lyapunov analysis. In addition, a whole new family of optimizers is revealed by our theoretical insight. Among them, we pick the simplest one for empirical experiments, showing speed-up on Llama and MAE pretraining up to 1.47times. Code is available at https://github.com/kyleliang919/C-Optim

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.

Large Transformer models achieved the state-of-the-art status for Natural Language Understanding tasks and are increasingly becoming the baseline model architecture for modeling source code. Transformers are usually pre-trained on large unsupervised corpora, learning token representations and transformations relevant to modeling generally available text, and are then fine-tuned on a particular downstream task of interest. While fine-tuning is a tried-and-true method for adapting a model to a new domain -- for example, question-answering on a given topic -- generalization remains an on-going challenge. In this paper, we explore and evaluate transformer model fine-tuning for personalization. In the context of generating unit tests for Java methods, we evaluate learning to personalize to a specific software project using several personalization techniques. We consider three key approaches: (i) custom fine-tuning, which allows all the model parameters to be tuned; (ii) lightweight fine-tuning, which freezes most of the model's parameters, allowing tuning of the token embeddings and softmax layer only or the final layer alone; (iii) prefix tuning, which keeps model parameters frozen, but optimizes a small project-specific prefix vector. Each of these techniques offers a trade-off in total compute cost and predictive performance, which we evaluate by code and task-specific metrics, training time, and total computational operations. We compare these fine-tuning strategies for code generation and discuss the potential generalization and cost benefits of each in various deployment scenarios.

Transformers have become the dominant model in deep learning, but the reason for their superior performance is poorly understood. Here, we hypothesize that the strong performance of Transformers stems from an architectural bias towards mesa-optimization, a learned process running within the forward pass of a model consisting of the following two steps: (i) the construction of an internal learning objective, and (ii) its corresponding solution found through optimization. To test this hypothesis, we reverse-engineer a series of autoregressive Transformers trained on simple sequence modeling tasks, uncovering underlying gradient-based mesa-optimization algorithms driving the generation of predictions. Moreover, we show that the learned forward-pass optimization algorithm can be immediately repurposed to solve supervised few-shot tasks, suggesting that mesa-optimization might underlie the in-context learning capabilities of large language models. Finally, we propose a novel self-attention layer, the mesa-layer, that explicitly and efficiently solves optimization problems specified in context. We find that this layer can lead to improved performance in synthetic and preliminary language modeling experiments, adding weight to our hypothesis that mesa-optimization is an important operation hidden within the weights of trained Transformers.

Attention-based neural networks such as transformers have demonstrated a remarkable ability to exhibit in-context learning (ICL): Given a short prompt sequence of tokens from an unseen task, they can formulate relevant per-token and next-token predictions without any parameter updates. By embedding a sequence of labeled training data and unlabeled test data as a prompt, this allows for transformers to behave like supervised learning algorithms. Indeed, recent work has shown that when training transformer architectures over random instances of linear regression problems, these models' predictions mimic those of ordinary least squares. Towards understanding the mechanisms underlying this phenomenon, we investigate the dynamics of ICL in transformers with a single linear self-attention layer trained by gradient flow on linear regression tasks. We show that despite non-convexity, gradient flow with a suitable random initialization finds a global minimum of the objective function. At this global minimum, when given a test prompt of labeled examples from a new prediction task, the transformer achieves prediction error competitive with the best linear predictor over the test prompt distribution. We additionally characterize the robustness of the trained transformer to a variety of distribution shifts and show that although a number of shifts are tolerated, shifts in the covariate distribution of the prompts are not. Motivated by this, we consider a generalized ICL setting where the covariate distributions can vary across prompts. We show that although gradient flow succeeds at finding a global minimum in this setting, the trained transformer is still brittle under mild covariate shifts. We complement this finding with experiments on large, nonlinear transformer architectures which we show are more robust under covariate shifts.

Recently, pre-trained Transformer based language models such as BERT and GPT, have shown great improvement in many Natural Language Processing (NLP) tasks. However, these models contain a large amount of parameters. The emergence of even larger and more accurate models such as GPT2 and Megatron, suggest a trend of large pre-trained Transformer models. However, using these large models in production environments is a complex task requiring a large amount of compute, memory and power resources. In this work we show how to perform quantization-aware training during the fine-tuning phase of BERT in order to compress BERT by 4times with minimal accuracy loss. Furthermore, the produced quantized model can accelerate inference speed if it is optimized for 8bit Integer supporting hardware.

Although the Transformer is currently the best-performing architecture in the homogeneous configuration (self-attention only) in Neural Machine Translation, many State-of-the-Art models in Natural Language Processing are made of a combination of different Deep Learning approaches. However, these models often focus on combining a couple of techniques only and it is unclear why some methods are chosen over others. In this work, we investigate the effectiveness of integrating an increasing number of heterogeneous methods. Based on a simple combination strategy and performance-driven synergy criteria, we designed the Multi-Encoder Transformer, which consists of up to five diverse encoders. Results showcased that our approach can improve the quality of the translation across a variety of languages and dataset sizes and it is particularly effective in low-resource languages where we observed a maximum increase of 7.16 BLEU compared to the single-encoder model.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Besides natural language processing, transformers exhibit extraordinary performance in solving broader applications, including scientific computing and computer vision. Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms. To empower transformers with algorithmic capabilities and motivated by the recently proposed looped transformer (Yang et al., 2024; Giannou et al., 2023), we design a novel transformer block, dubbed Algorithm Transformer (abbreviated as AlgoFormer). Compared with the standard transformer and vanilla looped transformer, the proposed AlgoFormer can achieve significantly higher expressiveness in algorithm representation when using the same number of parameters. In particular, inspired by the structure of human-designed learning algorithms, our transformer block consists of a pre-transformer that is responsible for task pre-processing, a looped transformer for iterative optimization algorithms, and a post-transformer for producing the desired results after post-processing. We provide theoretical evidence of the expressive power of the AlgoFormer in solving some challenging problems, mirroring human-designed algorithms. Furthermore, some theoretical and empirical results are presented to show that the designed transformer has the potential to be smarter than human-designed algorithms. Experimental results demonstrate the empirical superiority of the proposed transformer in that it outperforms the standard transformer and vanilla looped transformer in some challenging tasks.

Owing to the growing concerns about privacy and regulatory compliance, it is desirable to regulate the output of generative models. To that end, the objective of this work is to prevent the generation of outputs containing undesired features from a pre-trained Generative Adversarial Network (GAN) where the underlying training data set is inaccessible. Our approach is inspired by the observation that the parameter space of GANs exhibits meaningful directions that can be leveraged to suppress specific undesired features. However, such directions usually result in the degradation of the quality of generated samples. Our proposed two-stage method, known as 'Adapt-then-Unlearn,' excels at unlearning such undesirable features while also maintaining the quality of generated samples. In the initial stage, we adapt a pre-trained GAN on a set of negative samples (containing undesired features) provided by the user. Subsequently, we train the original pre-trained GAN using positive samples, along with a repulsion regularizer. This regularizer encourages the learned model parameters to move away from the parameters of the adapted model (first stage) while not degrading the generation quality. We provide theoretical insights into the proposed method. To the best of our knowledge, our approach stands as the first method addressing unlearning within the realm of high-fidelity GANs (such as StyleGAN). We validate the effectiveness of our method through comprehensive experiments, encompassing both class-level unlearning on the MNIST and AFHQ dataset and feature-level unlearning tasks on the CelebA-HQ dataset. Our code and implementation is available at: https://github.com/atriguha/Adapt_Unlearn.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.

The feedforward (FFW) layers in standard transformer architectures incur a linear increase in computational costs and activation memory as the hidden layer width grows. Sparse mixture-of-experts (MoE) architectures have emerged as a viable approach to address this issue by decoupling model size from computational cost. The recent discovery of the fine-grained MoE scaling law shows that higher granularity leads to better performance. However, existing MoE models are limited to a small number of experts due to computational and optimization challenges. This paper introduces PEER (parameter efficient expert retrieval), a novel layer design that utilizes the product key technique for sparse retrieval from a vast pool of tiny experts (over a million). Experiments on language modeling tasks demonstrate that PEER layers outperform dense FFWs and coarse-grained MoEs in terms of performance-compute trade-off. By enabling efficient utilization of a massive number of experts, PEER unlocks the potential for further scaling of transformer models while maintaining computational efficiency.

Ever since their conception, Transformers have taken over traditional sequence models in many tasks, such as NLP, image classification, and video/audio processing, for their fast training and superior performance. Much of the merit is attributable to positional encoding and multi-head attention. However, Transformers fall short in learning long-range dependencies mainly due to the quadratic complexity scaled with context length, in terms of both time and space. Consequently, over the past five years, a myriad of methods has been proposed to make Transformers more efficient. In this work, we first take a step back, study and compare existing solutions to long-sequence modeling in terms of their pure mathematical formulation. Specifically, we summarize them using a unified template, given their shared nature of token mixing. Through benchmarks, we then demonstrate that long context length does yield better performance, albeit application-dependent, and traditional Transformer models fall short in taking advantage of long-range dependencies. Next, inspired by emerging sparse models of huge capacity, we propose a machine learning system for handling million-scale dependencies. As a proof of concept, we evaluate the performance of one essential component of this system, namely, the distributed multi-head attention. We show that our algorithm can scale up attention computation by almost 40times using four GeForce RTX 4090 GPUs, compared to vanilla multi-head attention mechanism. We believe this study is an instrumental step towards modeling million-scale dependencies.

Transformers have shown improved performance when compared to previous architectures for sequence processing such as RNNs. Despite their sizeable performance gains, as recently suggested, the model is computationally expensive to train and with a high parameter budget. In light of this, we explore parameter-sharing methods in Transformers with a specific focus on generative models. We perform an analysis of different parameter sharing/reduction methods and develop the Subformer. Our model combines sandwich-style parameter sharing, which overcomes naive cross-layer parameter sharing in generative models, and self-attentive embedding factorization (SAFE). Experiments on machine translation, abstractive summarization and language modeling show that the Subformer can outperform the Transformer even when using significantly fewer parameters.

Foundation models, now powering most of the exciting applications in deep learning, are almost universally based on the Transformer architecture and its core attention module. Many subquadratic-time architectures such as linear attention, gated convolution and recurrent models, and structured state space models (SSMs) have been developed to address Transformers' computational inefficiency on long sequences, but they have not performed as well as attention on important modalities such as language. We identify that a key weakness of such models is their inability to perform content-based reasoning, and make several improvements. First, simply letting the SSM parameters be functions of the input addresses their weakness with discrete modalities, allowing the model to selectively propagate or forget information along the sequence length dimension depending on the current token. Second, even though this change prevents the use of efficient convolutions, we design a hardware-aware parallel algorithm in recurrent mode. We integrate these selective SSMs into a simplified end-to-end neural network architecture without attention or even MLP blocks (Mamba). Mamba enjoys fast inference (5times higher throughput than Transformers) and linear scaling in sequence length, and its performance improves on real data up to million-length sequences. As a general sequence model backbone, Mamba achieves state-of-the-art performance across several modalities such as language, audio, and genomics. On language modeling, our Mamba-3B model outperforms Transformers of the same size and matches Transformers twice its size, both in pretraining and downstream evaluation.

Text-to-image (T2I) generation has been actively studied using Diffusion Models and Autoregressive Models. Recently, Masked Generative Transformers have gained attention as an alternative to Autoregressive Models to overcome the inherent limitations of causal attention and autoregressive decoding through bidirectional attention and parallel decoding, enabling efficient and high-quality image generation. However, compositional T2I generation remains challenging, as even state-of-the-art Diffusion Models often fail to accurately bind attributes and achieve proper text-image alignment. While Diffusion Models have been extensively studied for this issue, Masked Generative Transformers exhibit similar limitations but have not been explored in this context. To address this, we propose Unmasking with Contrastive Attention Guidance (UNCAGE), a novel training-free method that improves compositional fidelity by leveraging attention maps to prioritize the unmasking of tokens that clearly represent individual objects. UNCAGE consistently improves performance in both quantitative and qualitative evaluations across multiple benchmarks and metrics, with negligible inference overhead. Our code is available at https://github.com/furiosa-ai/uncage.

Time series forecasting (TSF) remains a challenging and largely unsolved problem in machine learning, despite significant recent efforts leveraging Large Language Models (LLMs), which predominantly rely on Transformer architectures. Empirical evidence consistently shows that even powerful Transformers often fail to outperform much simpler models, e.g., linear models, on TSF tasks; however, a rigorous theoretical understanding of this phenomenon remains limited. In this paper, we provide a theoretical analysis of Transformers' limitations for TSF through the lens of In-Context Learning (ICL) theory. Specifically, under AR(p) data, we establish that: (1) Linear Self-Attention (LSA) models cannot achieve lower expected MSE than classical linear models for in-context forecasting; (2) as the context length approaches to infinity, LSA asymptotically recovers the optimal linear predictor; and (3) under Chain-of-Thought (CoT) style inference, predictions collapse to the mean exponentially. We empirically validate these findings through carefully designed experiments. Our theory not only sheds light on several previously underexplored phenomena but also offers practical insights for designing more effective forecasting architectures. We hope our work encourages the broader research community to revisit the fundamental theoretical limitations of TSF and to critically evaluate the direct application of increasingly sophisticated architectures without deeper scrutiny.

Recent studies have demonstrated the great power of Transformer models for time series forecasting. One of the key elements that lead to the transformer's success is the channel-independent (CI) strategy to improve the training robustness. However, the ignorance of the correlation among different channels in CI would limit the model's forecasting capacity. In this work, we design a special Transformer, i.e., Channel Aligned Robust Blend Transformer (CARD for short), that addresses key shortcomings of CI type Transformer in time series forecasting. First, CARD introduces a channel-aligned attention structure that allows it to capture both temporal correlations among signals and dynamical dependence among multiple variables over time. Second, in order to efficiently utilize the multi-scale knowledge, we design a token blend module to generate tokens with different resolutions. Third, we introduce a robust loss function for time series forecasting to alleviate the potential overfitting issue. This new loss function weights the importance of forecasting over a finite horizon based on prediction uncertainties. Our evaluation of multiple long-term and short-term forecasting datasets demonstrates that CARD significantly outperforms state-of-the-art time series forecasting methods. The code is available at the following repository:https://github.com/wxie9/CARD

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

Linear transformers aim to reduce the quadratic space-time complexity of vanilla transformers. However, they usually suffer from degraded performances on various tasks and corpus. In this paper, we examine existing kernel-based linear transformers and identify two key issues that lead to such performance gaps: 1) unbounded gradients in the attention computation adversely impact the convergence of linear transformer models; 2) attention dilution which trivially distributes attention scores over long sequences while neglecting neighbouring structures. To address these issues, we first identify that the scaling of attention matrices is the devil in unbounded gradients, which turns out unnecessary in linear attention as we show theoretically and empirically. To this end, we propose a new linear attention that replaces the scaling operation with a normalization to stabilize gradients. For the issue of attention dilution, we leverage a diagonal attention to confine attention to only neighbouring tokens in early layers. Benefiting from the stable gradients and improved attention, our new linear transformer model, transNormer, demonstrates superior performance on text classification and language modeling tasks, as well as on the challenging Long-Range Arena benchmark, surpassing vanilla transformer and existing linear variants by a clear margin while being significantly more space-time efficient. The code is available at https://github.com/OpenNLPLab/Transnormer .

We introduce Attention Free Transformer (AFT), an efficient variant of Transformers that eliminates the need for dot product self attention. In an AFT layer, the key and value are first combined with a set of learned position biases, the result of which is multiplied with the query in an element-wise fashion. This new operation has a memory complexity linear w.r.t. both the context size and the dimension of features, making it compatible to both large input and model sizes. We also introduce AFT-local and AFT-conv, two model variants that take advantage of the idea of locality and spatial weight sharing while maintaining global connectivity. We conduct extensive experiments on two autoregressive modeling tasks (CIFAR10 and Enwik8) as well as an image recognition task (ImageNet-1K classification). We show that AFT demonstrates competitive performance on all the benchmarks, while providing excellent efficiency at the same time.

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the expressivity of LLMs with CoT in solving fundamental mathematical and decision-making problems. By using circuit complexity theory, we first give impossibility results showing that bounded-depth Transformers are unable to directly produce correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of constant size suffice to solve both tasks by generating CoT derivations using a commonly used math language format. Moreover, we show LLMs with CoT can handle a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, an extensive set of experiments show that, while Transformers always fail to directly predict the answers, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

Classifier guidance is a recently introduced method to trade off mode coverage and sample fidelity in conditional diffusion models post training, in the same spirit as low temperature sampling or truncation in other types of generative models. Classifier guidance combines the score estimate of a diffusion model with the gradient of an image classifier and thereby requires training an image classifier separate from the diffusion model. It also raises the question of whether guidance can be performed without a classifier. We show that guidance can be indeed performed by a pure generative model without such a classifier: in what we call classifier-free guidance, we jointly train a conditional and an unconditional diffusion model, and we combine the resulting conditional and unconditional score estimates to attain a trade-off between sample quality and diversity similar to that obtained using classifier guidance.

This thesis provides methods and analysis of models which make progress on this goal. The techniques outlined are task agnostic, and should provide benefit when used with nearly any transformer LM. We introduce two new finetuning methods which add new capabilities to the models they are used on. The first adds a recurrence mechanism, which removes the fixed-window sized constraint and improves the efficiency of a transformer decoder. The second allows masked language models (MLMs) to be used for initialization of both the encoder and decoder of a non-autoregressive sequence-to-sequence transformer, opening up generative applications of models which were previously only used for natural language understanding tasks. We also introduce two new techniques for improving the quality of predictions of any transformer decoder without additional finetuning. One, hidden state optimization, can be applied to any transformer decoder to improve the quality of predictions at inference time, especially for few-shot classification. The other, conditional beam search, allows practitioners to search for natural language generation (NLG) model outputs with high likelihood while conditioning on the event that the output is not degenerate (e.g. empty, repetitive, etc.). Finally, we provide theoretical and empirical insights on the divergence of model-likelihood and output quality which has widely been observed in prior work. These insights apply to any model which represents a distribution over text, and apply to language models which are not transformers or even autoregressive. We argue that the NLP community has, to some extent, misunderstood the implications of these findings, and encourage a point of view which has more nuance.

With ChatGPT as a representative, tons of companies have began to provide services based on large Transformers models. However, using such a service inevitably leak users' prompts to the model provider. Previous studies have studied secure inference for Transformer models using secure multiparty computation (MPC), where model parameters and clients' prompts are kept secret. Despite this, these frameworks are still limited in terms of model performance, efficiency, and deployment. To address these limitations, we propose framework PUMA to enable fast and secure Transformer model inference. Our framework designs high quality approximations for expensive functions, such as GeLU and Softmax, which significantly reduce the cost of secure inference while preserving the model performance. Additionally, we design secure Embedding and LayerNorm procedures that faithfully implement the desired functionality without undermining the Transformer architecture. PUMA is about 2x faster than the state-of-the-art MPC framework MPCFORMER(ICLR 2023) and has similar accuracy as plaintext models without fine-tuning (which the previous works failed to achieve). One more thing, PUMA can evaluate LLaMA-7B in around 5 minutes to generate 1 token. To our best knowledge, this is the first time that a model with such a parameter size is able to be evaluated under MPC. PUMA has been open-sourced in the Github repository of SecretFlow-SPU.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.

Transformers have become the predominant architecture in foundation models due to their excellent performance across various domains. However, the substantial cost of scaling these models remains a significant concern. This problem arises primarily from their dependence on a fixed number of parameters within linear projections. When architectural modifications (e.g., channel dimensions) are introduced, the entire model typically requires retraining from scratch. As model sizes continue growing, this strategy results in increasingly high computational costs and becomes unsustainable. To overcome this problem, we introduce TokenFormer, a natively scalable architecture that leverages the attention mechanism not only for computations among input tokens but also for interactions between tokens and model parameters, thereby enhancing architectural flexibility. By treating model parameters as tokens, we replace all the linear projections in Transformers with our token-parameter attention layer, where input tokens act as queries and model parameters as keys and values. This reformulation allows for progressive and efficient scaling without necessitating retraining from scratch. Our model scales from 124M to 1.4B parameters by incrementally adding new key-value parameter pairs, achieving performance comparable to Transformers trained from scratch while greatly reducing training costs. Code and models are available at https://github.com/Haiyang-W/TokenFormer.

This paper introduces a novel training methodology that enables a small Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at: https://github.com/AGPatriota/ALGA-R/.

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences, as the standard self-attention mechanism of the Transformer uses O(n^2) time and space with respect to sequence length. In this paper, we demonstrate that the self-attention mechanism can be approximated by a low-rank matrix. We further exploit this finding to propose a new self-attention mechanism, which reduces the overall self-attention complexity from O(n^2) to O(n) in both time and space. The resulting linear transformer, the Linformer, performs on par with standard Transformer models, while being much more memory- and time-efficient.

Generative pre-trained transformer (GPT) models have revolutionized the field of natural language processing (NLP) with remarkable performance in various tasks and also extend their power to multimodal domains. Despite their success, large GPT models like GPT-4 face inherent limitations such as considerable size, high computational requirements, complex deployment processes, and closed development loops. These constraints restrict their widespread adoption and raise concerns regarding their responsible development and usage. The need for user-friendly, relatively small, and open-sourced alternative GPT models arises from the desire to overcome these limitations while retaining high performance. In this survey paper, we provide an examination of alternative open-sourced models of large GPTs, focusing on user-friendly and relatively small models that facilitate easier deployment and accessibility. Through this extensive survey, we aim to equip researchers, practitioners, and enthusiasts with a thorough understanding of user-friendly and relatively small open-sourced models of large GPTs, their current state, challenges, and future research directions, inspiring the development of more efficient, accessible, and versatile GPT models that cater to the broader scientific community and advance the field of general artificial intelligence. The source contents are continuously updating in https://github.com/GPT-Alternatives/gpt_alternatives.

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

The design choices in Transformer feed-forward neural networks have resulted in significant computational and parameter overhead. In this work, we emphasize the importance of hidden dimension in designing lightweight FFNs, a factor often overlooked in previous architectures. Guided by this principle, we introduce PartialFormer, a parameter-efficient Transformer architecture utilizing multiple smaller FFNs to reduce parameters and computation while maintaining essential hidden dimensions. These smaller FFNs are integrated into a multi-head attention system to enable effective collaboration. We also propose a tailored head scaling strategy to enhance PartialFormer's capabilities. Furthermore, we present a residual-like attention calculation to improve depth scaling within PartialFormer. Extensive experiments on 9 translation tasks and 1 abstractive summarization task validate the effectiveness of our PartialFormer approach. Our code would be available at: https://github.com/zhengkid/PartialFormer.