Daily Papers

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual object recognition tasks has been limited because of the prohibitive cost of the optimization algorithms required to compute the sparse representation. In this work we propose a simple and efficient algorithm to learn basis functions. After training, this model also provides a fast and smooth approximator to the optimal representation, achieving even better accuracy than exact sparse coding algorithms on visual object recognition tasks.

Many large-scale systems rely on high-quality deep representations (embeddings) to facilitate tasks like retrieval, search, and generative modeling. Matryoshka Representation Learning (MRL) recently emerged as a solution for adaptive embedding lengths, but it requires full model retraining and suffers from noticeable performance degradations at short lengths. In this paper, we show that sparse coding offers a compelling alternative for achieving adaptive representation with minimal overhead and higher fidelity. We propose Contrastive Sparse Representation (CSR), a method that sparsifies pre-trained embeddings into a high-dimensional but selectively activated feature space. By leveraging lightweight autoencoding and task-aware contrastive objectives, CSR preserves semantic quality while allowing flexible, cost-effective inference at different sparsity levels. Extensive experiments on image, text, and multimodal benchmarks demonstrate that CSR consistently outperforms MRL in terms of both accuracy and retrieval speed-often by large margins-while also cutting training time to a fraction of that required by MRL. Our results establish sparse coding as a powerful paradigm for adaptive representation learning in real-world applications where efficiency and fidelity are both paramount. Code is available at https://github.com/neilwen987/CSR_Adaptive_Rep

Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ell_1 norm as a penalty due to its convexity, which makes it amenable to fast and simple algorithmic solvers. In this work, we use biological vision as a test-bed and show that the soft thresholding operation associated to the use of the ell_1 norm is highly suboptimal compared to other functions suited to approximating ell_q with 0 leq q < 1 (including recently proposed Continuous Exact relaxations), both in terms of performance and in the production of features that are akin to signatures of the primary visual cortex. We show that ell_1 sparsity produces a denser code or employs a pool with more neurons, i.e. has a higher degree of overcompleteness, in order to maintain the same reconstruction error as the other methods considered. For all the penalty functions tested, a subset of the neurons develop orientation selectivity similarly to V1 neurons. When their code is sparse enough, the methods also develop receptive fields with varying functionalities, another signature of V1. Compared to other methods, soft thresholding achieves this level of sparsity at the expense of much degraded reconstruction performance, that more likely than not is not acceptable in biological vision. Our results indicate that V1 uses a sparsity inducing regularization that is closer to the ell_0 pseudo-norm rather than to the ell_1 norm.

ProSper is a python library containing probabilistic algorithms to learn dictionaries. Given a set of data points, the implemented algorithms seek to learn the elementary components that have generated the data. The library widens the scope of dictionary learning approaches beyond implementations of standard approaches such as ICA, NMF or standard L1 sparse coding. The implemented algorithms are especially well-suited in cases when data consist of components that combine non-linearly and/or for data requiring flexible prior distributions. Furthermore, the implemented algorithms go beyond standard approaches by inferring prior and noise parameters of the data, and they provide rich a-posteriori approximations for inference. The library is designed to be extendable and it currently includes: Binary Sparse Coding (BSC), Ternary Sparse Coding (TSC), Discrete Sparse Coding (DSC), Maximal Causes Analysis (MCA), Maximum Magnitude Causes Analysis (MMCA), and Gaussian Sparse Coding (GSC, a recent spike-and-slab sparse coding approach). The algorithms are scalable due to a combination of variational approximations and parallelization. Implementations of all algorithms allow for parallel execution on multiple CPUs and multiple machines for medium to large-scale applications. Typical large-scale runs of the algorithms can use hundreds of CPUs to learn hundreds of dictionary elements from data with tens of millions of floating-point numbers such that models with several hundred thousand parameters can be optimized. The library is designed to have minimal dependencies and to be easy to use. It targets users of dictionary learning algorithms and Machine Learning researchers.

Recently, it has been observed that when representations are learnt in a way that encourages sparsity, improved performance is obtained on classification tasks. These methods involve combinations of activation functions, sampling steps and different kinds of penalties. To investigate the effectiveness of sparsity by itself, we propose the k-sparse autoencoder, which is an autoencoder with linear activation function, where in hidden layers only the k highest activities are kept. When applied to the MNIST and NORB datasets, we find that this method achieves better classification results than denoising autoencoders, networks trained with dropout, and RBMs. k-sparse autoencoders are simple to train and the encoding stage is very fast, making them well-suited to large problem sizes, where conventional sparse coding algorithms cannot be applied.

The interest of the deep learning community in image synthesis has grown massively in recent years. Nowadays, deep generative methods, and especially Generative Adversarial Networks (GANs), are leading to state-of-the-art performance, capable of synthesizing images that appear realistic. While the efforts for improving the quality of the generated images are extensive, most attempts still consider the generator part as an uncorroborated "black-box". In this paper, we aim to provide a better understanding and design of the image generation process. We interpret existing generators as implicitly relying on sparsity-inspired models. More specifically, we show that generators can be viewed as manifestations of the Convolutional Sparse Coding (CSC) and its Multi-Layered version (ML-CSC) synthesis processes. We leverage this observation by explicitly enforcing a sparsifying regularization on appropriately chosen activation layers in the generator, and demonstrate that this leads to improved image synthesis. Furthermore, we show that the same rationale and benefits apply to generators serving inverse problems, demonstrated on the Deep Image Prior (DIP) method.

Sparse autoencoders (SAEs) have emerged as powerful techniques for interpretability of large language models (LLMs), aiming to decompose hidden states into meaningful semantic features. While several SAE variants have been proposed, there remains no principled framework to derive SAEs from the original dictionary learning formulation. In this work, we introduce such a framework by unrolling the proximal gradient method for sparse coding. We show that a single-step update naturally recovers common SAE variants, including ReLU, JumpReLU, and TopK. Through this lens, we reveal a fundamental limitation of existing SAEs: their sparsity-inducing regularizers enforce non-negativity, preventing a single feature from representing bidirectional concepts (e.g., male vs. female). This structural constraint fragments semantic axes into separate, redundant features, limiting representational completeness. To address this issue, we propose AbsTopK SAE, a new variant derived from the ell_0 sparsity constraint that applies hard thresholding over the largest-magnitude activations. By preserving both positive and negative activations, AbsTopK uncovers richer, bidirectional conceptual representations. Comprehensive experiments across four LLMs and seven probing and steering tasks show that AbsTopK improves reconstruction fidelity, enhances interpretability, and enables single features to encode contrasting concepts. Remarkably, AbsTopK matches or even surpasses the Difference-in-Mean method, a supervised approach that requires labeled data for each concept and has been shown in prior work to outperform SAEs.

Motivated by the hypothesis that neural network representations encode abstract, interpretable features as linearly accessible, approximately orthogonal directions, sparse autoencoders (SAEs) have become a popular tool in interpretability. However, recent work has demonstrated phenomenology of model representations that lies outside the scope of this hypothesis, showing signatures of hierarchical, nonlinear, and multi-dimensional features. This raises the question: do SAEs represent features that possess structure at odds with their motivating hypothesis? If not, does avoiding this mismatch help identify said features and gain further insights into neural network representations? To answer these questions, we take a construction-based approach and re-contextualize the popular matching pursuits (MP) algorithm from sparse coding to design MP-SAE -- an SAE that unrolls its encoder into a sequence of residual-guided steps, allowing it to capture hierarchical and nonlinearly accessible features. Comparing this architecture with existing SAEs on a mixture of synthetic and natural data settings, we show: (i) hierarchical concepts induce conditionally orthogonal features, which existing SAEs are unable to faithfully capture, and (ii) the nonlinear encoding step of MP-SAE recovers highly meaningful features, helping us unravel shared structure in the seemingly dichotomous representation spaces of different modalities in a vision-language model, hence demonstrating the assumption that useful features are solely linearly accessible is insufficient. We also show that the sequential encoder principle of MP-SAE affords an additional benefit of adaptive sparsity at inference time, which may be of independent interest. Overall, we argue our results provide credence to the idea that interpretability should begin with the phenomenology of representations, with methods emerging from assumptions that fit it.

We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low/high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage. We explore different network structures and parameter settings to achieve trade-offs between performance and speed. Moreover, we extend our network to cope with three color channels simultaneously, and show better overall reconstruction quality.

Both biological and artificial neural networks inherently balance their performance with their operational cost, which balances their computational abilities. Typically, an efficient neuromorphic neural network is one that learns representations that reduce the redundancies and dimensionality of its input. This is for instance achieved in sparse coding, and sparse representations derived from natural images yield representations that are heterogeneous, both in their sampling of input features and in the variance of those features. Here, we investigated the connection between natural images' structure, particularly oriented features, and their corresponding sparse codes. We showed that representations of input features scattered across multiple levels of variance substantially improve the sparseness and resilience of sparse codes, at the cost of reconstruction performance. This echoes the structure of the model's input, allowing to account for the heterogeneously aleatoric structures of natural images. We demonstrate that learning kernel from natural images produces heterogeneity by balancing between approximate and dense representations, which improves all reconstruction metrics. Using a parametrized control of the kernels' heterogeneity used by a convolutional sparse coding algorithm, we show that heterogeneity emphasizes sparseness, while homogeneity improves representation granularity. In a broader context, these encoding strategy can serve as inputs to deep convolutional neural networks. We prove that such variance-encoded sparse image datasets enhance computational efficiency, emphasizing the benefits of kernel heterogeneity to leverage naturalistic and variant input structures and possible applications to improve the throughput of neuromorphic hardware.

Diffusion-weighted magnetic resonance imaging (DW-MRI) can be used to characterise the microstructure of the nervous tissue, e.g. to delineate brain white matter connections in a non-invasive manner via fibre tracking. Magnetic Resonance Imaging (MRI) in high spatial resolution would play an important role in visualising such fibre tracts in a superior manner. However, obtaining an image of such resolution comes at the expense of longer scan time. Longer scan time can be associated with the increase of motion artefacts, due to the patient's psychological and physical conditions. Single Image Super-Resolution (SISR), a technique aimed to obtain high-resolution (HR) details from one single low-resolution (LR) input image, achieved with Deep Learning, is the focus of this study. Compared to interpolation techniques or sparse-coding algorithms, deep learning extracts prior knowledge from big datasets and produces superior MRI images from the low-resolution counterparts. In this research, a deep learning based super-resolution technique is proposed and has been applied for DW-MRI. Images from the IXI dataset have been used as the ground-truth and were artificially downsampled to simulate the low-resolution images. The proposed method has shown statistically significant improvement over the baselines and achieved an SSIM of 0.913pm0.045.

Supervised contour detection methods usually require many labeled training images to obtain satisfactory performance. However, a large set of annotated data might be unavailable or extremely labor intensive. In this paper, we investigate the usage of semi-supervised learning (SSL) to obtain competitive detection accuracy with very limited training data (three labeled images). Specifically, we propose a semi-supervised structured ensemble learning approach for contour detection built on structured random forests (SRF). To allow SRF to be applicable to unlabeled data, we present an effective sparse representation approach to capture inherent structure in image patches by finding a compact and discriminative low-dimensional subspace representation in an unsupervised manner, enabling the incorporation of abundant unlabeled patches with their estimated structured labels to help SRF perform better node splitting. We re-examine the role of sparsity and propose a novel and fast sparse coding algorithm to boost the overall learning efficiency. To the best of our knowledge, this is the first attempt to apply SSL for contour detection. Extensive experiments on the BSDS500 segmentation dataset and the NYU Depth dataset demonstrate the superiority of the proposed method.

Neural architecture search (NAS) for Graph neural networks (GNNs), called NAS-GNNs, has achieved significant performance over manually designed GNN architectures. However, these methods inherit issues from the conventional NAS methods, such as high computational cost and optimization difficulty. More importantly, previous NAS methods have ignored the uniqueness of GNNs, where GNNs possess expressive power without training. With the randomly-initialized weights, we can then seek the optimal architecture parameters via the sparse coding objective and derive a novel NAS-GNNs method, namely neural architecture coding (NAC). Consequently, our NAC holds a no-update scheme on GNNs and can efficiently compute in linear time. Empirical evaluations on multiple GNN benchmark datasets demonstrate that our approach leads to state-of-the-art performance, which is up to 200times faster and 18.8% more accurate than the strong baselines.

Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings, exploiting the shared structure between similar problem instances. These methods have been crucial in variational inference and reinforcement learning and are capable of solving optimization problems many orders of magnitudes times faster than traditional optimization methods that do not use amortization. This tutorial presents an introduction to the amortized optimization foundations behind these advancements and overviews their applications in variational inference, sparse coding, gradient-based meta-learning, control, reinforcement learning, convex optimization, optimal transport, and deep equilibrium networks. The source code for this tutorial is available at https://github.com/facebookresearch/amortized-optimization-tutorial.

Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the dictionary. The resulting dictionary is in general a dense matrix, and its manipulation can be computationally costly both at the learning stage and later in the usage of this dictionary, for tasks such as sparse coding. Dictionary learning is thus limited to relatively small-scale problems. In this paper, inspired by usual fast transforms, we consider a general dictionary structure that allows cheaper manipulation, and propose an algorithm to learn such dictionaries --and their fast implementation-- over training data. The approach is demonstrated experimentally with the factorization of the Hadamard matrix and with synthetic dictionary learning experiments.

Feature representation in the form of spatio-spectral decomposition is one of the robust techniques adopted in automatic handwritten character recognition systems. In this regard, we propose a new image representation approach for unconstrained handwritten alphanumeric characters using sparse concept coded Tetrolets. Tetrolets, which does not use fixed dyadic square blocks for spectral decomposition like conventional wavelets, preserve the localized variations in handwritings by adopting tetrominoes those capture the shape geometry. The sparse concept coding of low entropy Tetrolet representation is found to extract the important hidden information (concept) for superior pattern discrimination. Large scale experimentation using ten databases in six different scripts (Bangla, Devanagari, Odia, English, Arabic and Telugu) has been performed. The proposed feature representation along with standard classifiers such as random forest, support vector machine (SVM), nearest neighbor and modified quadratic discriminant function (MQDF) is found to achieve state-of-the-art recognition performance in all the databases, viz. 99.40% (MNIST); 98.72% and 93.24% (IITBBS); 99.38% and 99.22% (ISI Kolkata). The proposed OCR system is shown to perform better than other sparse based techniques such as PCA, SparsePCA and SparseLDA, as well as better than existing transforms (Wavelet, Slantlet and Stockwell).

This article does not propose any novel algorithm or new hardware for sparsity. Instead, it aims to serve the "common good" for the increasingly prosperous Sparse Neural Network (SNN) research community. We attempt to summarize some most common confusions in SNNs, that one may come across in various scenarios such as paper review/rebuttal and talks - many drawn from the authors' own bittersweet experiences! We feel that doing so is meaningful and timely, since the focus of SNN research is notably shifting from traditional pruning to more diverse and profound forms of sparsity before, during, and after training. The intricate relationships between their scopes, assumptions, and approaches lead to misunderstandings, for non-experts or even experts in SNNs. In response, we summarize ten Q\&As of SNNs from many key aspects, including dense vs. sparse, unstructured sparse vs. structured sparse, pruning vs. sparse training, dense-to-sparse training vs. sparse-to-sparse training, static sparsity vs. dynamic sparsity, before-training/during-training vs. post-training sparsity, and many more. We strive to provide proper and generically applicable answers to clarify those confusions to the best extent possible. We hope our summary provides useful general knowledge for people who want to enter and engage with this exciting community; and also provides some "mind of ease" convenience for SNN researchers to explain their work in the right contexts. At the very least (and perhaps as this article's most insignificant target functionality), if you are writing/planning to write a paper or rebuttal in the field of SNNs, we hope some of our answers could help you!

Obtaining versions of deep neural networks that are both highly-accurate and highly-sparse is one of the main challenges in the area of model compression, and several high-performance pruning techniques have been investigated by the community. Yet, much less is known about the interaction between sparsity and the standard stochastic optimization techniques used for training sparse networks, and most existing work uses standard dense schedules and hyperparameters for training sparse networks. In this work, we examine the impact of high sparsity on model training using the standard computer vision and natural language processing sparsity benchmarks. We begin by showing that using standard dense training recipes for sparse training is suboptimal, and results in under-training. We provide new approaches for mitigating this issue for both sparse pre-training of vision models (e.g. ResNet50/ImageNet) and sparse fine-tuning of language models (e.g. BERT/GLUE), achieving state-of-the-art results in both settings in the high-sparsity regime, and providing detailed analyses for the difficulty of sparse training in both scenarios. Our work sets a new threshold in terms of the accuracies that can be achieved under high sparsity, and should inspire further research into improving sparse model training, to reach higher accuracies under high sparsity, but also to do so efficiently.

Sparse neural networks have shown similar or better generalization performance than their dense counterparts while having higher parameter efficiency. This has motivated a number of works to learn or search for high performing sparse networks. While reports of task performance or efficiency gains are impressive, standard baselines are lacking leading to poor comparability and unreliable reproducibility across methods. In this work, we propose Random Search as a baseline algorithm for finding good sparse configurations and study its performance. We apply Random Search on the node space of an overparameterized network with the goal of finding better initialized sparse sub-networks that are positioned more advantageously in the loss landscape. We record the post-training performances of the found sparse networks and at various levels of sparsity, and compare against both their fully connected parent networks and random sparse configurations at the same sparsity levels. First, we demonstrate performance at different levels of sparsity and highlight that a significant level of performance can still be preserved even when the network is highly sparse. Second, we observe that for this sparse architecture search task, initialized sparse networks found by Random Search neither perform better nor converge more efficiently than their random counterparts. Thus we conclude that Random Search may be viewed as a reasonable neutral baseline for sparsity search methods.

Recent developments in representational learning for information retrieval can be organized in a conceptual framework that establishes two pairs of contrasts: sparse vs. dense representations and unsupervised vs. learned representations. Sparse learned representations can further be decomposed into expansion and term weighting components. This framework allows us to understand the relationship between recently proposed techniques such as DPR, ANCE, DeepCT, DeepImpact, and COIL, and furthermore, gaps revealed by our analysis point to "low hanging fruit" in terms of techniques that have yet to be explored. We present a novel technique dubbed "uniCOIL", a simple extension of COIL that achieves to our knowledge the current state-of-the-art in sparse retrieval on the popular MS MARCO passage ranking dataset. Our implementation using the Anserini IR toolkit is built on the Lucene search library and thus fully compatible with standard inverted indexes.

As deep learning models grow, sparsity is becoming an increasingly critical component of deep neural networks, enabling improved performance and reduced storage. However, existing frameworks offer poor support for sparsity. Specialized sparsity engines focus exclusively on sparse inference, while general frameworks primarily focus on sparse tensors in classical formats and neglect the broader sparsification pipeline necessary for using sparse models, especially during training. Further, existing frameworks are not easily extensible: adding a new sparse tensor format or operator is challenging and time-consuming. To address this, we propose STen, a sparsity programming model and interface for PyTorch, which incorporates sparsity layouts, operators, and sparsifiers, in an efficient, customizable, and extensible framework that supports virtually all sparsification methods. We demonstrate this by developing a high-performance grouped n:m sparsity layout for CPU inference at moderate sparsity. STen brings high performance and ease of use to the ML community, making sparsity easily accessible.

Dual encoders perform retrieval by encoding documents and queries into dense lowdimensional vectors, scoring each document by its inner product with the query. We investigate the capacity of this architecture relative to sparse bag-of-words models and attentional neural networks. Using both theoretical and empirical analysis, we establish connections between the encoding dimension, the margin between gold and lower-ranked documents, and the document length, suggesting limitations in the capacity of fixed-length encodings to support precise retrieval of long documents. Building on these insights, we propose a simple neural model that combines the efficiency of dual encoders with some of the expressiveness of more costly attentional architectures, and explore sparse-dense hybrids to capitalize on the precision of sparse retrieval. These models outperform strong alternatives in large-scale retrieval.

The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, an unsupervised, hierarchical, spatial/spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only minutes on a single CPU.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

Sparse attention offers a promising strategy to extend long-context capabilities in Transformer LLMs, yet its viability, its efficiency-accuracy trade-offs, and systematic scaling studies remain unexplored. To address this gap, we perform a careful comparison of training-free sparse attention methods at varying model scales, sequence lengths, and sparsity levels on a diverse collection of long-sequence tasks-including novel ones that rely on natural language while remaining controllable and easy to evaluate. Based on our experiments, we report a series of key findings: 1) an isoFLOPS analysis reveals that for very long sequences, larger and highly sparse models are preferable to smaller and dense ones. 2) The level of sparsity attainable while statistically guaranteeing accuracy preservation is higher during decoding than prefilling, and correlates with model size in the former. 3) There is no clear strategy that performs best across tasks and phases, with different units of sparsification or budget adaptivity needed for different scenarios. Even moderate sparsity levels often result in significant performance degradation on at least one task, highlighting that sparse attention is not a universal solution. 4) We introduce and validate novel scaling laws specifically tailored for sparse attention, providing evidence that our findings are likely to hold true beyond our range of experiments. Through these insights, we demonstrate that sparse attention is a key tool to enhance the capabilities of Transformer LLMs for processing longer sequences, but requires careful evaluation of trade-offs for performance-sensitive applications.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

The deployment of Deep Neural Networks (DNNs) on edge devices is hindered by the substantial gap between performance requirements and available processing power. While recent research has made significant strides in developing pruning methods to build a sparse network for reducing the computing overhead of DNNs, there remains considerable accuracy loss, especially at high pruning ratios. We find that the architectures designed for dense networks by differentiable architecture search methods are ineffective when pruning mechanisms are applied to them. The main reason is that the current method does not support sparse architectures in their search space and uses a search objective that is made for dense networks and does not pay any attention to sparsity. In this paper, we propose a new method to search for sparsity-friendly neural architectures. We do this by adding two new sparse operations to the search space and modifying the search objective. We propose two novel parametric SparseConv and SparseLinear operations in order to expand the search space to include sparse operations. In particular, these operations make a flexible search space due to using sparse parametric versions of linear and convolution operations. The proposed search objective lets us train the architecture based on the sparsity of the search space operations. Quantitative analyses demonstrate that our search architectures outperform those used in the stateof-the-art sparse networks on the CIFAR-10 and ImageNet datasets. In terms of performance and hardware effectiveness, DASS increases the accuracy of the sparse version of MobileNet-v2 from 73.44% to 81.35% (+7.91% improvement) with 3.87x faster inference time.

While transformer models are widely believed to operate in high-dimensional hidden spaces, we show that attention outputs are confined to a surprisingly low-dimensional subspace, where about 60\% of the directions account for 99\% of the variance--a phenomenon that is induced by the attention output projection matrix and consistently observed across diverse model families and datasets. Critically, we find this low-rank structure as a fundamental cause of the prevalent dead feature problem in sparse dictionary learning, where it creates a mismatch between randomly initialized features and the intrinsic geometry of the activation space. Building on this insight, we propose a subspace-constrained training method for sparse autoencoders (SAEs), initializing feature directions into the active subspace of activations. Our approach reduces dead features from 87\% to below 1\% in Attention Output SAEs with 1M features, and can further extend to other sparse dictionary learning methods. Our findings provide both new insights into the geometry of attention and practical tools for improving sparse dictionary learning in large language models.

Sparsity in the structure of Neural Networks can lead to less energy consumption, less memory usage, faster computation times on convenient hardware, and automated machine learning. If sparsity gives rise to certain kinds of structure, it can explain automatically obtained features during learning. We provide insights into experiments in which we show how sparsity can be achieved through prior initialization, pruning, and during learning, and answer questions on the relationship between the structure of Neural Networks and their performance. This includes the first work of inducing priors from network theory into Recurrent Neural Networks and an architectural performance prediction during a Neural Architecture Search. Within our experiments, we show how magnitude class blinded pruning achieves 97.5% on MNIST with 80% compression and re-training, which is 0.5 points more than without compression, that magnitude class uniform pruning is significantly inferior to it and how a genetic search enhanced with performance prediction achieves 82.4% on CIFAR10. Further, performance prediction for Recurrent Networks learning the Reber grammar shows an R^2 of up to 0.81 given only structural information.

In neural Information Retrieval, ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. In this work, we present a new first-stage ranker based on explicit sparsity regularization and a log-saturation effect on term weights, leading to highly sparse representations and competitive results with respect to state-of-the-art dense and sparse methods. Our approach is simple, trained end-to-end in a single stage. We also explore the trade-off between effectiveness and efficiency, by controlling the contribution of the sparsity regularization.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.

Neural retrievers based on dense representations combined with Approximate Nearest Neighbors search have recently received a lot of attention, owing their success to distillation and/or better sampling of examples for training -- while still relying on the same backbone architecture. In the meantime, sparse representation learning fueled by traditional inverted indexing techniques has seen a growing interest, inheriting from desirable IR priors such as explicit lexical matching. While some architectural variants have been proposed, a lesser effort has been put in the training of such models. In this work, we build on SPLADE -- a sparse expansion-based retriever -- and show to which extent it is able to benefit from the same training improvements as dense models, by studying the effect of distillation, hard-negative mining as well as the Pre-trained Language Model initialization. We furthermore study the link between effectiveness and efficiency, on in-domain and zero-shot settings, leading to state-of-the-art results in both scenarios for sufficiently expressive models.

Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity 1 / log(1/sparsity). This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.

Sparse dictionary learning has been a rapidly growing technique in mechanistic interpretability to attack superposition and extract more human-understandable features from model activations. We ask a further question based on the extracted more monosemantic features: How do we recognize circuits connecting the enormous amount of dictionary features? We propose a circuit discovery framework alternative to activation patching. Our framework suffers less from out-of-distribution and proves to be more efficient in terms of asymptotic complexity. The basic unit in our framework is dictionary features decomposed from all modules writing to the residual stream, including embedding, attention output and MLP output. Starting from any logit, dictionary feature or attention score, we manage to trace down to lower-level dictionary features of all tokens and compute their contribution to these more interpretable and local model behaviors. We dig in a small transformer trained on a synthetic task named Othello and find a number of human-understandable fine-grained circuits inside of it.

Dictionary learning (DL) has emerged as a powerful interpretability tool for large language models. By extracting known concepts (e.g., Golden-Gate Bridge) from human-interpretable data (e.g., text), sparse DL can elucidate a model's inner workings. In this work, we ask if DL can also be used to discover unknown concepts from less human-interpretable scientific data (e.g., cell images), ultimately enabling modern approaches to scientific discovery. As a first step, we use DL algorithms to study microscopy foundation models trained on multi-cell image data, where little prior knowledge exists regarding which high-level concepts should arise. We show that sparse dictionaries indeed extract biologically-meaningful concepts such as cell type and genetic perturbation type. We also propose a new DL algorithm, Iterative Codebook Feature Learning~(ICFL), and combine it with a pre-processing step that uses PCA whitening from a control dataset. In our experiments, we demonstrate that both ICFL and PCA improve the selectivity of extracted features compared to TopK sparse autoencoders.

Human visual recognition is a sparse process, where only a few salient visual cues are attended to rather than traversing every detail uniformly. However, most current vision networks follow a dense paradigm, processing every single visual unit (e.g,, pixel or patch) in a uniform manner. In this paper, we challenge this dense paradigm and present a new method, coined SparseFormer, to imitate human's sparse visual recognition in an end-to-end manner. SparseFormer learns to represent images using a highly limited number of tokens (down to 49) in the latent space with sparse feature sampling procedure instead of processing dense units in the original pixel space. Therefore, SparseFormer circumvents most of dense operations on the image space and has much lower computational costs. Experiments on the ImageNet classification benchmark dataset show that SparseFormer achieves performance on par with canonical or well-established models while offering better accuracy-throughput tradeoff. Moreover, the design of our network can be easily extended to the video classification with promising performance at lower computational costs. We hope that our work can provide an alternative way for visual modeling and inspire further research on sparse neural architectures. The code will be publicly available at https://github.com/showlab/sparseformer

We present Sparse R-CNN, a purely sparse method for object detection in images. Existing works on object detection heavily rely on dense object candidates, such as k anchor boxes pre-defined on all grids of image feature map of size Htimes W. In our method, however, a fixed sparse set of learned object proposals, total length of N, are provided to object recognition head to perform classification and location. By eliminating HWk (up to hundreds of thousands) hand-designed object candidates to N (e.g. 100) learnable proposals, Sparse R-CNN completely avoids all efforts related to object candidates design and many-to-one label assignment. More importantly, final predictions are directly output without non-maximum suppression post-procedure. Sparse R-CNN demonstrates accuracy, run-time and training convergence performance on par with the well-established detector baselines on the challenging COCO dataset, e.g., achieving 45.0 AP in standard 3times training schedule and running at 22 fps using ResNet-50 FPN model. We hope our work could inspire re-thinking the convention of dense prior in object detectors. The code is available at: https://github.com/PeizeSun/SparseR-CNN.

Self-attention has recently been adopted for a wide range of sequence modeling problems. Despite its effectiveness, self-attention suffers from quadratic compute and memory requirements with respect to sequence length. Successful approaches to reduce this complexity focused on attending to local sliding windows or a small set of locations independent of content. Our work proposes to learn dynamic sparse attention patterns that avoid allocating computation and memory to attend to content unrelated to the query of interest. This work builds upon two lines of research: it combines the modeling flexibility of prior work on content-based sparse attention with the efficiency gains from approaches based on local, temporal sparse attention. Our model, the Routing Transformer, endows self-attention with a sparse routing module based on online k-means while reducing the overall complexity of attention to Oleft(n^{1.5}dright) from Oleft(n^2dright) for sequence length n and hidden dimension d. We show that our model outperforms comparable sparse attention models on language modeling on Wikitext-103 (15.8 vs 18.3 perplexity) as well as on image generation on ImageNet-64 (3.43 vs 3.44 bits/dim) while using fewer self-attention layers. Additionally, we set a new state-of-the-art on the newly released PG-19 data-set, obtaining a test perplexity of 33.2 with a 22 layer Routing Transformer model trained on sequences of length 8192.

We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.

We explore the impact of parameter sparsity on the scaling behavior of Transformers trained on massive datasets (i.e., "foundation models"), in both vision and language domains. In this setting, we identify the first scaling law describing the relationship between weight sparsity, number of non-zero parameters, and amount of training data, which we validate empirically across model and data scales; on ViT/JFT-4B and T5/C4. These results allow us to characterize the "optimal sparsity", the sparsity level which yields the best performance for a given effective model size and training budget. For a fixed number of non-zero parameters, we identify that the optimal sparsity increases with the amount of data used for training. We also extend our study to different sparsity structures (such as the hardware-friendly n:m pattern) and strategies (such as starting from a pretrained dense model). Our findings shed light on the power and limitations of weight sparsity across various parameter and computational settings, offering both theoretical understanding and practical implications for leveraging sparsity towards computational efficiency improvements.

Historically, the pursuit of efficient inference has been one of the driving forces behind research into new deep learning architectures and building blocks. Some recent examples include: the squeeze-and-excitation module, depthwise separable convolutions in Xception, and the inverted bottleneck in MobileNet v2. Notably, in all of these cases, the resulting building blocks enabled not only higher efficiency, but also higher accuracy, and found wide adoption in the field. In this work, we further expand the arsenal of efficient building blocks for neural network architectures; but instead of combining standard primitives (such as convolution), we advocate for the replacement of these dense primitives with their sparse counterparts. While the idea of using sparsity to decrease the parameter count is not new, the conventional wisdom is that this reduction in theoretical FLOPs does not translate into real-world efficiency gains. We aim to correct this misconception by introducing a family of efficient sparse kernels for ARM and WebAssembly, which we open-source for the benefit of the community as part of the XNNPACK library. Equipped with our efficient implementation of sparse primitives, we show that sparse versions of MobileNet v1, MobileNet v2 and EfficientNet architectures substantially outperform strong dense baselines on the efficiency-accuracy curve. On Snapdragon 835 our sparse networks outperform their dense equivalents by 1.3-2.4times -- equivalent to approximately one entire generation of MobileNet-family improvement. We hope that our findings will facilitate wider adoption of sparsity as a tool for creating efficient and accurate deep learning architectures.

Sparse computation offers a compelling solution for the inference of Large Language Models (LLMs) in low-resource scenarios by dynamically skipping the computation of inactive neurons. While traditional approaches focus on ReLU-based LLMs, leveraging zeros in activation values, we broaden the scope of sparse LLMs beyond zero activation values. We introduce a general method that defines neuron activation through neuron output magnitudes and a tailored magnitude threshold, demonstrating that non-ReLU LLMs also exhibit sparse activation. To find the most efficient activation function for sparse computation, we propose a systematic framework to examine the sparsity of LLMs from three aspects: the trade-off between sparsity and performance, the predictivity of sparsity, and the hardware affinity. We conduct thorough experiments on LLMs utilizing different activation functions, including ReLU, SwiGLU, ReGLU, and ReLU^2. The results indicate that models employing ReLU^2 excel across all three evaluation aspects, highlighting its potential as an efficient activation function for sparse LLMs. We will release the code to facilitate future research.

Current pre-trained language model approaches to information retrieval can be broadly divided into two categories: sparse retrievers (to which belong also non-neural approaches such as bag-of-words methods, e.g., BM25) and dense retrievers. Each of these categories appears to capture different characteristics of relevance. Previous work has investigated how relevance signals from sparse retrievers could be combined with those from dense retrievers via interpolation. Such interpolation would generally lead to higher retrieval effectiveness. In this paper we consider the problem of combining the relevance signals from sparse and dense retrievers in the context of Pseudo Relevance Feedback (PRF). This context poses two key challenges: (1) When should interpolation occur: before, after, or both before and after the PRF process? (2) Which sparse representation should be considered: a zero-shot bag-of-words model (BM25), or a learnt sparse representation? To answer these questions we perform a thorough empirical evaluation considering an effective and scalable neural PRF approach (Vector-PRF), three effective dense retrievers (ANCE, TCTv2, DistillBERT), and one state-of-the-art learnt sparse retriever (uniCOIL). The empirical findings from our experiments suggest that, regardless of sparse representation and dense retriever, interpolation both before and after PRF achieves the highest effectiveness across most datasets and metrics.

Random pruning is arguably the most naive way to attain sparsity in neural networks, but has been deemed uncompetitive by either post-training pruning or sparse training. In this paper, we focus on sparse training and highlight a perhaps counter-intuitive finding, that random pruning at initialization can be quite powerful for the sparse training of modern neural networks. Without any delicate pruning criteria or carefully pursued sparsity structures, we empirically demonstrate that sparsely training a randomly pruned network from scratch can match the performance of its dense equivalent. There are two key factors that contribute to this revival: (i) the network sizes matter: as the original dense networks grow wider and deeper, the performance of training a randomly pruned sparse network will quickly grow to matching that of its dense equivalent, even at high sparsity ratios; (ii) appropriate layer-wise sparsity ratios can be pre-chosen for sparse training, which shows to be another important performance booster. Simple as it looks, a randomly pruned subnetwork of Wide ResNet-50 can be sparsely trained to outperforming a dense Wide ResNet-50, on ImageNet. We also observed such randomly pruned networks outperform dense counterparts in other favorable aspects, such as out-of-distribution detection, uncertainty estimation, and adversarial robustness. Overall, our results strongly suggest there is larger-than-expected room for sparse training at scale, and the benefits of sparsity might be more universal beyond carefully designed pruning. Our source code can be found at https://github.com/VITA-Group/Random_Pruning.

Sparse neural networks are a key factor in developing resource-efficient machine learning applications. We propose the novel and powerful sparse learning method Adaptive Regularized Training (ART) to compress dense into sparse networks. Instead of the commonly used binary mask during training to reduce the number of model weights, we inherently shrink weights close to zero in an iterative manner with increasing weight regularization. Our method compresses the pre-trained model knowledge into the weights of highest magnitude. Therefore, we introduce a novel regularization loss named HyperSparse that exploits the highest weights while conserving the ability of weight exploration. Extensive experiments on CIFAR and TinyImageNet show that our method leads to notable performance gains compared to other sparsification methods, especially in extremely high sparsity regimes up to 99.8 percent model sparsity. Additional investigations provide new insights into the patterns that are encoded in weights with high magnitudes.

Large language models (LLMs) encode a diverse range of linguistic features within their latent representations, which can be harnessed to steer their output toward specific target characteristics. In this paper, we modify the internal structure of LLMs by training sparse autoencoders to learn a sparse representation of the query embedding, allowing precise control over the model's attention distribution. We demonstrate that manipulating this sparse representation effectively transforms the output toward different stylistic and cognitive targets. Specifically, in an educational setting, we show that the cognitive complexity of LLM-generated feedback can be systematically adjusted by modifying the encoded query representation at a specific layer. To achieve this, we guide the learned sparse embedding toward the representation of samples from the desired cognitive complexity level, using gradient-based optimization in the latent space.

Sparse Neural Networks (SNNs) can potentially demonstrate similar performance to their dense counterparts while saving significant energy and memory at inference. However, the accuracy drop incurred by SNNs, especially at high pruning ratios, can be an issue in critical deployment conditions. While recent works mitigate this issue through sophisticated pruning techniques, we shift our focus to an overlooked factor: hyperparameters and activation functions. Our analyses have shown that the accuracy drop can additionally be attributed to (i) Using ReLU as the default choice for activation functions unanimously, and (ii) Fine-tuning SNNs with the same hyperparameters as dense counterparts. Thus, we focus on learning a novel way to tune activation functions for sparse networks and combining these with a separate hyperparameter optimization (HPO) regime for sparse networks. By conducting experiments on popular DNN models (LeNet-5, VGG-16, ResNet-18, and EfficientNet-B0) trained on MNIST, CIFAR-10, and ImageNet-16 datasets, we show that the novel combination of these two approaches, dubbed Sparse Activation Function Search, short: SAFS, results in up to 15.53%, 8.88%, and 6.33% absolute improvement in the accuracy for LeNet-5, VGG-16, and ResNet-18 over the default training protocols, especially at high pruning ratios. Our code can be found at https://github.com/automl/SAFS

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

Sparse expert models are a thirty-year old concept re-emerging as a popular architecture in deep learning. This class of architecture encompasses Mixture-of-Experts, Switch Transformers, Routing Networks, BASE layers, and others, all with the unifying idea that each example is acted on by a subset of the parameters. By doing so, the degree of sparsity decouples the parameter count from the compute per example allowing for extremely large, but efficient models. The resulting models have demonstrated significant improvements across diverse domains such as natural language processing, computer vision, and speech recognition. We review the concept of sparse expert models, provide a basic description of the common algorithms, contextualize the advances in the deep learning era, and conclude by highlighting areas for future work.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Information Retrieval using dense low-dimensional representations recently became popular and showed out-performance to traditional sparse-representations like BM25. However, no previous work investigated how dense representations perform with large index sizes. We show theoretically and empirically that the performance for dense representations decreases quicker than sparse representations for increasing index sizes. In extreme cases, this can even lead to a tipping point where at a certain index size sparse representations outperform dense representations. We show that this behavior is tightly connected to the number of dimensions of the representations: The lower the dimension, the higher the chance for false positives, i.e. returning irrelevant documents.

We introduce methods for discovering and applying sparse feature circuits. These are causally implicated subnetworks of human-interpretable features for explaining language model behaviors. Circuits identified in prior work consist of polysemantic and difficult-to-interpret units like attention heads or neurons, rendering them unsuitable for many downstream applications. In contrast, sparse feature circuits enable detailed understanding of unanticipated mechanisms. Because they are based on fine-grained units, sparse feature circuits are useful for downstream tasks: We introduce SHIFT, where we improve the generalization of a classifier by ablating features that a human judges to be task-irrelevant. Finally, we demonstrate an entirely unsupervised and scalable interpretability pipeline by discovering thousands of sparse feature circuits for automatically discovered model behaviors.

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

Dynamic Sparse Training (DST) methods achieve state-of-the-art results in sparse neural network training, matching the generalization of dense models while enabling sparse training and inference. Although the resulting models are highly sparse and theoretically less computationally expensive, achieving speedups with unstructured sparsity on real-world hardware is challenging. In this work, we propose a sparse-to-sparse DST method, Structured RigL (SRigL), to learn a variant of fine-grained structured N:M sparsity by imposing a constant fan-in constraint. Using our empirical analysis of existing DST methods at high sparsity, we additionally employ a neuron ablation method which enables SRigL to achieve state-of-the-art sparse-to-sparse structured DST performance on a variety of Neural Network (NN) architectures. We demonstrate reduced real-world timings on CPU for online inference -- 3.6x/2x faster at 90% sparsity than equivalent dense/unstructured sparse layers, respectively. Our source code is available at https://github.com/calgaryml/condensed-sparsity

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.

Non-uniformed 3D sparse data, e.g., point clouds or voxels in different spatial positions, make contribution to the task of 3D object detection in different ways. Existing basic components in sparse convolutional networks (Sparse CNNs) process all sparse data, regardless of regular or submanifold sparse convolution. In this paper, we introduce two new modules to enhance the capability of Sparse CNNs, both are based on making feature sparsity learnable with position-wise importance prediction. They are focal sparse convolution (Focals Conv) and its multi-modal variant of focal sparse convolution with fusion, or Focals Conv-F for short. The new modules can readily substitute their plain counterparts in existing Sparse CNNs and be jointly trained in an end-to-end fashion. For the first time, we show that spatially learnable sparsity in sparse convolution is essential for sophisticated 3D object detection. Extensive experiments on the KITTI, nuScenes and Waymo benchmarks validate the effectiveness of our approach. Without bells and whistles, our results outperform all existing single-model entries on the nuScenes test benchmark at the paper submission time. Code and models are at https://github.com/dvlab-research/FocalsConv.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

Learned sparse and dense representations capture different successful approaches to text retrieval and the fusion of their results has proven to be more effective and robust. Prior work combines dense and sparse retrievers by fusing their model scores. As an alternative, this paper presents a simple approach to densifying sparse representations for text retrieval that does not involve any training. Our densified sparse representations (DSRs) are interpretable and can be easily combined with dense representations for end-to-end retrieval. We demonstrate that our approach can jointly learn sparse and dense representations within a single model and then combine them for dense retrieval. Experimental results suggest that combining our DSRs and dense representations yields a balanced tradeoff between effectiveness and efficiency.

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.

Open-domain question answering can be formulated as a phrase retrieval problem, in which we can expect huge scalability and speed benefit but often suffer from low accuracy due to the limitation of existing phrase representation models. In this paper, we aim to improve the quality of each phrase embedding by augmenting it with a contextualized sparse representation (Sparc). Unlike previous sparse vectors that are term-frequency-based (e.g., tf-idf) or directly learned (only few thousand dimensions), we leverage rectified self-attention to indirectly learn sparse vectors in n-gram vocabulary space. By augmenting the previous phrase retrieval model (Seo et al., 2019) with Sparc, we show 4%+ improvement in CuratedTREC and SQuAD-Open. Our CuratedTREC score is even better than the best known retrieve & read model with at least 45x faster inference speed.

In the realm of deep learning-based recommendation systems, the increasing computational demands, driven by the growing number of users and items, pose a significant challenge to practical deployment. This challenge is primarily twofold: reducing the model size while effectively learning user and item representations for efficient recommendations. Despite considerable advancements in model compression and architecture search, prevalent approaches face notable constraints. These include substantial additional computational costs from pre-training/re-training in model compression and an extensive search space in architecture design. Additionally, managing complexity and adhering to memory constraints is problematic, especially in scenarios with strict time or space limitations. Addressing these issues, this paper introduces a novel learning paradigm, Dynamic Sparse Learning (DSL), tailored for recommendation models. DSL innovatively trains a lightweight sparse model from scratch, periodically evaluating and dynamically adjusting each weight's significance and the model's sparsity distribution during the training. This approach ensures a consistent and minimal parameter budget throughout the full learning lifecycle, paving the way for "end-to-end" efficiency from training to inference. Our extensive experimental results underline DSL's effectiveness, significantly reducing training and inference costs while delivering comparable recommendation performance.

Given the ever-increasing size of modern neural networks, the significance of sparse architectures has surged due to their accelerated inference speeds and minimal memory demands. When it comes to global pruning techniques, Iterative Magnitude Pruning (IMP) still stands as a state-of-the-art algorithm despite its simple nature, particularly in extremely sparse regimes. In light of the recent finding that the two successive matching IMP solutions are linearly connected without a loss barrier, we propose Sparse Weight Averaging with Multiple Particles (SWAMP), a straightforward modification of IMP that achieves performance comparable to an ensemble of two IMP solutions. For every iteration, we concurrently train multiple sparse models, referred to as particles, using different batch orders yet the same matching ticket, and then weight average such models to produce a single mask. We demonstrate that our method consistently outperforms existing baselines across different sparsities through extensive experiments on various data and neural network structures.

The emergence of long-context text applications utilizing large language models (LLMs) has presented significant scalability challenges, particularly in memory footprint. The linear growth of the Key-Value (KV) cache responsible for storing attention keys and values to minimize redundant computations can lead to substantial increases in memory consumption, potentially causing models to fail to serve with limited memory resources. To address this issue, we propose a novel approach called Cache Sparse Representation (CSR), which converts the KV cache by transforming the dense Key-Value cache tensor into sparse indexes and weights, offering a more memory-efficient representation during LLM inference. Furthermore, we introduce NeuralDict, a novel neural network-based method for automatically generating the dictionary used in our sparse representation. Our extensive experiments demonstrate that CSR achieves performance comparable to state-of-the-art KV cache quantization algorithms while maintaining robust functionality in memory-constrained environments.

Sparse autoencoders (SAEs) have shown promise in extracting interpretable features from complex neural networks. We present one of the first applications of SAEs to dense text embeddings from large language models, demonstrating their effectiveness in disentangling semantic concepts. By training SAEs on embeddings of over 420,000 scientific paper abstracts from computer science and astronomy, we show that the resulting sparse representations maintain semantic fidelity while offering interpretability. We analyse these learned features, exploring their behaviour across different model capacities and introducing a novel method for identifying ``feature families'' that represent related concepts at varying levels of abstraction. To demonstrate the practical utility of our approach, we show how these interpretable features can be used to precisely steer semantic search, allowing for fine-grained control over query semantics. This work bridges the gap between the semantic richness of dense embeddings and the interpretability of sparse representations. We open source our embeddings, trained sparse autoencoders, and interpreted features, as well as a web app for exploring them.

We analyze a family of large language models in such a lightweight manner that can be done on a single GPU. Specifically, we focus on the OPT family of models ranging from 125m to 66b parameters and rely only on whether an FFN neuron is activated or not. First, we find that the early part of the network is sparse and represents many discrete features. Here, many neurons (more than 70% in some layers of the 66b model) are "dead", i.e. they never activate on a large collection of diverse data. At the same time, many of the alive neurons are reserved for discrete features and act as token and n-gram detectors. Interestingly, their corresponding FFN updates not only promote next token candidates as could be expected, but also explicitly focus on removing the information about triggering them tokens, i.e., current input. To the best of our knowledge, this is the first example of mechanisms specialized at removing (rather than adding) information from the residual stream. With scale, models become more sparse in a sense that they have more dead neurons and token detectors. Finally, some neurons are positional: them being activated or not depends largely (or solely) on position and less so (or not at all) on textual data. We find that smaller models have sets of neurons acting as position range indicators while larger models operate in a less explicit manner.

Overparameterized neural networks generalize well but are expensive to train. Ideally, one would like to reduce their computational cost while retaining their generalization benefits. Sparse model training is a simple and promising approach to achieve this, but there remain challenges as existing methods struggle with accuracy loss, slow training runtime, or difficulty in sparsifying all model components. The core problem is that searching for a sparsity mask over a discrete set of sparse matrices is difficult and expensive. To address this, our main insight is to optimize over a continuous superset of sparse matrices with a fixed structure known as products of butterfly matrices. As butterfly matrices are not hardware efficient, we propose simple variants of butterfly (block and flat) to take advantage of modern hardware. Our method (Pixelated Butterfly) uses a simple fixed sparsity pattern based on flat block butterfly and low-rank matrices to sparsify most network layers (e.g., attention, MLP). We empirically validate that Pixelated Butterfly is 3x faster than butterfly and speeds up training to achieve favorable accuracy--efficiency tradeoffs. On the ImageNet classification and WikiText-103 language modeling tasks, our sparse models train up to 2.5x faster than the dense MLP-Mixer, Vision Transformer, and GPT-2 medium with no drop in accuracy.

Large pre-trained transformers are show-stealer in modern-day deep learning, and it becomes crucial to comprehend the parsimonious patterns that exist within them as they grow in scale. With exploding parameter counts, Lottery Ticket Hypothesis (LTH) and its variants, have lost their pragmatism in sparsifying them due to high computation and memory bottleneck of repetitive train-prune-retrain routine of iterative magnitude pruning (IMP) which worsens with increasing model size. This paper comprehensively studies induced sparse patterns across multiple large pre-trained vision and language transformers. We propose the existence of -- essential sparsity defined with a sharp dropping point beyond which the performance declines much faster w.r.t the rise of sparsity level, when we directly remove weights with the smallest magnitudes in one-shot without re-training. We also find essential sparsity to hold valid for N:M sparsity patterns as well as on modern-scale large language models (Vicuna-7B). We also present an intriguing emerging phenomenon of abrupt sparsification during the pre-training of BERT, i.e., BERT suddenly becomes heavily sparse in pre-training after certain iterations. Moreover, our observations also indicate a counter-intuitive finding that BERT trained with a larger amount of pre-training data tends to have a better ability to condense knowledge in comparatively relatively fewer parameters. Lastly, we investigate the effect of the pre-training loss on essential sparsity and discover that self-supervised learning (SSL) objectives trigger stronger emergent sparsification properties than supervised learning (SL). Our codes are available at https://github.com/VITA-Group/essential_sparsity.

While recent progress in video-text retrieval has been advanced by the exploration of better representation learning, in this paper, we present a novel multi-grained sparse learning framework, S3MA, to learn an aligned sparse space shared between the video and the text for video-text retrieval. The shared sparse space is initialized with a finite number of sparse concepts, each of which refers to a number of words. With the text data at hand, we learn and update the shared sparse space in a supervised manner using the proposed similarity and alignment losses. Moreover, to enable multi-grained alignment, we incorporate frame representations for better modeling the video modality and calculating fine-grained and coarse-grained similarities. Benefiting from the learned shared sparse space and multi-grained similarities, extensive experiments on several video-text retrieval benchmarks demonstrate the superiority of S3MA over existing methods. Our code is available at https://github.com/yimuwangcs/Better_Cross_Modal_Retrieval.

The semantic matching capabilities of neural information retrieval can ameliorate synonymy and polysemy problems of symbolic approaches. However, neural models' dense representations are more suitable for re-ranking, due to their inefficiency. Sparse representations, either in symbolic or latent form, are more efficient with an inverted index. Taking the merits of the sparse and dense representations, we propose an ultra-high dimensional (UHD) representation scheme equipped with directly controllable sparsity. UHD's large capacity and minimal noise and interference among the dimensions allow for binarized representations, which are highly efficient for storage and search. Also proposed is a bucketing method, where the embeddings from multiple layers of BERT are selected/merged to represent diverse linguistic aspects. We test our models with MS MARCO and TREC CAR, showing that our models outperforms other sparse models

While diffusion language models (DLMs) offer a promising alternative to autoregressive models (ARs), existing open-source DLMs suffer from high inference latency. This bottleneck is mainly due to the attention's quadratic complexity with respect to context length in computing all query-key pairs. Intuitively, to reduce this complexity, a natural strategy is to restrict attention to sparse patterns that retain only the most relevant connections. Such approaches are well-established in ARs, where attention follows fixed and clearly defined sparse patterns. However, in DLMs, we observe distinct sparsity behaviors: (1) attention patterns vary across heads, (2) attention patterns in each head remain highly similar across denoising steps, and (3) early denoising steps are critical for generation. These findings render sparse attention methods designed for ARs largely incompatible with DLMs, as they fail to capture head-specific structures and risk degrading generation when applied in early denoising steps. To address these challenges, we propose SparseD, a novel sparse attention method for DLMs. Leveraging the observations, SparseD only requires pre-computing head-specific sparse patterns one time, and reuses them across all steps. This prevents recomputing sparse patterns at each denoising step. Meanwhile, SparseD uses full attention in the early steps, then switches to sparse attention later to maintain generation quality. Together, these establish SparseD as a practical and efficient solution for deploying DLMs in long-context applications. Experimental results demonstrate that SparseD achieves lossless acceleration, delivering up to 1.50times speedup over FlashAttention at a 64k context length with 1,024 denoising steps.

Learned sparse retrieval, which can efficiently perform retrieval through mature inverted-index engines, has garnered growing attention in recent years. Particularly, the inference-free sparse retrievers are attractive as they eliminate online model inference in the retrieval phase thereby avoids huge computational cost, offering reasonable throughput and latency. However, even the state-of-the-art (SOTA) inference-free sparse models lag far behind in terms of search relevance when compared to both sparse and dense siamese models. Towards competitive search relevance for inference-free sparse retrievers, we argue that they deserve dedicated training methods other than using same ones with siamese encoders. In this paper, we propose two different approaches for performance improvement. First, we introduce the IDF-aware FLOPS loss, which introduces Inverted Document Frequency (IDF) to the sparsification of representations. We find that it mitigates the negative impact of the FLOPS regularization on search relevance, allowing the model to achieve a better balance between accuracy and efficiency. Moreover, we propose a heterogeneous ensemble knowledge distillation framework that combines siamese dense and sparse retrievers to generate supervisory signals during the pre-training phase. The ensemble framework of dense and sparse retriever capitalizes on their strengths respectively, providing a strong upper bound for knowledge distillation. To concur the diverse feedback from heterogeneous supervisors, we normalize and then aggregate the outputs of the teacher models to eliminate score scale differences. On the BEIR benchmark, our model outperforms existing SOTA inference-free sparse model by 3.3 NDCG@10 score. It exhibits search relevance comparable to siamese sparse retrievers and client-side latency only 1.1x that of BM25.

Learned Sparse Retrievers (LSR) have evolved into an effective retrieval strategy that can bridge the gap between traditional keyword-based sparse retrievers and embedding-based dense retrievers. At its core, learned sparse retrievers try to learn the most important semantic keyword expansions from a query and/or document which can facilitate better retrieval with overlapping keyword expansions. LSR like SPLADE has typically been using encoder only models with MLM (masked language modeling) style objective in conjunction with known ways of retrieval performance improvement such as hard negative mining, distillation, etc. In this work, we propose to use decoder-only model for learning semantic keyword expansion. We posit, decoder only models that have seen much higher magnitudes of data are better equipped to learn keyword expansions needed for improved retrieval. We use Mistral as the backbone to develop our Learned Sparse Retriever similar to SPLADE and train it on a subset of sentence-transformer data which is often used for training text embedding models. Our experiments support the hypothesis that a sparse retrieval model based on decoder only large language model (LLM) surpasses the performance of existing LSR systems, including SPLADE and all its variants. The LLM based model (Echo-Mistral-SPLADE) now stands as a state-of-the-art learned sparse retrieval model on the BEIR text retrieval benchmark.

Sparse Autoencoders (SAEs) have emerged as a useful tool for interpreting the internal representations of neural networks. However, naively optimising SAEs for reconstruction loss and sparsity results in a preference for SAEs that are extremely wide and sparse. We present an information-theoretic framework for interpreting SAEs as lossy compression algorithms for communicating explanations of neural activations. We appeal to the Minimal Description Length (MDL) principle to motivate explanations of activations which are both accurate and concise. We further argue that interpretable SAEs require an additional property, "independent additivity": features should be able to be understood separately. We demonstrate an example of applying our MDL-inspired framework by training SAEs on MNIST handwritten digits and find that SAE features representing significant line segments are optimal, as opposed to SAEs with features for memorised digits from the dataset or small digit fragments. We argue that using MDL rather than sparsity may avoid potential pitfalls with naively maximising sparsity such as undesirable feature splitting and that this framework naturally suggests new hierarchical SAE architectures which provide more concise explanations.

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. Code is at https://github.com/Ma-Lab-Berkeley/CRATE.

Accommodating long sequences efficiently in autoregressive Transformers, especially within an extended context window, poses significant challenges due to the quadratic computational complexity and substantial KV memory requirements inherent in self-attention mechanisms. In this work, we introduce SPARSEK Attention, a novel sparse attention mechanism designed to overcome these computational and memory obstacles while maintaining performance. Our approach integrates a scoring network and a differentiable top-k mask operator, SPARSEK, to select a constant number of KV pairs for each query, thereby enabling gradient-based optimization. As a result, SPARSEK Attention offers linear time complexity and constant memory footprint during generation. Experimental results reveal that SPARSEK Attention outperforms previous sparse attention methods and provides significant speed improvements during both training and inference, particularly in language modeling and downstream tasks. Furthermore, our method can be seamlessly integrated into pre-trained Large Language Models (LLMs) with minimal fine-tuning, offering a practical solution for effectively managing long-range dependencies in diverse applications.

Recent works have explored the use of weight sparsity to improve the training efficiency (test accuracy w.r.t training FLOPs) of deep neural networks (DNNs). These works aim to reduce training FLOPs but training with sparse weights often leads to accuracy loss or requires longer training schedules, making the resulting training efficiency less clear. In contrast, we focus on using sparsity to increase accuracy while using the same FLOPs as the dense model and show training efficiency gains through higher accuracy. In this work, we introduce Sparse-IFT, a family of Sparse Iso-FLOP Transformations which are used as drop-in replacements for dense layers to improve their representational capacity and FLOP efficiency. Each transformation is parameterized by a single hyperparameter (sparsity level) and provides a larger search space to find optimal sparse masks. Without changing any training hyperparameters, replacing dense layers with Sparse-IFT leads to significant improvements across computer vision (CV) and natural language processing (NLP) tasks, including ResNet-18 on ImageNet (+3.5%) and GPT-3 Small on WikiText-103 (-0.4 PPL), both matching larger dense model variants that use 2x or more FLOPs. To our knowledge, this is the first work to demonstrate the use of sparsity for improving the accuracy of dense models via a simple-to-use set of sparse transformations. Code is available at: https://github.com/CerebrasResearch/Sparse-IFT.

Sparse autoencoders (SAEs) have emerged as a powerful tool for interpreting neural networks by extracting the concepts represented in their activations. However, choosing the size of the SAE dictionary (i.e. number of learned concepts) creates a tension: as dictionary size increases to capture more relevant concepts, sparsity incentivizes features to be split or absorbed into more specific features, leaving high-level features missing or warped. We introduce Matryoshka SAEs, a novel variant that addresses these issues by simultaneously training multiple nested dictionaries of increasing size, forcing the smaller dictionaries to independently reconstruct the inputs without using the larger dictionaries. This organizes features hierarchically - the smaller dictionaries learn general concepts, while the larger dictionaries learn more specific concepts, without incentive to absorb the high-level features. We train Matryoshka SAEs on Gemma-2-2B and TinyStories and find superior performance on sparse probing and targeted concept erasure tasks, more disentangled concept representations, and reduced feature absorption. While there is a minor tradeoff with reconstruction performance, we believe Matryoshka SAEs are a superior alternative for practical tasks, as they enable training arbitrarily large SAEs while retaining interpretable features at different levels of abstraction.

Deep sparse networks are widely investigated as a neural network architecture for prediction tasks with high-dimensional sparse features, with which feature interaction selection is a critical component. While previous methods primarily focus on how to search feature interaction in a coarse-grained space, less attention has been given to a finer granularity. In this work, we introduce a hybrid-grained feature interaction selection approach that targets both feature field and feature value for deep sparse networks. To explore such expansive space, we propose a decomposed space which is calculated on the fly. We then develop a selection algorithm called OptFeature, which efficiently selects the feature interaction from both the feature field and the feature value simultaneously. Results from experiments on three large real-world benchmark datasets demonstrate that OptFeature performs well in terms of accuracy and efficiency. Additional studies support the feasibility of our method.

An efficient attention implementation is essential for large models due to its quadratic time complexity. Fortunately, attention commonly exhibits sparsity, i.e., many values in the attention map are near zero, allowing for the omission of corresponding computations. Many studies have utilized the sparse pattern to accelerate attention. However, most existing works focus on optimizing attention within specific models by exploiting certain sparse patterns of the attention map. A universal sparse attention that guarantees both the speedup and end-to-end performance of diverse models remains elusive. In this paper, we propose SpargeAttn, a universal sparse and quantized attention for any model. Our method uses a two-stage online filter: in the first stage, we rapidly and accurately predict the attention map, enabling the skip of some matrix multiplications in attention. In the second stage, we design an online softmax-aware filter that incurs no extra overhead and further skips some matrix multiplications. Experiments show that our method significantly accelerates diverse models, including language, image, and video generation, without sacrificing end-to-end metrics. The codes are available at https://github.com/thu-ml/SpargeAttn.

Exploiting sparsity underlying neural networks has become one of the most potential methodologies to reduce the memory footprint, I/O cost, and computation workloads during inference. And the degree of sparsity one can exploit has become higher as larger model sizes have been considered along with the trend of pre-training giant models. On the other hand, compared with quantization that has been a widely supported option, acceleration through high-degree sparsity is not supported in most computing platforms. In this work, we introduce the first commercial hardware platform supporting high-degree sparsity acceleration up to 32 times -- S4. Combined with state-of-the-art sparse pruning techniques, we demonstrate several-times practical inference speedup on S4 over mainstream inference platforms such as Nvidia T4. We also show that in practice a sparse model of larger size can achieve both higher accuracy and higher throughput on S4 than a dense model of smaller size.

The transformer architecture has driven breakthroughs in recent years on tasks which require modeling pairwise relationships between sequential elements, as is the case in natural language understanding. However, long seqeuences pose a problem due to the quadratic complexity of the attention operation. Previous research has aimed to lower the complexity by sparsifying or linearly approximating the attention matrix. Yet, these approaches cannot straightforwardly distill knowledge from a teacher's attention matrix and often require complete retraining from scratch. Furthermore, previous sparse and linear approaches lose interpretability if they cannot produce full attention matrices. To address these challenges, we propose SEA: Sparse linear attention with an Estimated Attention mask. SEA estimates the attention matrix with linear complexity via kernel-based linear attention, then subsequently creates a sparse attention matrix with a top-k selection to perform a sparse attention operation. For language modeling tasks (Wikitext2), previous linear and sparse attention methods show roughly two-fold worse perplexity scores over the quadratic OPT-1.3B baseline, while SEA achieves better perplexity than OPT-1.3B, using roughly half the memory of OPT-1.3B, providing interpretable attention matrix. We believe that our work will have a large practical impact, as it opens the possibility of running large transformers on resource-limited devices with less memory.

Despite their recent popularity and well-known advantages, dense retrievers still lag behind sparse methods such as BM25 in their ability to reliably match salient phrases and rare entities in the query and to generalize to out-of-domain data. It has been argued that this is an inherent limitation of dense models. We rebut this claim by introducing the Salient Phrase Aware Retriever (SPAR), a dense retriever with the lexical matching capacity of a sparse model. We show that a dense Lexical Model {\Lambda} can be trained to imitate a sparse one, and SPAR is built by augmenting a standard dense retriever with {\Lambda}. Empirically, SPAR shows superior performance on a range of tasks including five question answering datasets, MS MARCO passage retrieval, as well as the EntityQuestions and BEIR benchmarks for out-of-domain evaluation, exceeding the performance of state-of-the-art dense and sparse retrievers. The code and models of SPAR are available at: https://github.com/facebookresearch/dpr-scale/tree/main/spar

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of generalization performance of overparametrized networks. We propose in this paper a method for learning sparse neural topologies via a regularization technique which identifies non relevant weights and selectively shrinks their norm, while performing a classic update for relevant ones. This technique, which is an improvement of classical weight decay, is based on the definition of a regularization term which can be added to any loss functional regardless of its form, resulting in a unified general framework exploitable in many different contexts. The actual elimination of parameters identified as irrelevant is handled by an iterative pruning algorithm. We tested the proposed technique on different image classification and Natural language generation tasks, obtaining results on par or better then competitors in terms of sparsity and metrics, while achieving strong models compression.

In neural Information Retrieval (IR), ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. Introduced recently, the SPLADE model provides highly sparse representations and competitive results with respect to state-of-the-art dense and sparse approaches. In this paper, we build on SPLADE and propose several significant improvements in terms of effectiveness and/or efficiency. More specifically, we modify the pooling mechanism, benchmark a model solely based on document expansion, and introduce models trained with distillation. We also report results on the BEIR benchmark. Overall, SPLADE is considerably improved with more than 9\% gains on NDCG@10 on TREC DL 2019, leading to state-of-the-art results on the BEIR benchmark.

We investigate feature universality in large language models (LLMs), a research field that aims to understand how different models similarly represent concepts in the latent spaces of their intermediate layers. Demonstrating feature universality allows discoveries about latent representations to generalize across several models. However, comparing features across LLMs is challenging due to polysemanticity, in which individual neurons often correspond to multiple features rather than distinct ones. This makes it difficult to disentangle and match features across different models. To address this issue, we employ a method known as dictionary learning by using sparse autoencoders (SAEs) to transform LLM activations into more interpretable spaces spanned by neurons corresponding to individual features. After matching feature neurons across models via activation correlation, we apply representational space similarity metrics like Singular Value Canonical Correlation Analysis to analyze these SAE features across different LLMs. Our experiments reveal significant similarities in SAE feature spaces across various LLMs, providing new evidence for feature universality.

DETR-like models have significantly boosted the performance of detectors and even outperformed classical convolutional models. However, all tokens are treated equally without discrimination brings a redundant computational burden in the traditional encoder structure. The recent sparsification strategies exploit a subset of informative tokens to reduce attention complexity maintaining performance through the sparse encoder. But these methods tend to rely on unreliable model statistics. Moreover, simply reducing the token population hinders the detection performance to a large extent, limiting the application of these sparse models. We propose Focus-DETR, which focuses attention on more informative tokens for a better trade-off between computation efficiency and model accuracy. Specifically, we reconstruct the encoder with dual attention, which includes a token scoring mechanism that considers both localization and category semantic information of the objects from multi-scale feature maps. We efficiently abandon the background queries and enhance the semantic interaction of the fine-grained object queries based on the scores. Compared with the state-of-the-art sparse DETR-like detectors under the same setting, our Focus-DETR gets comparable complexity while achieving 50.4AP (+2.2) on COCO. The code is available at https://github.com/huawei-noah/noah-research/tree/master/Focus-DETR and https://gitee.com/mindspore/models/tree/master/research/cv/Focus-DETR.

Large Language Models (LLMs), while demonstrating remarkable capabilities across various applications, present significant challenges during inference due to their substantial model size, especially when deployed on edge devices. Activation sparsity offers a promising solution to reduce computation and memory movement, enabling more efficient inference, particularly for small-batch on-device applications. However, current approaches face limitations with non-ReLU activation function, which are foundational to most advanced LLMs, or require heavy continual training. Additionally, the difficulty in predicting active channels and limited achievable sparsity ratios constrain the effectiveness of activation sparsity-based methods. In this paper, we introduce R-Sparse, a training-free activation sparsity approach capable of achieving high sparsity levels in advanced LLMs. We conducted two preliminary investigations into how different components contribute to the output within a single linear layer and found two key observations: (i) the non-sparse components of the input function can be regarded as a few bias terms, and (ii) The full computation can be effectively approximated by an appropriate combination of input channels and weight singular values. Building on this, we replace the linear layers in LLMs with a rank-aware sparse inference method that leverages the sparsity of input channels and singular value components, eliminating the need for active channel prediction like the output sparsity based approaches. Experiments on Llama-2/3 and Mistral models across ten diverse tasks demonstrate that R-Sparse achieves comparable performance at 50% model-level sparsity, resulting in a significant 43% end-to-end efficient improvements with customized kernels.

Disentangling model activations into meaningful features is a central problem in interpretability. However, the absence of ground-truth for these features in realistic scenarios makes validating recent approaches, such as sparse dictionary learning, elusive. To address this challenge, we propose a framework for evaluating feature dictionaries in the context of specific tasks, by comparing them against supervised feature dictionaries. First, we demonstrate that supervised dictionaries achieve excellent approximation, control, and interpretability of model computations on the task. Second, we use the supervised dictionaries to develop and contextualize evaluations of unsupervised dictionaries along the same three axes. We apply this framework to the indirect object identification (IOI) task using GPT-2 Small, with sparse autoencoders (SAEs) trained on either the IOI or OpenWebText datasets. We find that these SAEs capture interpretable features for the IOI task, but they are less successful than supervised features in controlling the model. Finally, we observe two qualitative phenomena in SAE training: feature occlusion (where a causally relevant concept is robustly overshadowed by even slightly higher-magnitude ones in the learned features), and feature over-splitting (where binary features split into many smaller, less interpretable features). We hope that our framework will provide a useful step towards more objective and grounded evaluations of sparse dictionary learning methods.

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

Sparse autoencoders (SAEs) have emerged as a powerful technique for extracting human-interpretable features from neural networks activations. Previous works compared different models based on SAE-derived features but those comparisons have been restricted to models within the same modality. We propose a novel indicator allowing quantitative comparison of models across SAE features, and use it to conduct a comparative study of visual, textual and multimodal encoders. We also propose to quantify the Comparative Sharedness of individual features between different classes of models. With these two new tools, we conduct several studies on 21 encoders of the three types, with two significantly different sizes, and considering generalist and domain specific datasets. The results allow to revisit previous studies at the light of encoders trained in a multimodal context and to quantify to which extent all these models share some representations or features. They also suggest that visual features that are specific to VLMs among vision encoders are shared with text encoders, highlighting the impact of text pretraining. The code is available at https://github.com/CEA-LIST/SAEshareConcepts

Learned sparse retrieval (LSR) is a family of first-stage retrieval methods that are trained to generate sparse lexical representations of queries and documents for use with an inverted index. Many LSR methods have been recently introduced, with Splade models achieving state-of-the-art performance on MSMarco. Despite similarities in their model architectures, many LSR methods show substantial differences in effectiveness and efficiency. Differences in the experimental setups and configurations used make it difficult to compare the methods and derive insights. In this work, we analyze existing LSR methods and identify key components to establish an LSR framework that unifies all LSR methods under the same perspective. We then reproduce all prominent methods using a common codebase and re-train them in the same environment, which allows us to quantify how components of the framework affect effectiveness and efficiency. We find that (1) including document term weighting is most important for a method's effectiveness, (2) including query weighting has a small positive impact, and (3) document expansion and query expansion have a cancellation effect. As a result, we show how removing query expansion from a state-of-the-art model can reduce latency significantly while maintaining effectiveness on MSMarco and TripClick benchmarks. Our code is publicly available at https://github.com/thongnt99/learned-sparse-retrieval

Attention is the cornerstone of modern Large Language Models (LLMs). Yet its quadratic complexity limits the efficiency and scalability of LLMs, especially for those with a long-context window. A promising approach addressing this limitation is to leverage the sparsity in attention. However, existing sparsity-based solutions predominantly rely on predefined patterns or heuristics to approximate sparsity. This practice falls short to fully capture the dynamic nature of attention sparsity in language-based tasks. This paper argues that attention sparsity should be learned rather than predefined. To this end, we design SeerAttention, a new Attention mechanism that augments the conventional attention with a learnable gate that adaptively selects significant blocks in an attention map and deems the rest blocks sparse. Such block-level sparsity effectively balances accuracy and speedup. To enable efficient learning of the gating network, we develop a customized FlashAttention implementation that extracts the block-level ground truth of attention map with minimum overhead. SeerAttention not only applies to post-training, but also excels in long-context fine-tuning. Our results show that at post-training stages, SeerAttention significantly outperforms state-of-the-art static or heuristic-based sparse attention methods, while also being more versatile and flexible to adapt to varying context lengths and sparsity ratios. When applied to long-context fine-tuning with YaRN, SeerAttention can achieve a remarkable 90% sparsity ratio at a 32k context length with minimal perplexity loss, offering a 5.67x speedup over FlashAttention-2.

Term-based sparse representations dominate the first-stage text retrieval in industrial applications, due to its advantage in efficiency, interpretability, and exact term matching. In this paper, we study the problem of transferring the deep knowledge of the pre-trained language model (PLM) to Term-based Sparse representations, aiming to improve the representation capacity of bag-of-words(BoW) method for semantic-level matching, while still keeping its advantages. Specifically, we propose a novel framework SparTerm to directly learn sparse text representations in the full vocabulary space. The proposed SparTerm comprises an importance predictor to predict the importance for each term in the vocabulary, and a gating controller to control the term activation. These two modules cooperatively ensure the sparsity and flexibility of the final text representation, which unifies the term-weighting and expansion in the same framework. Evaluated on MSMARCO dataset, SparTerm significantly outperforms traditional sparse methods and achieves state of the art ranking performance among all the PLM-based sparse models.

Over-parameterization of deep neural networks (DNNs) has shown high prediction accuracy for many applications. Although effective, the large number of parameters hinders its popularity on resource-limited devices and has an outsize environmental impact. Sparse training (using a fixed number of nonzero weights in each iteration) could significantly mitigate the training costs by reducing the model size. However, existing sparse training methods mainly use either random-based or greedy-based drop-and-grow strategies, resulting in local minimal and low accuracy. In this work, we consider the dynamic sparse training as a sparse connectivity search problem and design an exploitation and exploration acquisition function to escape from local optima and saddle points. We further design an acquisition function and provide the theoretical guarantees for the proposed method and clarify its convergence property. Experimental results show that sparse models (up to 98\% sparsity) obtained by our proposed method outperform the SOTA sparse training methods on a wide variety of deep learning tasks. On VGG-19 / CIFAR-100, ResNet-50 / CIFAR-10, ResNet-50 / CIFAR-100, our method has even higher accuracy than dense models. On ResNet-50 / ImageNet, the proposed method has up to 8.2\% accuracy improvement compared to SOTA sparse training methods.

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.

Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on ell_1 regularization, attention, and other techniques, typically select the entire feature subset in one evaluation round, ignoring the residual value of features during selection, i.e., the marginal contribution of a feature given that other features have already been selected. We propose a feature selection algorithm called Sequential Attention that achieves state-of-the-art empirical results for neural networks. This algorithm is based on an efficient one-pass implementation of greedy forward selection and uses attention weights at each step as a proxy for feature importance. We give theoretical insights into our algorithm for linear regression by showing that an adaptation to this setting is equivalent to the classical Orthogonal Matching Pursuit (OMP) algorithm, and thus inherits all of its provable guarantees. Our theoretical and empirical analyses offer new explanations towards the effectiveness of attention and its connections to overparameterization, which may be of independent interest.

With the dramatically increased number of parameters in language models, sparsity methods have received ever-increasing research focus to compress and accelerate the models. While most research focuses on how to accurately retain appropriate weights while maintaining the performance of the compressed model, there are challenges in the computational overhead and memory footprint of sparse training when compressing large-scale language models. To address this problem, we propose a Parameter-efficient Sparse Training (PST) method to reduce the number of trainable parameters during sparse-aware training in downstream tasks. Specifically, we first combine the data-free and data-driven criteria to efficiently and accurately measure the importance of weights. Then we investigate the intrinsic redundancy of data-driven weight importance and derive two obvious characteristics i.e., low-rankness and structuredness. Based on that, two groups of small matrices are introduced to compute the data-driven importance of weights, instead of using the original large importance score matrix, which therefore makes the sparse training resource-efficient and parameter-efficient. Experiments with diverse networks (i.e., BERT, RoBERTa and GPT-2) on dozens of datasets demonstrate PST performs on par or better than previous sparsity methods, despite only training a small number of parameters. For instance, compared with previous sparsity methods, our PST only requires 1.5% trainable parameters to achieve comparable performance on BERT.

Hallucinations in large language models are a widespread problem, yet the mechanisms behind whether models will hallucinate are poorly understood, limiting our ability to solve this problem. Using sparse autoencoders as an interpretability tool, we discover that a key part of these mechanisms is entity recognition, where the model detects if an entity is one it can recall facts about. Sparse autoencoders uncover meaningful directions in the representation space, these detect whether the model recognizes an entity, e.g. detecting it doesn't know about an athlete or a movie. This suggests that models can have self-knowledge: internal representations about their own capabilities. These directions are causally relevant: capable of steering the model to refuse to answer questions about known entities, or to hallucinate attributes of unknown entities when it would otherwise refuse. We demonstrate that despite the sparse autoencoders being trained on the base model, these directions have a causal effect on the chat model's refusal behavior, suggesting that chat finetuning has repurposed this existing mechanism. Furthermore, we provide an initial exploration into the mechanistic role of these directions in the model, finding that they disrupt the attention of downstream heads that typically move entity attributes to the final token.

In vision-language models (VLMs), visual tokens usually consume a significant amount of computational overhead, despite their sparser information density compared to text tokens. To address this, most existing methods learn a network to prune redundant visual tokens and require additional training data. Differently, we propose an efficient training-free token optimization mechanism dubbed SparseVLM without extra parameters or fine-tuning costs. Concretely, given that visual tokens complement text tokens in VLMs for linguistic reasoning, we select visual-relevant text tokens to rate the significance of vision tokens within the self-attention matrix extracted from the VLMs. Then we progressively prune irrelevant tokens. To maximize sparsity while retaining essential information, we introduce a rank-based strategy to adaptively determine the sparsification ratio for each layer, alongside a token recycling method that compresses pruned tokens into more compact representations. Experimental results show that our SparseVLM improves the efficiency of various VLMs across a range of image and video understanding tasks. In particular, LLaVA equipped with SparseVLM reduces 61% to 67% FLOPs with a compression ratio of 78% while maintaining 93% of the accuracy. Our code is available at https://github.com/Gumpest/SparseVLMs.

Transformer-based language models have found many diverse applications requiring them to process sequences of increasing length. For these applications, the causal self-attention -- which is the only component scaling quadratically w.r.t. the sequence length -- becomes a central concern. While many works have proposed schemes to sparsify the attention patterns and reduce the computational overhead of self-attention, those are often limited by implementations concerns and end up imposing a simple and static structure over the attention matrix. Conversely, implementing more dynamic sparse attentions often results in runtimes significantly slower than computing the full attention using the Flash implementation from Dao et al. (2022). We extend FlashAttention to accommodate a large class of attention sparsity patterns that, in particular, encompass key/query dropping and hashing-based attention. This leads to implementations with no computational complexity overhead and a multi-fold runtime speedup on top of FlashAttention. Even with relatively low degrees of sparsity, our method improves visibly upon FlashAttention as the sequence length increases. Without sacrificing perplexity, we increase the training speed of a transformer language model by 2.0times and 3.3times for sequences of respectively 8k and 16k tokens.

We identify and overcome two key obstacles in extending the success of BERT-style pre-training, or the masked image modeling, to convolutional networks (convnets): (i) convolution operation cannot handle irregular, random-masked input images; (ii) the single-scale nature of BERT pre-training is inconsistent with convnet's hierarchical structure. For (i), we treat unmasked pixels as sparse voxels of 3D point clouds and use sparse convolution to encode. This is the first use of sparse convolution for 2D masked modeling. For (ii), we develop a hierarchical decoder to reconstruct images from multi-scale encoded features. Our method called Sparse masKed modeling (SparK) is general: it can be used directly on any convolutional model without backbone modifications. We validate it on both classical (ResNet) and modern (ConvNeXt) models: on three downstream tasks, it surpasses both state-of-the-art contrastive learning and transformer-based masked modeling by similarly large margins (around +1.0%). Improvements on object detection and instance segmentation are more substantial (up to +3.5%), verifying the strong transferability of features learned. We also find its favorable scaling behavior by observing more gains on larger models. All this evidence reveals a promising future of generative pre-training on convnets. Codes and models are released at https://github.com/keyu-tian/SparK.

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to use maximum likelihood principle to optimize the model. However, softmax leaves a large margin for loss function to conduct optimizing operation when it comes to high-dimensional classification, which results in low-performance to some extent. In this paper, we provide an empirical study on a simple and concise softmax variant, namely sparse-softmax, to alleviate the problem that occurred in traditional softmax in terms of high-dimensional classification problems. We evaluate our approach in several interdisciplinary tasks, the experimental results show that sparse-softmax is simpler, faster, and produces better results than the baseline models.

We combine the capacity of sparsely gated Mixture-of-Experts (MoE) with the speed and stability of linear, mixing transformations to design the Sparse Mixer encoder model. Sparse Mixer slightly outperforms (<1%) BERT on GLUE and SuperGLUE, but more importantly trains 65% faster and runs inference 61% faster. We also present a faster variant, prosaically named Fast Sparse Mixer, that marginally underperforms BERT on SuperGLUE, but trains and runs nearly twice as fast. We justify the design of these two models by carefully ablating through various mixing mechanisms, MoE configurations and hyperparameters. Sparse Mixer overcomes many of the latency and stability concerns of MoE models and offers the prospect of serving sparse student models, without resorting to distilling them to dense variants.

Scaling the capacity of language models has consistently proven to be a reliable approach for improving performance and unlocking new capabilities. Capacity can be primarily defined by two dimensions: the number of model parameters and the compute per example. While scaling typically involves increasing both, the precise interplay between these factors and their combined contribution to overall capacity remains not fully understood. We explore this relationship in the context of sparse Mixture-of-Experts (MoEs), which allow scaling the number of parameters without proportionally increasing the FLOPs per example. We investigate how varying the sparsity level, i.e., the fraction of inactive parameters, impacts model's performance during pretraining and downstream few-shot evaluation. We find that under different constraints (e.g., parameter size and total training compute), there is an optimal level of sparsity that improves both training efficiency and model performance. These results provide a better understanding of the impact of sparsity in scaling laws for MoEs and complement existing works in this area, offering insights for designing more efficient architectures.

Recent sparse detectors with multiple, e.g. six, decoder layers achieve promising performance but much inference time due to complex heads. Previous works have explored using dense priors as initialization and built one-decoder-layer detectors. Although they gain remarkable acceleration, their performance still lags behind their six-decoder-layer counterparts by a large margin. In this work, we aim to bridge this performance gap while retaining fast speed. We find that the architecture discrepancy between dense and sparse detectors leads to feature conflict, hampering the performance of one-decoder-layer detectors. Thus we propose Adaptive Sparse Anchor Generator (ASAG) which predicts dynamic anchors on patches rather than grids in a sparse way so that it alleviates the feature conflict problem. For each image, ASAG dynamically selects which feature maps and which locations to predict, forming a fully adaptive way to generate image-specific anchors. Further, a simple and effective Query Weighting method eases the training instability from adaptiveness. Extensive experiments show that our method outperforms dense-initialized ones and achieves a better speed-accuracy trade-off. The code is available at https://github.com/iSEE-Laboratory/ASAG.

Sparse autoencoders provide a promising unsupervised approach for extracting interpretable features from a language model by reconstructing activations from a sparse bottleneck layer. Since language models learn many concepts, autoencoders need to be very large to recover all relevant features. However, studying the properties of autoencoder scaling is difficult due to the need to balance reconstruction and sparsity objectives and the presence of dead latents. We propose using k-sparse autoencoders [Makhzani and Frey, 2013] to directly control sparsity, simplifying tuning and improving the reconstruction-sparsity frontier. Additionally, we find modifications that result in few dead latents, even at the largest scales we tried. Using these techniques, we find clean scaling laws with respect to autoencoder size and sparsity. We also introduce several new metrics for evaluating feature quality based on the recovery of hypothesized features, the explainability of activation patterns, and the sparsity of downstream effects. These metrics all generally improve with autoencoder size. To demonstrate the scalability of our approach, we train a 16 million latent autoencoder on GPT-4 activations for 40 billion tokens. We release training code and autoencoders for open-source models, as well as a visualizer.

Attention mechanisms have become ubiquitous in NLP. Recent architectures, notably the Transformer, learn powerful context-aware word representations through layered, multi-headed attention. The multiple heads learn diverse types of word relationships. However, with standard softmax attention, all attention heads are dense, assigning a non-zero weight to all context words. In this work, we introduce the adaptively sparse Transformer, wherein attention heads have flexible, context-dependent sparsity patterns. This sparsity is accomplished by replacing softmax with alpha-entmax: a differentiable generalization of softmax that allows low-scoring words to receive precisely zero weight. Moreover, we derive a method to automatically learn the alpha parameter -- which controls the shape and sparsity of alpha-entmax -- allowing attention heads to choose between focused or spread-out behavior. Our adaptively sparse Transformer improves interpretability and head diversity when compared to softmax Transformers on machine translation datasets. Findings of the quantitative and qualitative analysis of our approach include that heads in different layers learn different sparsity preferences and tend to be more diverse in their attention distributions than softmax Transformers. Furthermore, at no cost in accuracy, sparsity in attention heads helps to uncover different head specializations.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they serve as algebraic primitives that can be analysed without reference to input and can describe structures ranging from linear concepts to complicated manifolds. This work uses bilinear autoencoders to efficiently decompose representations into quadratic polynomials. We discuss improvements that induce importance ordering, clustering, and activation sparsity. This is an initial step toward nonlinear yet analysable latents through their algebraic properties.

This paper introduces an efficient and robust method for discovering interpretable circuits in large language models using discrete sparse autoencoders. Our approach addresses key limitations of existing techniques, namely computational complexity and sensitivity to hyperparameters. We propose training sparse autoencoders on carefully designed positive and negative examples, where the model can only correctly predict the next token for the positive examples. We hypothesise that learned representations of attention head outputs will signal when a head is engaged in specific computations. By discretising the learned representations into integer codes and measuring the overlap between codes unique to positive examples for each head, we enable direct identification of attention heads involved in circuits without the need for expensive ablations or architectural modifications. On three well-studied tasks - indirect object identification, greater-than comparisons, and docstring completion - the proposed method achieves higher precision and recall in recovering ground-truth circuits compared to state-of-the-art baselines, while reducing runtime from hours to seconds. Notably, we require only 5-10 text examples for each task to learn robust representations. Our findings highlight the promise of discrete sparse autoencoders for scalable and efficient mechanistic interpretability, offering a new direction for analysing the inner workings of large language models.

Recent advances in large language models highlighted the excessive quadratic cost of self-attention. Despite the significant research efforts, subquadratic attention methods still suffer from inferior performance in practice. We hypothesize that dynamic, learned content-based sparsity can lead to more efficient attention mechanisms. We present Mixture of Sparse Attention (MoSA), a novel approach inspired by Mixture of Experts (MoE) with expert choice routing. MoSA dynamically selects tokens for each attention head, allowing arbitrary sparse attention patterns. By selecting k tokens from a sequence of length T, MoSA reduces the computational complexity of each attention head from O(T^2) to O(k^2 + T). This enables using more heads within the same computational budget, allowing higher specialization. We show that among the tested sparse attention variants, MoSA is the only one that can outperform the dense baseline, sometimes with up to 27% better perplexity for an identical compute budget. MoSA can also reduce the resource usage compared to dense self-attention. Despite using torch implementation without an optimized kernel, perplexity-matched MoSA models are simultaneously faster in wall-clock time, require less memory for training, and drastically reduce the size of the KV-cache compared to the dense transformer baselines.

Decomposing model activations into interpretable components is a key open problem in mechanistic interpretability. Sparse autoencoders (SAEs) are a popular method for decomposing the internal activations of trained transformers into sparse, interpretable features, and have been applied to MLP layers and the residual stream. In this work we train SAEs on attention layer outputs and show that also here SAEs find a sparse, interpretable decomposition. We demonstrate this on transformers from several model families and up to 2B parameters. We perform a qualitative study of the features computed by attention layers, and find multiple families: long-range context, short-range context and induction features. We qualitatively study the role of every head in GPT-2 Small, and estimate that at least 90% of the heads are polysemantic, i.e. have multiple unrelated roles. Further, we show that Sparse Autoencoders are a useful tool that enable researchers to explain model behavior in greater detail than prior work. For example, we explore the mystery of why models have so many seemingly redundant induction heads, use SAEs to motivate the hypothesis that some are long-prefix whereas others are short-prefix, and confirm this with more rigorous analysis. We use our SAEs to analyze the computation performed by the Indirect Object Identification circuit (Wang et al.), validating that the SAEs find causally meaningful intermediate variables, and deepening our understanding of the semantics of the circuit. We open-source the trained SAEs and a tool for exploring arbitrary prompts through the lens of Attention Output SAEs.

In the past few years, neural networks have evolved from simple Feedforward Neural Networks to more complex neural networks, such as Convolutional Neural Networks and Recurrent Neural Networks. Where CNNs are a perfect fit for tasks where the sequence is not important such as image recognition, RNNs are useful when order is important such as machine translation. An increasing number of layers in a neural network is one way to improve its performance, but it also increases its complexity making it much more time and power-consuming to train. One way to tackle this problem is to introduce sparsity in the architecture of the neural network. Pruning is one of the many methods to make a neural network architecture sparse by clipping out weights below a certain threshold while keeping the performance near to the original. Another way is to generate arbitrary structures using random graphs and embed them between an input and output layer of an Artificial Neural Network. Many researchers in past years have focused on pruning mainly CNNs, while hardly any research is done for the same in RNNs. The same also holds in creating sparse architectures for RNNs by generating and embedding arbitrary structures. Therefore, this thesis focuses on investigating the effects of the before-mentioned two techniques on the performance of RNNs. We first describe the pruning of RNNs, its impact on the performance of RNNs, and the number of training epochs required to regain accuracy after the pruning is performed. Next, we continue with the creation and training of Sparse Recurrent Neural Networks and identify the relation between the performance and the graph properties of its underlying arbitrary structure. We perform these experiments on RNN with Tanh nonlinearity (RNN-Tanh), RNN with ReLU nonlinearity (RNN-ReLU), GRU, and LSTM. Finally, we analyze and discuss the results achieved from both the experiments.

Sparse Autoencoders (SAEs) have emerged as a promising approach to decompose the activations of Large Language Models (LLMs) into human-interpretable latents. In this paper, we pose two questions. First, to what extent do SAEs extract monosemantic and interpretable latents? Second, to what extent does varying the sparsity or the size of the SAE affect monosemanticity / interpretability? By investigating these questions in the context of a simple first-letter identification task where we have complete access to ground truth labels for all tokens in the vocabulary, we are able to provide more detail than prior investigations. Critically, we identify a problematic form of feature-splitting we call feature absorption where seemingly monosemantic latents fail to fire in cases where they clearly should. Our investigation suggests that varying SAE size or sparsity is insufficient to solve this issue, and that there are deeper conceptual issues in need of resolution.

Identifying the features learned by neural networks is a core challenge in mechanistic interpretability. Sparse autoencoders (SAEs), which learn a sparse, overcomplete dictionary that reconstructs a network's internal activations, have been used to identify these features. However, SAEs may learn more about the structure of the datatset than the computational structure of the network. There is therefore only indirect reason to believe that the directions found in these dictionaries are functionally important to the network. We propose end-to-end (e2e) sparse dictionary learning, a method for training SAEs that ensures the features learned are functionally important by minimizing the KL divergence between the output distributions of the original model and the model with SAE activations inserted. Compared to standard SAEs, e2e SAEs offer a Pareto improvement: They explain more network performance, require fewer total features, and require fewer simultaneously active features per datapoint, all with no cost to interpretability. We explore geometric and qualitative differences between e2e SAE features and standard SAE features. E2e dictionary learning brings us closer to methods that can explain network behavior concisely and accurately. We release our library for training e2e SAEs and reproducing our analysis at https://github.com/ApolloResearch/e2e_sae

Large language models (LLMs) have driven significant advancements across diverse NLP tasks, with long-context models gaining prominence for handling extended inputs. However, the expanding key-value (KV) cache size required by Transformer architectures intensifies the memory constraints, particularly during the decoding phase, creating a significant bottleneck. Existing sparse attention mechanisms designed to address this bottleneck have two limitations: (1) they often fail to reliably identify the most relevant tokens for attention, and (2) they overlook the spatial coherence of token selection across consecutive Transformer layers, which can lead to performance degradation and substantial overhead in token selection. This paper introduces TidalDecode, a simple yet effective algorithm and system for fast and accurate LLM decoding through position persistent sparse attention. TidalDecode leverages the spatial coherence of tokens selected by existing sparse attention methods and introduces a few token selection layers that perform full attention to identify the tokens with the highest attention scores, while all other layers perform sparse attention with the pre-selected tokens. This design enables TidalDecode to substantially reduce the overhead of token selection for sparse attention without sacrificing the quality of the generated results. Evaluation on a diverse set of LLMs and tasks shows that TidalDecode closely matches the generative performance of full attention methods while reducing the LLM decoding latency by up to 2.1x.

Large language models (LLMs) with billions of parameters have sparked a new wave of exciting AI applications. However, their high computational costs and memory demands during inference pose significant challenges. Adaptive sparse activation inference, which activates only a small number of neurons for each token, offers a novel way to accelerate model inference without degrading performance, showing great potential for resource-constrained hardware devices. Nevertheless, existing methods predict activated neurons based on individual tokens with additional MLP, which involve frequent changes in activation maps and resource calls, limiting the acceleration benefits of sparse activation. In this paper, we introduce CoreInfer, an MLP-free adaptive sparse activation inference method based on sentence-level prediction. Specifically, we propose the concept of sentence-wise core neurons, which refers to the subset of neurons most critical for a given sentence, and empirically demonstrate its effectiveness. To determine the core neurons, we explore the correlation between core neurons and the sentence's semantics. Remarkably, we discovered that core neurons exhibit both stability and similarity in relation to the sentence's semantics -- an insight overlooked by previous studies. Building on this finding, we further design two semantic-based methods for predicting core neurons to fit different input scenarios. In CoreInfer, the core neurons are determined during the pre-filling stage and fixed during the encoding stage, enabling zero-cost sparse inference. We evaluated the model generalization and task generalization of CoreInfer across various models and tasks. Notably, on an NVIDIA TITAN XP GPU, CoreInfer achieved a 10.33 times and 2.72 times speedup compared to the Huggingface implementation and PowerInfer, respectively.

Transformers-based models, such as BERT, have been one of the most successful deep learning models for NLP. Unfortunately, one of their core limitations is the quadratic dependency (mainly in terms of memory) on the sequence length due to their full attention mechanism. To remedy this, we propose, BigBird, a sparse attention mechanism that reduces this quadratic dependency to linear. We show that BigBird is a universal approximator of sequence functions and is Turing complete, thereby preserving these properties of the quadratic, full attention model. Along the way, our theoretical analysis reveals some of the benefits of having O(1) global tokens (such as CLS), that attend to the entire sequence as part of the sparse attention mechanism. The proposed sparse attention can handle sequences of length up to 8x of what was previously possible using similar hardware. As a consequence of the capability to handle longer context, BigBird drastically improves performance on various NLP tasks such as question answering and summarization. We also propose novel applications to genomics data.

Major complications arise from the recent increase in the amount of high-dimensional data, including high computational costs and memory requirements. Feature selection, which identifies the most relevant and informative attributes of a dataset, has been introduced as a solution to this problem. Most of the existing feature selection methods are computationally inefficient; inefficient algorithms lead to high energy consumption, which is not desirable for devices with limited computational and energy resources. In this paper, a novel and flexible method for unsupervised feature selection is proposed. This method, named QuickSelection, introduces the strength of the neuron in sparse neural networks as a criterion to measure the feature importance. This criterion, blended with sparsely connected denoising autoencoders trained with the sparse evolutionary training procedure, derives the importance of all input features simultaneously. We implement QuickSelection in a purely sparse manner as opposed to the typical approach of using a binary mask over connections to simulate sparsity. It results in a considerable speed increase and memory reduction. When tested on several benchmark datasets, including five low-dimensional and three high-dimensional datasets, the proposed method is able to achieve the best trade-off of classification and clustering accuracy, running time, and maximum memory usage, among widely used approaches for feature selection. Besides, our proposed method requires the least amount of energy among the state-of-the-art autoencoder-based feature selection methods.

The lottery ticket hypothesis (LTH) has increased attention to pruning neural networks at initialization. We study this problem in the linear setting. We show that finding a sparse mask at initialization is equivalent to the sketching problem introduced for efficient matrix multiplication. This gives us tools to analyze the LTH problem and gain insights into it. Specifically, using the mask found at initialization, we bound the approximation error of the pruned linear model at the end of training. We theoretically justify previous empirical evidence that the search for sparse networks may be data independent. By using the sketching perspective, we suggest a generic improvement to existing algorithms for pruning at initialization, which we show to be beneficial in the data-independent case.

While large language models (LLMs) have achieved remarkable performance across a wide range of tasks, their massive scale incurs prohibitive computational and memory costs for pre-training from scratch. Recent studies have investigated the use of low-rank parameterization as a means of reducing model size and training cost. In this context, sparsity is often employed as a complementary technique to recover important information lost in low-rank compression by capturing salient features in the residual space. However, existing approaches typically combine low-rank and sparse components in a simplistic or ad hoc manner, often resulting in undesirable performance degradation compared to full-rank training. In this paper, we propose LOw-rank and Sparse pre-Training (LOST) for LLMs, a novel method that ingeniously integrates low-rank and sparse structures to enable effective training of LLMs from scratch under strict efficiency constraints. LOST applies singular value decomposition to weight matrices, preserving the dominant low-rank components, while allocating the remaining singular values to construct channel-wise sparse components to complement the expressiveness of low-rank training. We evaluate LOST on LLM pretraining ranging from 60M to 7B parameters. Our experiments show that LOST achieves competitive or superior performance compared to full-rank models, while significantly reducing both memory and compute overhead. Moreover, Code is available at https://github.com/JiaxiLi1/LOST-Low-rank-and-Sparse-Training-for-Large-Language-Models{LOST Repo}

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from computation for efficient inference. Sparse attention inference methods aim to reduce this computational burden; however, they also come with a troublesome performance degradation. We discover that one reason for this degradation is that the sparse calculation induces a distributional shift in the attention outputs. The distributional shift causes decoding-time queries to fail to align well with the appropriate keys from the prefill stage, leading to a drop in performance. We propose a simple, novel, and effective procedure for correcting this distributional shift, bringing the distribution of sparse attention outputs closer to that of quadratic attention. Our method can be applied on top of any sparse attention method, and results in an average 36%pt performance increase, recovering 88% of quadratic attention accuracy on the 131K RULER benchmark when applied on top of sliding window attention with sink tokens while only adding a small overhead. Our method can maintain approximately 98.5% sparsity over full quadratic attention, making our model 32 times faster than Flash Attention 2 when processing 1M token prefills.

Large language models (LLMs) now support extremely long context windows, but the quadratic complexity of vanilla attention results in significantly long Time-to-First-Token (TTFT) latency. Existing approaches to address this complexity require additional pretraining or finetuning, and often sacrifice model accuracy. In this paper, we first provide both theoretical and empirical foundations for near-lossless sparse attention. We find dynamically capturing head-specific sparse patterns at runtime with low overhead is crucial. To address this, we propose SampleAttention, an adaptive structured and near-lossless sparse attention. Leveraging observed significant sparse patterns, SampleAttention attends to a fixed percentage of adjacent tokens to capture local window patterns, and employs a two-stage query-guided key-value filtering approach, which adaptively select a minimum set of key-values with low overhead, to capture column stripe patterns. Comprehensive evaluations show that SampleAttention can seamlessly replace vanilla attention in off-the-shelf LLMs with nearly no accuracy loss, and reduces TTFT by up to 2.42times compared with FlashAttention.

Due to the auto-regressive nature of current video large language models (Video-LLMs), the inference latency increases as the input sequence length grows, posing challenges for the efficient processing of video sequences that are usually very long. We observe that during decoding, the attention scores of most tokens in Video-LLMs tend to be sparse and concentrated, with only certain tokens requiring comprehensive full attention. Based on this insight, we introduce Sparse-to-Dense (StD), a novel decoding strategy that integrates two distinct modules: one leveraging sparse top-K attention and the other employing dense full attention. These modules collaborate to accelerate Video-LLMs without loss. The fast (sparse) model speculatively decodes multiple tokens, while the slow (dense) model verifies them in parallel. StD is a tuning-free, plug-and-play solution that achieves up to a 1.94times walltime speedup in video processing. It maintains model performance while enabling a seamless transition from a standard Video-LLM to a sparse Video-LLM with minimal code modifications.

Training with sparse annotations is known to reduce the performance of object detectors. Previous methods have focused on proxies for missing ground truth annotations in the form of pseudo-labels for unlabeled boxes. We observe that existing methods suffer at higher levels of sparsity in the data due to noisy pseudo-labels. To prevent this, we propose an end-to-end system that learns to separate the proposals into labeled and unlabeled regions using Pseudo-positive mining. While the labeled regions are processed as usual, self-supervised learning is used to process the unlabeled regions thereby preventing the negative effects of noisy pseudo-labels. This novel approach has multiple advantages such as improved robustness to higher sparsity when compared to existing methods. We conduct exhaustive experiments on five splits on the PASCAL-VOC and COCO datasets achieving state-of-the-art performance. We also unify various splits used across literature for this task and present a standardized benchmark. On average, we improve by 2.6, 3.9 and 9.6 mAP over previous state-of-the-art methods on three splits of increasing sparsity on COCO. Our project is publicly available at https://www.cs.umd.edu/~sakshams/SparseDet.

Large Language Models (LLMs) with extended context lengths face significant computational challenges during the pre-filling phase, primarily due to the quadratic complexity of self-attention. Existing methods typically employ dynamic pattern matching and block-sparse low-level implementations. However, their reliance on local information for pattern identification fails to capture global contexts, and the coarse granularity of blocks leads to persistent internal sparsity, resulting in suboptimal accuracy and efficiency. To address these limitations, we propose AnchorAttention, a difference-aware, dynamic sparse attention mechanism that efficiently identifies critical attention regions at a finer stripe granularity while adapting to global contextual information, achieving superior speed and accuracy. AnchorAttention comprises three key components: (1) Pattern-based Anchor Computation, leveraging the commonalities present across all inputs to rapidly compute a set of near-maximum scores as the anchor; (2) Difference-aware Stripe Sparsity Identification, performing difference-aware comparisons with the anchor to quickly obtain discrete coordinates of significant regions in a stripe-like sparsity pattern; (3) Fine-grained Sparse Computation, replacing the traditional contiguous KV block loading approach with simultaneous discrete KV position loading to maximize sparsity rates while preserving full hardware computational potential. With its finer-grained sparsity strategy, AnchorAttention achieves higher sparsity rates at the same recall level, significantly reducing computation time. Compared to previous state-of-the-art methods, at a text length of 128k, it achieves a speedup of 1.44times while maintaining higher recall rates.

Neural networks are trained by choosing an architecture and training the parameters. The choice of architecture is often by trial and error or with Neural Architecture Search (NAS) methods. While NAS provides some automation, it often relies on discrete steps that optimize the architecture and then train the parameters. We introduce a novel neural network training framework that fundamentally transforms the process by learning architecture and parameters simultaneously with gradient descent. With the appropriate setting of the loss function, it can discover sparse and compact neural networks for given datasets. Central to our approach is a multi-scale encoder-decoder, in which the encoder embeds pairs of neural networks with similar functionalities close to each other (irrespective of their architectures and weights). To train a neural network with a given dataset, we randomly sample a neural network embedding in the embedding space and then perform gradient descent using our custom loss function, which incorporates a sparsity penalty to encourage compactness. The decoder generates a neural network corresponding to the embedding. Experiments demonstrate that our framework can discover sparse and compact neural networks maintaining a high performance.

Training large, deep neural networks to convergence can be prohibitively expensive. As a result, often only a small selection of popular, dense models are reused across different contexts and tasks. Increasingly, sparsely activated models, which seek to decouple model size from computation costs, are becoming an attractive alternative to dense models. Although more efficient in terms of quality and computation cost, sparse models remain data-hungry and costly to train from scratch in the large scale regime. In this work, we propose sparse upcycling -- a simple way to reuse sunk training costs by initializing a sparsely activated Mixture-of-Experts model from a dense checkpoint. We show that sparsely upcycled T5 Base, Large, and XL language models and Vision Transformer Base and Large models, respectively, significantly outperform their dense counterparts on SuperGLUE and ImageNet, using only ~50% of the initial dense pretraining sunk cost. The upcycled models also outperform sparse models trained from scratch on 100% of the initial dense pretraining computation budget.

Neurons in large language models often exhibit polysemanticity, simultaneously encoding multiple unrelated concepts and obscuring interpretability. Instead of relying on post-hoc methods, we present MoE-X, a Mixture-of-Experts (MoE) language model designed to be intrinsically interpretable. Our approach is motivated by the observation that, in language models, wider networks with sparse activations are more likely to capture interpretable factors. However, directly training such large sparse networks is computationally prohibitive. MoE architectures offer a scalable alternative by activating only a subset of experts for any given input, inherently aligning with interpretability objectives. In MoE-X, we establish this connection by rewriting the MoE layer as an equivalent sparse, large MLP. This approach enables efficient scaling of the hidden size while maintaining sparsity. To further enhance interpretability, we enforce sparse activation within each expert and redesign the routing mechanism to prioritize experts with the highest activation sparsity. These designs ensure that only the most salient features are routed and processed by the experts. We evaluate MoE-X on chess and natural language tasks, showing that it achieves performance comparable to dense models while significantly improving interpretability. MoE-X achieves a perplexity better than GPT-2, with interpretability surpassing even sparse autoencoder (SAE)-based approaches.

Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems. That changed with the recent development of approximate algorithms that leverage the distributional properties of sparse embeddings to speed up retrieval. Nonetheless, in much of the existing literature, evaluation has been limited to datasets with only a few million documents such as MSMARCO. It remains unclear how these systems behave on much larger datasets and what challenges lurk in larger scales. To bridge that gap, we investigate the behavior of state-of-the-art retrieval algorithms on massive datasets. We compare and contrast the recently-proposed Seismic and graph-based solutions adapted from dense retrieval. We extensively evaluate Splade embeddings of 138M passages from MsMarco-v2 and report indexing time and other efficiency and effectiveness metrics.

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical networks.

Camera-based 3D object detection in BEV (Bird's Eye View) space has drawn great attention over the past few years. Dense detectors typically follow a two-stage pipeline by first constructing a dense BEV feature and then performing object detection in BEV space, which suffers from complex view transformations and high computation cost. On the other side, sparse detectors follow a query-based paradigm without explicit dense BEV feature construction, but achieve worse performance than the dense counterparts. In this paper, we find that the key to mitigate this performance gap is the adaptability of the detector in both BEV and image space. To achieve this goal, we propose SparseBEV, a fully sparse 3D object detector that outperforms the dense counterparts. SparseBEV contains three key designs, which are (1) scale-adaptive self attention to aggregate features with adaptive receptive field in BEV space, (2) adaptive spatio-temporal sampling to generate sampling locations under the guidance of queries, and (3) adaptive mixing to decode the sampled features with dynamic weights from the queries. On the test split of nuScenes, SparseBEV achieves the state-of-the-art performance of 67.5 NDS. On the val split, SparseBEV achieves 55.8 NDS while maintaining a real-time inference speed of 23.5 FPS. Code is available at https://github.com/MCG-NJU/SparseBEV.

Vision-Language Models (VLMs) excel across diverse tasks but suffer from high inference costs in time and memory. Token sparsity mitigates inefficiencies in token usage, while neuron sparsity reduces high-dimensional computations, both offering promising solutions to enhance efficiency. Recently, these two sparsity paradigms have evolved largely in parallel, fostering the prevailing assumption that they function independently. However, a fundamental yet underexplored question remains: Do they truly operate in isolation, or is there a deeper underlying interplay that has yet to be uncovered? In this paper, we conduct the first comprehensive investigation into this question. By introducing and analyzing the matching mechanism between Core Neurons and Core Tokens, we found that key neurons and tokens for inference mutually influence and reinforce each other. Building on this insight, we propose CoreMatching, a co-adaptive sparse inference framework, which leverages the synergy between token and neuron sparsity to enhance inference efficiency. Through theoretical analysis and efficiency evaluations, we demonstrate that the proposed method surpasses state-of-the-art baselines on ten image understanding tasks and three hardware devices. Notably, on the NVIDIA Titan Xp, it achieved 5x FLOPs reduction and a 10x overall speedup. Code is released at https://github.com/wangqinsi1/2025-ICML-CoreMatching/tree/main.

With increasing demands for efficiency, information retrieval has developed a branch of sparse retrieval, further advancing towards inference-free retrieval where the documents are encoded during indexing time and there is no model-inference for queries. Existing sparse retrieval models rely on FLOPS regularization for sparsification, while this mechanism was originally designed for Siamese encoders, it is considered to be suboptimal in inference-free scenarios which is asymmetric. Previous attempts to adapt FLOPS for inference-free scenarios have been limited to rule-based methods, leaving the potential of sparsification approaches for inference-free retrieval models largely unexplored. In this paper, we explore ell_0 inspired sparsification manner for inference-free retrievers. Through comprehensive out-of-domain evaluation on the BEIR benchmark, our method achieves state-of-the-art performance among inference-free sparse retrieval models and is comparable to leading Siamese sparse retrieval models. Furthermore, we provide insights into the trade-off between retrieval effectiveness and computational efficiency, demonstrating practical value for real-world applications.

Scaling the context length of large language models (LLMs) offers significant benefits but is computationally expensive. This expense stems primarily from the self-attention mechanism, whose O(N^2) complexity with respect to sequence length presents a major bottleneck for both memory and latency. Fortunately, the attention matrix is often sparse, particularly for long sequences, suggesting an opportunity for optimization. Block-sparse attention has emerged as a promising solution that partitions sequences into blocks and skips computation for a subset of these blocks. However, the effectiveness of this method is highly dependent on the underlying attention patterns, which can lead to sub-optimal block-level sparsity. For instance, important key tokens for queries within a single block may be scattered across numerous other blocks, leading to computational redundancy. In this work, we propose Permuted Block-Sparse Attention (PBS-Attn), a plug-and-play method that leverages the permutation properties of attention to increase block-level sparsity and enhance the computational efficiency of LLM prefilling. We conduct comprehensive experiments on challenging real-world long-context datasets, demonstrating that PBS-Attn consistently outperforms existing block-sparse attention methods in model accuracy and closely matches the full attention baseline. Powered by our custom permuted-FlashAttention kernels, PBS-Attn achieves an end-to-end speedup of up to 2.75times in long-context prefilling, confirming its practical viability. Code available at https://github.com/xinghaow99/pbs-attn

Activation sparsity denotes the existence of substantial weakly-contributed elements within activation outputs that can be eliminated, benefiting many important applications concerned with large language models (LLMs). Although promoting greater activation sparsity within LLMs deserves deep studies, existing works lack comprehensive and quantitative research on the correlation between activation sparsity and potentially influential factors. In this paper, we present a comprehensive study on the quantitative scaling properties and influential factors of the activation sparsity within decoder-only Transformer-based LLMs. Specifically, we propose PPL-p% sparsity, a precise and performance-aware activation sparsity metric that is applicable to any activation function. Through extensive experiments, we find several important phenomena. Firstly, different activation functions exhibit comparable performance but opposite training-time sparsity trends. The activation ratio (i.e., 1-sparsity ratio) evolves as a convergent increasing power-law and decreasing logspace power-law with the amount of training data for SiLU-activated and ReLU-activated LLMs, respectively. These demonstrate that ReLU is more efficient as the activation function than SiLU and can leverage more training data to improve activation sparsity. Secondly, the activation ratio linearly increases with the width-depth ratio below a certain bottleneck point, indicating the potential advantage of a deeper architecture at a fixed parameter scale. Finally, at similar width-depth ratios, we surprisingly find that the limit value of activation sparsity varies weakly with the parameter scale, i.e., the activation patterns within LLMs are insensitive to the parameter scale. These empirical laws towards LLMs with greater activation sparsity have important implications for making LLMs more efficient and interpretable.

Recently, inspired by the concept of sparsity, Mixture-of-Experts (MoE) models have gained increasing popularity for scaling model size while keeping the number of activated parameters constant. In this study, we thoroughly investigate the sparsity of the dense LLaMA model by constructing MoE for both the attention (i.e., Attention MoE) and MLP (i.e., MLP MoE) modules in the transformer blocks. Specifically, we investigate different expert construction methods and granularities under the same activation conditions to analyze the impact of sparsifying the model. Additionally, to comprehensively evaluate the model's capabilities across various domains (e.g., conversation, code, math) after sparsification, we apply sparsity to the instructed large language models (LLMs) and construct instructed MoE models. To counteract the performance degradation resulting from increased sparsity, we design a two-stage post-training strategy to enhance model performance. Experiments on the LLaMA3 model demonstrate the potential effectiveness of this approach for future developments of instructed MoE models. The source codes and models are available at: https://github.com/OpenSparseLLMs/LLaMA-MoE-v2.

The recent literature in text classification is biased towards short text sequences (e.g., sentences or paragraphs). In real-world applications, multi-page multi-paragraph documents are common and they cannot be efficiently encoded by vanilla Transformer-based models. We compare different Transformer-based Long Document Classification (TrLDC) approaches that aim to mitigate the computational overhead of vanilla transformers to encode much longer text, namely sparse attention and hierarchical encoding methods. We examine several aspects of sparse attention (e.g., size of local attention window, use of global attention) and hierarchical (e.g., document splitting strategy) transformers on four document classification datasets covering different domains. We observe a clear benefit from being able to process longer text, and, based on our results, we derive practical advice of applying Transformer-based models on long document classification tasks.

Transformer-based architectures have become the prevailing backbone of large language models. However, the quadratic time and memory complexity of self-attention remains a fundamental obstacle to efficient long-context modeling. To address this limitation, recent research has introduced two principal categories of efficient attention mechanisms. Linear attention methods achieve linear complexity through kernel approximations, recurrent formulations, or fastweight dynamics, thereby enabling scalable inference with reduced computational overhead. Sparse attention techniques, in contrast, limit attention computation to selected subsets of tokens based on fixed patterns, block-wise routing, or clustering strategies, enhancing efficiency while preserving contextual coverage. This survey provides a systematic and comprehensive overview of these developments, integrating both algorithmic innovations and hardware-level considerations. In addition, we analyze the incorporation of efficient attention into largescale pre-trained language models, including both architectures built entirely on efficient attention and hybrid designs that combine local and global components. By aligning theoretical foundations with practical deployment strategies, this work aims to serve as a foundational reference for advancing the design of scalable and efficient language models.

Predicting high-dimensional or extreme multilabels, such as in medical coding, requires both accuracy and interpretability. Existing works often rely on local interpretability methods, failing to provide comprehensive explanations of the overall mechanism behind each label prediction within a multilabel set. We propose a mechanistic interpretability module called DIctionary Label Attention (\method) that disentangles uninterpretable dense embeddings into a sparse embedding space, where each nonzero element (a dictionary feature) represents a globally learned medical concept. Through human evaluations, we show that our sparse embeddings are more human understandable than its dense counterparts by at least 50 percent. Our automated dictionary feature identification pipeline, leveraging large language models (LLMs), uncovers thousands of learned medical concepts by examining and summarizing the highest activating tokens for each dictionary feature. We represent the relationships between dictionary features and medical codes through a sparse interpretable matrix, enhancing the mechanistic and global understanding of the model's predictions while maintaining competitive performance and scalability without extensive human annotation.

Long-context modeling is crucial for next-generation language models, yet the high computational cost of standard attention mechanisms poses significant computational challenges. Sparse attention offers a promising direction for improving efficiency while maintaining model capabilities. We present NSA, a Natively trainable Sparse Attention mechanism that integrates algorithmic innovations with hardware-aligned optimizations to achieve efficient long-context modeling. NSA employs a dynamic hierarchical sparse strategy, combining coarse-grained token compression with fine-grained token selection to preserve both global context awareness and local precision. Our approach advances sparse attention design with two key innovations: (1) We achieve substantial speedups through arithmetic intensity-balanced algorithm design, with implementation optimizations for modern hardware. (2) We enable end-to-end training, reducing pretraining computation without sacrificing model performance. As shown in Figure 1, experiments show the model pretrained with NSA maintains or exceeds Full Attention models across general benchmarks, long-context tasks, and instruction-based reasoning. Meanwhile, NSA achieves substantial speedups over Full Attention on 64k-length sequences across decoding, forward propagation, and backward propagation, validating its efficiency throughout the model lifecycle.

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.

Inference on large language models can be expensive in terms of the compute and memory costs involved, especially when long sequence lengths are used. In particular, the self-attention mechanism used in such models contributes significantly to these costs, which has resulted in several recent works that propose sparse attention approximations for inference. In this work, we propose to approximate the self-attention computation by focusing on the dimensionality of key vectors computed in the attention block. Our analysis reveals that the key vectors lie in a significantly lower-dimensional space, consistently across several datasets and models. Exploiting this observation, we propose Loki, a novel sparse attention method that ranks and selects tokens in the KV-cache based on attention scores computed in low-dimensional space. Our evaluations show that Loki is able to maintain the efficacy of the models better than other popular approximation methods, while speeding up the attention computation due to reduced data movement (load/store) and compute costs.

Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not environmental-friendly with much power cost. In this paper, we focus on low-rank optimization for efficient deep learning techniques. In the space domain, deep neural networks are compressed by low rank approximation of the network parameters, which directly reduces the storage requirement with a smaller number of network parameters. In the time domain, the network parameters can be trained in a few subspaces, which enables efficient training for fast convergence. The model compression in the spatial domain is summarized into three categories as pre-train, pre-set, and compression-aware methods, respectively. With a series of integrable techniques discussed, such as sparse pruning, quantization, and entropy coding, we can ensemble them in an integration framework with lower computational complexity and storage. Besides of summary of recent technical advances, we have two findings for motivating future works: one is that the effective rank outperforms other sparse measures for network compression. The other is a spatial and temporal balance for tensorized neural networks.

Recent work has proposed the linear representation hypothesis: that language models perform computation by manipulating one-dimensional representations of concepts ("features") in activation space. In contrast, we explore whether some language model representations may be inherently multi-dimensional. We begin by developing a rigorous definition of irreducible multi-dimensional features based on whether they can be decomposed into either independent or non-co-occurring lower-dimensional features. Motivated by these definitions, we design a scalable method that uses sparse autoencoders to automatically find multi-dimensional features in GPT-2 and Mistral 7B. These auto-discovered features include strikingly interpretable examples, e.g. circular features representing days of the week and months of the year. We identify tasks where these exact circles are used to solve computational problems involving modular arithmetic in days of the week and months of the year. Finally, we provide evidence that these circular features are indeed the fundamental unit of computation in these tasks with intervention experiments on Mistral 7B and Llama 3 8B, and we find further circular representations by breaking down the hidden states for these tasks into interpretable components.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

Understanding the internal representations of large language models (LLMs) remains a central challenge for interpretability research. Sparse autoencoders (SAEs) offer a promising solution by decomposing activations into interpretable features, but existing approaches rely on fixed sparsity constraints that fail to account for input complexity. We propose Adaptive Top K Sparse Autoencoders (AdaptiveK), a novel framework that dynamically adjusts sparsity levels based on the semantic complexity of each input. Leveraging linear probes, we demonstrate that context complexity is linearly encoded in LLM representations, and we use this signal to guide feature allocation during training. Experiments across three language models (Pythia-70M, Pythia-160M, and Gemma-2-2B) demonstrate that this complexity-driven adaptation significantly outperforms fixed-sparsity approaches on reconstruction fidelity, explained variance, and cosine similarity metrics while eliminating the computational burden of extensive hyperparameter tuning.

Large language models have high compute, latency, and memory requirements. While specialized accelerators such as GPUs and TPUs typically run these workloads, CPUs are more widely available and consume less energy. Accelerating LLMs with CPUs enables broader AI access at a lower cost and power consumption. This acceleration potential for CPUs is especially relevant during the memory-bound decoding stage of LLM inference, which processes one token at a time and is becoming increasingly utilized with reasoning models. We utilize Advanced Matrix Extensions (AMX) support on the latest Intel CPUs together with unstructured sparsity to achieve a 1.42 times reduction in end-to-end latency compared to the current PyTorch implementation by applying our technique in linear layers. We provide a set of open-source customized sparse kernels that can speed up any PyTorch model by automatically replacing all linear layers with our custom sparse implementation. Furthermore, we demonstrate for the first time the use of unstructured sparsity in the attention computation achieving a 1.14 times speedup over the current systems without compromising accuracy. Code: https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning/tree/main/SparAMX

In the era of foundation models with huge pre-training budgets, the downstream tasks have been shifted to the narrative of efficient and fast adaptation. For classification-based tasks in the domain of computer vision, the two most efficient approaches have been linear probing (LP) and visual prompting/reprogramming (VP); the former aims to learn a classifier in the form of a linear head on the features extracted by the pre-trained model, while the latter maps the input data to the domain of the source data on which the model was originally pre-trained on. Although extensive studies have demonstrated the differences between LP and VP in terms of downstream performance, we explore the capabilities of the two aforementioned methods via the sparsity axis: (a) Data sparsity: the impact of few-shot adaptation and (b) Model sparsity: the impact of lottery tickets (LT). We demonstrate that LT are not universal reprogrammers, i.e., for certain target datasets, reprogramming an LT yields significantly lower performance than the reprogrammed dense model although their corresponding upstream performance is similar. Further, we demonstrate that the calibration of dense models is always superior to that of their lottery ticket counterparts under both LP and VP regimes. Our empirical study opens a new avenue of research into VP for sparse models and encourages further understanding of the performance beyond the accuracy achieved by VP under constraints of sparsity. Code and logs can be accessed at https://github.com/landskape-ai/Reprogram_LT.

With growing size of Neural Networks (NNs), model sparsification to reduce the computational cost and memory demand for model inference has become of vital interest for both research and production. While many sparsification methods have been proposed and successfully applied on individual models, to the best of our knowledge their behavior and robustness has not yet been studied on large populations of models. With this paper, we address that gap by applying two popular sparsification methods on populations of models (so called model zoos) to create sparsified versions of the original zoos. We investigate the performance of these two methods for each zoo, compare sparsification layer-wise, and analyse agreement between original and sparsified populations. We find both methods to be very robust with magnitude pruning able outperform variational dropout with the exception of high sparsification ratios above 80%. Further, we find sparsified models agree to a high degree with their original non-sparsified counterpart, and that the performance of original and sparsified model is highly correlated. Finally, all models of the model zoos and their sparsified model twins are publicly available: modelzoos.cc.

The Backpropagation algorithm, widely used to train neural networks, has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, and avoid to back-propagate gradients in favour of using local learning rules, the recently introduced Forward-Forward algorithm replaces the traditional forward and backward passes of Backpropagation with two forward passes. In this work, we show that internal representations obtained with the Forward-Forward algorithm organize into robust, category-specific ensembles, composed by an extremely low number of active units (high sparsity). This is remarkably similar to what is observed in cortical representations during sensory processing. While not found in models trained with standard Backpropagation, sparsity emerges also in networks optimized by Backpropagation, on the same training objective of Forward-Forward. These results suggest that the learning procedure proposed by Forward-Forward may be superior to Backpropagation in modelling learning in the cortex, even when a backward pass is used.

Sparse autoencoders (SAEs) are widely used in mechanistic interpretability research for large language models; however, the state-of-the-art method of using k-sparse autoencoders lacks a theoretical grounding for selecting the hyperparameter k that represents the number of nonzero activations, often denoted by ell_0. In this paper, we reveal a theoretical link that the ell_2-norm of the sparse feature vector can be approximated with the ell_2-norm of the dense vector with a closed-form error, which allows sparse autoencoders to be trained without the need to manually determine ell_0. Specifically, we validate two applications of our theoretical findings. First, we introduce a new methodology that can assess the feature activations of pre-trained SAEs by computing the theoretically expected value from the input embedding, which has been overlooked by existing SAE evaluation methods and loss functions. Second, we introduce a novel activation function, top-AFA, which builds upon our formulation of approximate feature activation (AFA). This function enables top-k style activation without requiring a constant hyperparameter k to be tuned, dynamically determining the number of activated features for each input. By training SAEs on three intermediate layers to reconstruct GPT2 hidden embeddings for over 80 million tokens from the OpenWebText dataset, we demonstrate the empirical merits of this approach and compare it with current state-of-the-art k-sparse autoencoders. Our code is available at: https://github.com/SewoongLee/top-afa-sae.

Sparse Autoencoders (SAEs) have been proposed as an unsupervised approach to learn a decomposition of a model's latent space. This enables useful applications such as steering - influencing the output of a model towards a desired concept - without requiring labeled data. Current methods identify SAE features to steer by analyzing the input tokens that activate them. However, recent work has highlighted that activations alone do not fully describe the effect of a feature on the model's output. In this work, we draw a distinction between two types of features: input features, which mainly capture patterns in the model's input, and output features, which have a human-understandable effect on the model's output. We propose input and output scores to characterize and locate these types of features, and show that high values for both scores rarely co-occur in the same features. These findings have practical implications: after filtering out features with low output scores, we obtain 2-3x improvements when steering with SAEs, making them competitive with supervised methods.