Daily Papers

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

Vision tokenizers have gained a lot of attraction due to their scalability and compactness; previous works depend on old-school GAN-based hyperparameters, biased comparisons, and a lack of comprehensive analysis of the scaling behaviours. To tackle those issues, we introduce Grouped Spherical Quantization (GSQ), featuring spherical codebook initialization and lookup regularization to constrain codebook latent to a spherical surface. Our empirical analysis of image tokenizer training strategies demonstrates that GSQ-GAN achieves superior reconstruction quality over state-of-the-art methods with fewer training iterations, providing a solid foundation for scaling studies. Building on this, we systematically examine the scaling behaviours of GSQ, specifically in latent dimensionality, codebook size, and compression ratios, and their impact on model performance. Our findings reveal distinct behaviours at high and low spatial compression levels, underscoring challenges in representing high-dimensional latent spaces. We show that GSQ can restructure high-dimensional latent into compact, low-dimensional spaces, thus enabling efficient scaling with improved quality. As a result, GSQ-GAN achieves a 16x down-sampling with a reconstruction FID (rFID) of 0.50.

Scaling laws are a critical component of the LLM development pipeline, most famously as a way to forecast training decisions such as 'compute-optimally' trading-off parameter count and dataset size, alongside a more recent growing list of other crucial decisions. In this work, we ask whether compute-optimal scaling behaviour can be skill-dependent. In particular, we examine knowledge and reasoning-based skills such as knowledge-based QA and code generation, and we answer this question in the affirmative: scaling laws are skill-dependent. Next, to understand whether skill-dependent scaling is an artefact of the pretraining datamix, we conduct an extensive ablation of different datamixes and find that, also when correcting for datamix differences, knowledge and code exhibit fundamental differences in scaling behaviour. We conclude with an analysis of how our findings relate to standard compute-optimal scaling using a validation set, and find that a misspecified validation set can impact compute-optimal parameter count by nearly 50%, depending on its skill composition.

Most state-of-the-art point trackers are trained on synthetic data due to the difficulty of annotating real videos for this task. However, this can result in suboptimal performance due to the statistical gap between synthetic and real videos. In order to understand these issues better, we introduce CoTracker3, comprising a new tracking model and a new semi-supervised training recipe. This allows real videos without annotations to be used during training by generating pseudo-labels using off-the-shelf teachers. The new model eliminates or simplifies components from previous trackers, resulting in a simpler and often smaller architecture. This training scheme is much simpler than prior work and achieves better results using 1,000 times less data. We further study the scaling behaviour to understand the impact of using more real unsupervised data in point tracking. The model is available in online and offline variants and reliably tracks visible and occluded points.

The stability of language model pre-training and its effects on downstream performance are still understudied. Prior work shows that the training process can yield significantly different results in response to slight variations in initial conditions, e.g., the random seed. Crucially, the research community still lacks sufficient resources and tools to systematically investigate pre-training stability, particularly for decoder-only language models. We introduce the PolyPythias, a set of 45 new training runs for the Pythia model suite: 9 new seeds across 5 model sizes, from 14M to 410M parameters, resulting in about 7k new checkpoints that we release. Using these new 45 training runs, in addition to the 5 already available, we study the effects of different initial conditions determined by the seed -- i.e., parameters' initialisation and data order -- on (i) downstream performance, (ii) learned linguistic representations, and (iii) emergence of training phases. In addition to common scaling behaviours, our analyses generally reveal highly consistent training dynamics across both model sizes and initial conditions. Further, the new seeds for each model allow us to identify outlier training runs and delineate their characteristics. Our findings show the potential of using these methods to predict training stability.

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

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

In this work we revisit the most fundamental building block in deep learning, the multi-layer perceptron (MLP), and study the limits of its performance on vision tasks. Empirical insights into MLPs are important for multiple reasons. (1) Given the recent narrative "less inductive bias is better", popularized due to transformers eclipsing convolutional models, it is natural to explore the limits of this hypothesis. To that end, MLPs offer an ideal test bed, being completely free of any inductive bias. (2) MLPs have almost exclusively been the main protagonist in the deep learning theory literature due to their mathematical simplicity, serving as a proxy to explain empirical phenomena observed for more complex architectures. Surprisingly, experimental datapoints for MLPs are very difficult to find in the literature, especially when coupled with large pre-training protocols. This discrepancy between practice and theory is worrying: Do MLPs reflect the empirical advances exhibited by practical models? Or do theorists need to rethink the role of MLPs as a proxy? We provide insights into both these aspects. We show that the performance of MLPs drastically improves with scale (93% on CIFAR10, 79% on CIFAR100, 69% on TinyImageNet), highlighting that lack of inductive bias can indeed be compensated. We observe that MLPs mimic the behaviour of their modern counterparts faithfully, with some components in the learning setting however surprisingly exhibiting stronger or unexpected behaviours. Due to their inherent computational efficiency, large pre-training experiments become more accessible for academic researchers. All of our experiments were run on a single GPU.

Language modelling provides a step towards intelligent communication systems by harnessing large repositories of written human knowledge to better predict and understand the world. In this paper, we present an analysis of Transformer-based language model performance across a wide range of model scales -- from models with tens of millions of parameters up to a 280 billion parameter model called Gopher. These models are evaluated on 152 diverse tasks, achieving state-of-the-art performance across the majority. Gains from scale are largest in areas such as reading comprehension, fact-checking, and the identification of toxic language, but logical and mathematical reasoning see less benefit. We provide a holistic analysis of the training dataset and model's behaviour, covering the intersection of model scale with bias and toxicity. Finally we discuss the application of language models to AI safety and the mitigation of downstream harms.

This paper is the second in the series Commutative Scaling of Width and Depth (WD) about commutativity of infinite width and depth limits in deep neural networks. Our aim is to understand the behaviour of neural functions (functions that depend on a neural network model) as width and depth go to infinity (in some sense), and eventually identify settings under which commutativity holds, i.e. the neural function tends to the same limit no matter how width and depth limits are taken. In this paper, we formally introduce and define the commutativity framework, and discuss its implications on neural network design and scaling. We study commutativity for the neural covariance kernel which reflects how network layers separate data. Our findings extend previous results established in [55] by showing that taking the width and depth to infinity in a deep neural network with skip connections, when branches are suitably scaled to avoid exploding behaviour, result in the same covariance structure no matter how that limit is taken. This has a number of theoretical and practical implications that we discuss in the paper. The proof techniques in this paper are novel and rely on tools that are more accessible to readers who are not familiar with stochastic calculus (used in the proofs of WD(I))).

Activation Patching is a method of directly computing causal attributions of behavior to model components. However, applying it exhaustively requires a sweep with cost scaling linearly in the number of model components, which can be prohibitively expensive for SoTA Large Language Models (LLMs). We investigate Attribution Patching (AtP), a fast gradient-based approximation to Activation Patching and find two classes of failure modes of AtP which lead to significant false negatives. We propose a variant of AtP called AtP*, with two changes to address these failure modes while retaining scalability. We present the first systematic study of AtP and alternative methods for faster activation patching and show that AtP significantly outperforms all other investigated methods, with AtP* providing further significant improvement. Finally, we provide a method to bound the probability of remaining false negatives of AtP* estimates.

This work aims to understand how scaling improves language models, specifically in terms of training dynamics. We find that language models undergo loss deceleration early in training; an abrupt slowdown in the rate of loss improvement, resulting in piecewise linear behaviour of the loss curve in log-log space. Scaling up the model mitigates this transition by (1) decreasing the loss at which deceleration occurs, and (2) improving the log-log rate of loss improvement after deceleration. We attribute loss deceleration to a type of degenerate training dynamics we term zero-sum learning (ZSL). In ZSL, per-example gradients become systematically opposed, leading to destructive interference in per-example changes in loss. As a result, improving loss on one subset of examples degrades it on another, bottlenecking overall progress. Loss deceleration and ZSL provide new insights into the training dynamics underlying language model scaling laws, and could potentially be targeted directly to improve language models independent of scale. We make our code and artefacts available at: https://github.com/mirandrom/zsl

Deep learning approaches for black-box modelling of audio effects have shown promise, however, the majority of existing work focuses on nonlinear effects with behaviour on relatively short time-scales, such as guitar amplifiers and distortion. While recurrent and convolutional architectures can theoretically be extended to capture behaviour at longer time scales, we show that simply scaling the width, depth, or dilation factor of existing architectures does not result in satisfactory performance when modelling audio effects such as fuzz and dynamic range compression. To address this, we propose the integration of time-varying feature-wise linear modulation into existing temporal convolutional backbones, an approach that enables learnable adaptation of the intermediate activations. We demonstrate that our approach more accurately captures long-range dependencies for a range of fuzz and compressor implementations across both time and frequency domain metrics. We provide sound examples, source code, and pretrained models to faciliate reproducibility.

Humans are remarkably efficient at learning tasks from demonstrations, but today's imitation learning methods for robot manipulation often require hundreds or thousands of demonstrations per task. We investigate two fundamental priors for improving learning efficiency: decomposing manipulation trajectories into sequential alignment and interaction phases, and retrieval-based generalisation. Through 3,450 real-world rollouts, we systematically study this decomposition. We compare different design choices for the alignment and interaction phases, and examine generalisation and scaling trends relative to today's dominant paradigm of behavioural cloning with a single-phase monolithic policy. In the few-demonstrations-per-task regime (<10 demonstrations), decomposition achieves an order of magnitude improvement in data efficiency over single-phase learning, with retrieval consistently outperforming behavioural cloning for both alignment and interaction. Building on these insights, we develop Multi-Task Trajectory Transfer (MT3), an imitation learning method based on decomposition and retrieval. MT3 learns everyday manipulation tasks from as little as a single demonstration each, whilst also generalising to novel object instances. This efficiency enables us to teach a robot 1,000 distinct everyday tasks in under 24 hours of human demonstrator time. Through 2,200 additional real-world rollouts, we reveal MT3's capabilities and limitations across different task families. Videos of our experiments can be found on at https://www.robot-learning.uk/learning-1000-tasks.

Though Large Language Models (LLMs) have shown remarkable abilities in mathematics reasoning, they are still struggling with performing numeric operations accurately, such as addition and multiplication. Numbers can be tokenized into tokens in various ways by different LLMs and affect the numeric operations performance. Currently, there are two representatives: 1) Tokenize into 1-digit, and 2) Tokenize into 1sim 3 digit. The difference is roughly equivalent to using different numeral systems (namely base 10 or base 10^{3}). In light of this, we study the scaling behavior of different numeral systems in the context of transformer-based large language models. We empirically show that a base 10 system is consistently more data-efficient than a base 10^{2} or 10^{3} system across training data scale, model sizes under from-scratch training settings, while different number systems have very similar fine-tuning performances. We attribute this to higher token frequencies of a base 10 system. Additionally, we reveal extrapolation behavior patterns on addition and multiplication. We identify that base 100 and base 1000 systems struggle on token-level discernment and token-level operations. We also sheds light on the mechanism learnt by the models.

We describe our early efforts to red team language models in order to simultaneously discover, measure, and attempt to reduce their potentially harmful outputs. We make three main contributions. First, we investigate scaling behaviors for red teaming across 3 model sizes (2.7B, 13B, and 52B parameters) and 4 model types: a plain language model (LM); an LM prompted to be helpful, honest, and harmless; an LM with rejection sampling; and a model trained to be helpful and harmless using reinforcement learning from human feedback (RLHF). We find that the RLHF models are increasingly difficult to red team as they scale, and we find a flat trend with scale for the other model types. Second, we release our dataset of 38,961 red team attacks for others to analyze and learn from. We provide our own analysis of the data and find a variety of harmful outputs, which range from offensive language to more subtly harmful non-violent unethical outputs. Third, we exhaustively describe our instructions, processes, statistical methodologies, and uncertainty about red teaming. We hope that this transparency accelerates our ability to work together as a community in order to develop shared norms, practices, and technical standards for how to red team language models.

Scaling up language models has been empirically shown to improve performance on a wide range of downstream tasks. However, if we were to observe worse performance as a function of scale ("inverse scaling") on certain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al. 2022) identified eleven such inverse scaling tasks, evaluated on models of up to 280B parameters and up to 500 zettaFLOPs of training compute. This paper takes a closer look at these inverse scaling tasks. We evaluate models of up to 540B parameters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and training compute, only four out of the eleven tasks remain inverse scaling. Six out of the eleven tasks exhibit "U-shaped scaling", where performance decreases up to a certain size, and then increases again up to the largest model evaluated (the one remaining task displays positive scaling). In addition, we find that 1-shot examples and chain-of-thought can help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed in McKenzie et al. (2022) may not continue to hold for larger models, which we attribute to the presence of distractor tasks that only sufficiently large models can avoid.

One of the roadblocks for training generalist robotic models today is heterogeneity. Previous robot learning methods often collect data to train with one specific embodiment for one task, which is expensive and prone to overfitting. This work studies the problem of learning policy representations through heterogeneous pre-training on robot data across different embodiments and tasks at scale. We propose Heterogeneous Pre-trained Transformers (HPT), which pre-train a large, shareable trunk of a policy neural network to learn a task and embodiment agnostic shared representation. This general architecture aligns the specific proprioception and vision inputs from distinct embodiments to a short sequence of tokens and then processes such tokens to map to control robots for different tasks. Leveraging the recent large-scale multi-embodiment real-world robotic datasets as well as simulation, deployed robots, and human video datasets, we investigate pre-training policies across heterogeneity. We conduct experiments to investigate the scaling behaviors of training objectives, to the extent of 52 datasets. HPTs outperform several baselines and enhance the fine-tuned policy performance by over 20% on unseen tasks in multiple simulator benchmarks and real-world settings. See the project website (https://liruiw.github.io/hpt/) for code and videos.

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.

In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and segmentation under image-to-image translation, and show how diffusion models benefit from scaling training and test-time compute for these perception tasks. Through a careful analysis of these scaling behaviors, we present various techniques to efficiently train diffusion models for visual perception tasks. Our models achieve improved or comparable performance to state-of-the-art methods using significantly less data and compute. To use our code and models, see https://scaling-diffusion-perception.github.io .

The Eigenstate Thermalization Hypothesis (ETH) has been established as a cornerstone for understanding thermalization in quantum many-body systems. Recently, there has been growing interest in the full ETH, which extends the framework of the conventional ETH and postulates a smooth function to describe the multi-point correlations among matrix elements. Within this framework, free cumulants play a central role, and most previous studies have primarily focused on closed systems. In this paper, we extend the analysis to a system-bath setup, considering both an idealized case with a random-matrix bath and a more realistic scenario where the bath is modeled as a defect Ising chain. In both cases, we uncover a universal scaling of microcanonical free cumulants of system observables with respect to the interaction strength. Furthermore we establish a connection between this scaling behavior and the thermalization dynamics of the thermal free cumulants of corresponding observables.

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their parameters while processing an input. For these models, parameter count and computational requirement form two independent axes along which an increase leads to better performance. In this work we derive and justify scaling laws defined on these two variables which generalize those known for standard language models and describe the performance of a wide range of routing architectures trained via three different techniques. Afterwards we provide two applications of these laws: first deriving an Effective Parameter Count along which all models scale at the same rate, and then using the scaling coefficients to give a quantitative comparison of the three routing techniques considered. Our analysis derives from an extensive evaluation of Routing Networks across five orders of magnitude of size, including models with hundreds of experts and hundreds of billions of parameters.

Large language models (LLMs) demand substantial computational and memory resources, creating deployment challenges. Quantization-aware training (QAT) addresses these challenges by reducing model precision while maintaining performance. However, the scaling behavior of QAT, especially at 4-bit precision (W4A4), is not well understood. Existing QAT scaling laws often ignore key factors such as the number of training tokens and quantization granularity, which limits their applicability. This paper proposes a unified scaling law for QAT that models quantization error as a function of model size, training data volume, and quantization group size. Through 268 QAT experiments, we show that quantization error decreases as model size increases, but rises with more training tokens and coarser quantization granularity. To identify the sources of W4A4 quantization error, we decompose it into weight and activation components. Both components follow the overall trend of W4A4 quantization error, but with different sensitivities. Specifically, weight quantization error increases more rapidly with more training tokens. Further analysis shows that the activation quantization error in the FC2 layer, caused by outliers, is the primary bottleneck of W4A4 QAT quantization error. By applying mixed-precision quantization to address this bottleneck, we demonstrate that weight and activation quantization errors can converge to similar levels. Additionally, with more training data, weight quantization error eventually exceeds activation quantization error, suggesting that reducing weight quantization error is also important in such scenarios. These findings offer key insights for improving QAT research and development.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

For decades, researchers have developed task-specific models to address scientific challenges across diverse disciplines. Recently, large language models (LLMs) have shown enormous capabilities in handling general tasks; however, these models encounter difficulties in addressing real-world scientific problems, particularly in domains involving large-scale numerical data analysis, such as experimental high energy physics. This limitation is primarily due to BPE tokenization's inefficacy with numerical data. In this paper, we propose a task-agnostic architecture, BBT-Neutron, which employs a binary tokenization method to facilitate pretraining on a mixture of textual and large-scale numerical experimental data. We demonstrate the application of BBT-Neutron to Jet Origin Identification (JoI), a critical categorization challenge in high-energy physics that distinguishes jets originating from various quarks or gluons. Our results indicate that BBT-Neutron achieves comparable performance to state-of-the-art task-specific JoI models. Furthermore, we examine the scaling behavior of BBT-Neutron's performance with increasing data volume, suggesting the potential for BBT-Neutron to serve as a foundational model for particle physics data analysis, with possible extensions to a broad spectrum of scientific computing applications for Big Science experiments, industrial manufacturing and spacial computing. The project code is available at https://github.com/supersymmetry-technologies/bbt-neutron.

Large Multimodal Models (LMMs) excel in natural language and visual understanding but are challenged by exacting tasks such as Knowledge-based Visual Question Answering (KB-VQA) which involve the retrieval of relevant information from document collections to use in shaping answers to questions. We present an extensive training and evaluation framework, M2KR, for KB-VQA. M2KR contains a collection of vision and language tasks which we have incorporated into a single suite of benchmark tasks for training and evaluating general-purpose multi-modal retrievers. We use M2KR to develop PreFLMR, a pre-trained version of the recently developed Fine-grained Late-interaction Multi-modal Retriever (FLMR) approach to KB-VQA, and we report new state-of-the-art results across a range of tasks. We also present investigations into the scaling behaviors of PreFLMR intended to be useful in future developments in general-purpose multi-modal retrievers.

The success of today's large language models (LLMs) depends on the observation that larger models perform better. However, the origin of this neural scaling law -- the finding that loss decreases as a power law with model size -- remains unclear. Starting from two empirical principles -- that LLMs represent more things than the model dimensions (widths) they have (i.e., representations are superposed), and that words or concepts in language occur with varying frequencies -- we constructed a toy model to study the loss scaling with model size. We found that when superposition is weak, meaning only the most frequent features are represented without interference, the scaling of loss with model size depends on the underlying feature frequency; if feature frequencies follow a power law, so does the loss. In contrast, under strong superposition, where all features are represented but overlap with each other, the loss becomes inversely proportional to the model dimension across a wide range of feature frequency distributions. This robust scaling behavior is explained geometrically: when many more vectors are packed into a lower dimensional space, the interference (squared overlaps) between vectors scales inversely with that dimension. We then analyzed four families of open-sourced LLMs and found that they exhibit strong superposition and quantitatively match the predictions of our toy model. The Chinchilla scaling law turned out to also agree with our results. We conclude that representation superposition is an important mechanism underlying the observed neural scaling laws. We anticipate that these insights will inspire new training strategies and model architectures to achieve better performance with less computation and fewer parameters.

Scaling laws provide important insights that can guide the design of large language models (LLMs). Existing work has primarily focused on studying scaling laws for pretraining (upstream) loss. However, in transfer learning settings, in which LLMs are pretrained on an unsupervised dataset and then finetuned on a downstream task, we often also care about the downstream performance. In this work, we study the scaling behavior in a transfer learning setting, where LLMs are finetuned for machine translation tasks. Specifically, we investigate how the choice of the pretraining data and its size affect downstream performance (translation quality) as judged by two metrics: downstream cross-entropy and BLEU score. Our experiments indicate that the size of the finetuning dataset and the distribution alignment between the pretraining and downstream data significantly influence the scaling behavior. With sufficient alignment, both downstream cross-entropy and BLEU score improve monotonically with more pretraining data. In such cases, we show that it is possible to predict the downstream BLEU score with good accuracy using a log-law. However, there are also cases where moderate misalignment causes the BLEU score to fluctuate or get worse with more pretraining, whereas downstream cross-entropy monotonically improves. By analyzing these observations, we provide new practical insights for choosing appropriate pretraining data.

We present Fast Language-Image Pre-training (FLIP), a simple and more efficient method for training CLIP. Our method randomly masks out and removes a large portion of image patches during training. Masking allows us to learn from more image-text pairs given the same wall-clock time and contrast more samples per iteration with similar memory footprint. It leads to a favorable trade-off between accuracy and training time. In our experiments on 400 million image-text pairs, FLIP improves both accuracy and speed over the no-masking baseline. On a large diversity of downstream tasks, FLIP dominantly outperforms the CLIP counterparts trained on the same data. Facilitated by the speedup, we explore the scaling behavior of increasing the model size, data size, or training length, and report encouraging results and comparisons. We hope that our work will foster future research on scaling vision-language learning.

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of and connects these scaling laws. We identify variance-limited and resolution-limited scaling behavior for both dataset and model size, for a total of four scaling regimes. The variance-limited scaling follows simply from the existence of a well-behaved infinite data or infinite width limit, while the resolution-limited regime can be explained by positing that models are effectively resolving a smooth data manifold. In the large width limit, this can be equivalently obtained from the spectrum of certain kernels, and we present evidence that large width and large dataset resolution-limited scaling exponents are related by a duality. We exhibit all four scaling regimes in the controlled setting of large random feature and pretrained models and test the predictions empirically on a range of standard architectures and datasets. We also observe several empirical relationships between datasets and scaling exponents under modifications of task and architecture aspect ratio. Our work provides a taxonomy for classifying different scaling regimes, underscores that there can be different mechanisms driving improvements in loss, and lends insight into the microscopic origins of and relationships between scaling exponents.

Enabling LLMs to improve their outputs by using more test-time computation is a critical step towards building generally self-improving agents that can operate on open-ended natural language. In this paper, we study the scaling of inference-time computation in LLMs, with a focus on answering the question: if an LLM is allowed to use a fixed but non-trivial amount of inference-time compute, how much can it improve its performance on a challenging prompt? Answering this question has implications not only on the achievable performance of LLMs, but also on the future of LLM pretraining and how one should tradeoff inference-time and pre-training compute. Despite its importance, little research attempted to understand the scaling behaviors of various test-time inference methods. Moreover, current work largely provides negative results for a number of these strategies. In this work, we analyze two primary mechanisms to scale test-time computation: (1) searching against dense, process-based verifier reward models; and (2) updating the model's distribution over a response adaptively, given the prompt at test time. We find that in both cases, the effectiveness of different approaches to scaling test-time compute critically varies depending on the difficulty of the prompt. This observation motivates applying a "compute-optimal" scaling strategy, which acts to most effectively allocate test-time compute adaptively per prompt. Using this compute-optimal strategy, we can improve the efficiency of test-time compute scaling by more than 4x compared to a best-of-N baseline. Additionally, in a FLOPs-matched evaluation, we find that on problems where a smaller base model attains somewhat non-trivial success rates, test-time compute can be used to outperform a 14x larger model.

Speech Language Models (SLMs) aim to learn language from raw audio, without textual resources. Despite significant advances, our current models exhibit weak syntax and semantic abilities. However, if the scaling properties of neural language models hold for the speech modality, these abilities will improve as the amount of compute used for training increases. In this paper, we use models of this scaling behavior to estimate the scale at which our current methods will yield a SLM with the English proficiency of text-based Large Language Models (LLMs). We establish a strong correlation between pre-training loss and downstream syntactic and semantic performance in SLMs and LLMs, which results in predictable scaling of linguistic performance. We show that the linguistic performance of SLMs scales up to three orders of magnitude more slowly than that of text-based LLMs. Additionally, we study the benefits of synthetic data designed to boost semantic understanding and the effects of coarser speech tokenization.

Generative models have made significant impacts across various domains, largely due to their ability to scale during training by increasing data, computational resources, and model size, a phenomenon characterized by the scaling laws. Recent research has begun to explore inference-time scaling behavior in Large Language Models (LLMs), revealing how performance can further improve with additional computation during inference. Unlike LLMs, diffusion models inherently possess the flexibility to adjust inference-time computation via the number of denoising steps, although the performance gains typically flatten after a few dozen. In this work, we explore the inference-time scaling behavior of diffusion models beyond increasing denoising steps and investigate how the generation performance can further improve with increased computation. Specifically, we consider a search problem aimed at identifying better noises for the diffusion sampling process. We structure the design space along two axes: the verifiers used to provide feedback, and the algorithms used to find better noise candidates. Through extensive experiments on class-conditioned and text-conditioned image generation benchmarks, our findings reveal that increasing inference-time compute leads to substantial improvements in the quality of samples generated by diffusion models, and with the complicated nature of images, combinations of the components in the framework can be specifically chosen to conform with different application scenario.

As the marginal cost of scaling computation (data and parameters) during model pre-training continues to increase substantially, test-time scaling (TTS) has emerged as a promising direction for improving generative model performance by allocating additional computation at inference time. While TTS has demonstrated significant success across multiple language tasks, there remains a notable gap in understanding the test-time scaling behaviors of image and video generative models (diffusion-based or flow-based models). Although recent works have initiated exploration into inference-time strategies for vision tasks, these approaches face critical limitations: being constrained to task-specific domains, exhibiting poor scalability, or falling into reward over-optimization that sacrifices sample diversity. In this paper, we propose Evolutionary Search (EvoSearch), a novel, generalist, and efficient TTS method that effectively enhances the scalability of both image and video generation across diffusion and flow models, without requiring additional training or model expansion. EvoSearch reformulates test-time scaling for diffusion and flow models as an evolutionary search problem, leveraging principles from biological evolution to efficiently explore and refine the denoising trajectory. By incorporating carefully designed selection and mutation mechanisms tailored to the stochastic differential equation denoising process, EvoSearch iteratively generates higher-quality offspring while preserving population diversity. Through extensive evaluation across both diffusion and flow architectures for image and video generation tasks, we demonstrate that our method consistently outperforms existing approaches, achieves higher diversity, and shows strong generalizability to unseen evaluation metrics. Our project is available at the website https://tinnerhrhe.github.io/evosearch.

Recent significant advances in text-to-image models unlock the possibility of training vision systems using synthetic images, potentially overcoming the difficulty of collecting curated data at scale. It is unclear, however, how these models behave at scale, as more synthetic data is added to the training set. In this paper we study the scaling laws of synthetic images generated by state of the art text-to-image models, for the training of supervised models: image classifiers with label supervision, and CLIP with language supervision. We identify several factors, including text prompts, classifier-free guidance scale, and types of text-to-image models, that significantly affect scaling behavior. After tuning these factors, we observe that synthetic images demonstrate a scaling trend similar to, but slightly less effective than, real images in CLIP training, while they significantly underperform in scaling when training supervised image classifiers. Our analysis indicates that the main reason for this underperformance is the inability of off-the-shelf text-to-image models to generate certain concepts, a limitation that significantly impairs the training of image classifiers. Our findings also suggest that scaling synthetic data can be particularly effective in scenarios such as: (1) when there is a limited supply of real images for a supervised problem (e.g., fewer than 0.5 million images in ImageNet), (2) when the evaluation dataset diverges significantly from the training data, indicating the out-of-distribution scenario, or (3) when synthetic data is used in conjunction with real images, as demonstrated in the training of CLIP models.

Pretraining large language models (LLMs) is resource-intensive, often requiring months of training time even with high-end GPU clusters. There are two approaches of mitigating such computational demands: reusing smaller models to train larger ones (upcycling), and training computationally efficient models like mixture-of-experts (MoE). In this paper, we study the upcycling of LLMs to MoE models, of which the scaling behavior remains underexplored. Through extensive experiments, we identify empirical scaling laws that describe how performance depends on dataset size and model configuration. Particularly, we show that, while scaling these factors improves performance, there is a novel interaction term between the dense and upcycled training dataset that limits the efficiency of upcycling at large computational budgets. Based on these findings, we provide guidance to scale upcycling, and establish conditions under which upcycling outperforms from-scratch trainings within budget constraints.

In this work, we provide a large-scale empirical study of the scaling properties of multilingual neural machine translation models. We examine how increases in the model size affect the model performance and investigate the role of the training mixture composition on the scaling behavior. We find that changing the weightings of the individual language pairs in the training mixture only affect the multiplicative factor of the scaling law. In particular, we observe that multilingual models trained using different mixing rates all exhibit the same scaling exponent. Through a novel joint scaling law formulation, we compute the effective number of parameters allocated to each language pair and examine the role of language similarity in the scaling behavior of our models. We find little evidence that language similarity has any impact. In contrast, the direction of the multilinguality plays a significant role, with models translating from multiple languages into English having a larger number of effective parameters per task than their reversed counterparts. Finally, we leverage our observations to predict the performance of multilingual models trained with any language weighting at any scale, significantly reducing efforts required for language balancing in large multilingual models. Our findings apply to both in-domain and out-of-domain test sets and to multiple evaluation metrics, such as ChrF and BLEURT.

Large language models exhibit exceptional generalization capabilities, primarily attributed to the utilization of diversely sourced data. However, conventional practices in integrating this diverse data heavily rely on heuristic schemes, lacking theoretical guidance. This research tackles these limitations by investigating strategies based on low-cost proxies for data mixtures, with the aim of streamlining data curation to enhance training efficiency. Specifically, we propose a unified scaling law, termed BiMix, which accurately models the bivariate scaling behaviors of both data quantity and mixing proportions. We conduct systematic experiments and provide empirical evidence for the predictive power and fundamental principles of BiMix. Notably, our findings reveal that entropy-driven training-free data mixtures can achieve comparable or even better performance than more resource-intensive methods. We hope that our quantitative insights can shed light on further judicious research and development in cost-effective language modeling.

Scaling up neural networks has led to remarkable performance across a wide range of tasks. Moreover, performance often follows reliable scaling laws as a function of training set size, model size, and compute, which offers valuable guidance as large-scale experiments are becoming increasingly expensive. However, previous work on scaling laws has primarily used private data \& models or focused on uni-modal language or vision learning. To address these limitations, we investigate scaling laws for contrastive language-image pre-training (CLIP) with the public LAION dataset and the open-source OpenCLIP repository. Our large-scale experiments involve models trained on up to two billion image-text pairs and identify power law scaling for multiple downstream tasks including zero-shot classification, retrieval, linear probing, and end-to-end fine-tuning. We find that the training distribution plays a key role in scaling laws as the OpenAI and OpenCLIP models exhibit different scaling behavior despite identical model architectures and similar training recipes. We open-source our evaluation workflow and all models, including the largest public CLIP models, to ensure reproducibility and make scaling laws research more accessible. Source code and instructions to reproduce this study will be available at https://github.com/LAION-AI/scaling-laws-openclip

Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks. However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using heuristics, without verifying the underlying reasoning steps. This limitation results in false positive solutions, where models may produce correct final answers but with flawed deduction paths. In this paper, we systematically examine the prevalence of false positive solutions in mathematical problem solving for language models. We analyze the characteristics and extent of this issue across different open-source models, datasets of varying difficulty levels, and decoding strategies. Specifically, we explore how false positives influence the inference time scaling behavior of language models. Our experimental results reveal that: (1) false positive solutions persist across different models, datasets, and decoding methods, (2) sampling-based inference time scaling methods do not alleviate the problem, and (3) the pass@N evaluation metric is more susceptible to false positives, suggesting a significantly lower scaling ceiling than what automatic evaluations indicate. Additionally, we analyze specific instances of false positives and discuss potential limitations in self-improvement techniques and synthetic data generation under such conditions. Our data and code are publicly available at https://github.com/Wloner0809/False-Positives-in-Math.

Scaling laws offer valuable insights into the design of time series foundation models (TSFMs). However, previous research has largely focused on the scaling laws of TSFMs for in-distribution (ID) data, leaving their out-of-distribution (OOD) scaling behavior and the influence of model architectures less explored. In this work, we examine two common TSFM architectures, encoder-only and decoder-only Transformers, and investigate their scaling behavior on both ID and OOD data. These models are trained and evaluated across varying parameter counts, compute budgets, and dataset sizes. Our experiments reveal that the log-likelihood loss of TSFMs exhibits similar scaling behavior in both OOD and ID settings. We further compare the scaling properties across different architectures, incorporating two state-of-the-art TSFMs as case studies, showing that model architecture plays a significant role in scaling. The encoder-only Transformers demonstrate better scalability than the decoder-only Transformers, while the architectural enhancements in the two advanced TSFMs primarily improve ID performance but reduce OOD scalability. While scaling up TSFMs is expected to drive performance breakthroughs, the lack of a comprehensive understanding of TSFM scaling laws has hindered the development of a robust framework to guide model scaling. We fill this gap in this work by synthesizing our findings and providing practical guidelines for designing and scaling larger TSFMs with enhanced model capabilities.

Large Language Models (LLMs) excel in diverse tasks but often underperform in specialized fields due to limited domain-specific or proprietary corpus. Continual pre-training (CPT) enhances LLM capabilities by imbuing new domain-specific or proprietary knowledge while replaying general corpus to prevent catastrophic forgetting. The data mixture ratio of general corpus and domain-specific corpus, however, has been chosen heuristically, leading to sub-optimal training efficiency in practice. In this context, we attempt to re-visit the scaling behavior of LLMs under the hood of CPT, and discover a power-law relationship between loss, mixture ratio, and training tokens scale. We formalize the trade-off between general and domain-specific capabilities, leading to a well-defined Critical Mixture Ratio (CMR) of general and domain data. By striking the balance, CMR maintains the model's general ability and achieves the desired domain transfer, ensuring the highest utilization of available resources. Considering the balance between efficiency and effectiveness, CMR can be regarded as the optimal mixture ratio. Through extensive experiments, we ascertain the predictability of CMR, propose CMR scaling law and have substantiated its generalization. These findings offer practical guidelines for optimizing LLM training in specialized domains, ensuring both general and domain-specific performance while efficiently managing training resources.

While large language models (LLMs) often adopt finetuning to unlock their capabilities for downstream applications, our understanding on the inductive biases (especially the scaling properties) of different finetuning methods is still limited. To fill this gap, we conduct systematic experiments studying whether and how different scaling factors, including LLM model size, pretraining data size, new finetuning parameter size and finetuning data size, affect the finetuning performance. We consider two types of finetuning -- full-model tuning (FMT) and parameter efficient tuning (PET, including prompt tuning and LoRA), and explore their scaling behaviors in the data-limited regime where the LLM model size substantially outweighs the finetuning data size. Based on two sets of pretrained bilingual LLMs from 1B to 16B and experiments on bilingual machine translation and multilingual summarization benchmarks, we find that 1) LLM finetuning follows a powerbased multiplicative joint scaling law between finetuning data size and each other scaling factor; 2) LLM finetuning benefits more from LLM model scaling than pretraining data scaling, and PET parameter scaling is generally ineffective; and 3) the optimal finetuning method is highly task- and finetuning data-dependent. We hope our findings could shed light on understanding, selecting and developing LLM finetuning methods.

Scaling laws for large language models (LLMs) predict model performance based on parameters like size and training data. However, differences in training configurations and data processing across model families lead to significant variations in benchmark performance, making it difficult for a single scaling law to generalize across all LLMs. On the other hand, training family-specific scaling laws requires training models of varying sizes for every family. In this work, we propose Skills Scaling Laws (SSLaws, pronounced as Sloth), a novel scaling law that leverages publicly available benchmark data and assumes LLM performance is driven by low-dimensional latent skills, such as reasoning and instruction following. These latent skills are influenced by computational resources like model size and training tokens but with varying efficiencies across model families. Sloth exploits correlations across benchmarks to provide more accurate and interpretable predictions while alleviating the need to train multiple LLMs per family. We present both theoretical results on parameter identification and empirical evaluations on 12 prominent benchmarks, from Open LLM Leaderboard v1/v2, demonstrating that Sloth predicts LLM performance efficiently and offers insights into scaling behaviors for complex downstream tasks and increased test-time compute.

The current focus of AI research is shifting from emphasizing model training towards enhancing evaluation quality, a transition that is crucial for driving further advancements in AI systems. Traditional evaluation methods typically rely on reward models assigning scalar preference scores to outputs. Although effective, such approaches lack interpretability, leaving users often uncertain about why a reward model rates a particular response as high or low. The advent of LLM-as-a-Judge provides a more scalable and interpretable method of supervision, offering insights into the decision-making process. Moreover, with the emergence of large reasoning models, which consume more tokens for deeper thinking and answer refinement, scaling test-time computation in the LLM-as-a-Judge paradigm presents an avenue for further boosting performance and providing more interpretability through reasoning traces. In this paper, we introduce J1-7B, which is first supervised fine-tuned on reflection-enhanced datasets collected via rejection-sampling and subsequently trained using Reinforcement Learning (RL) with verifiable rewards. At inference time, we apply Simple Test-Time Scaling (STTS) strategies for additional performance improvement. Experimental results demonstrate that J1-7B surpasses the previous state-of-the-art LLM-as-a-Judge by 4.8\% and exhibits a 5.1\% stronger scaling trend under STTS. Additionally, we present three key findings: (1) Existing LLM-as-a-Judge does not inherently exhibit such scaling trend. (2) Model simply fine-tuned on reflection-enhanced datasets continues to demonstrate similarly weak scaling behavior. (3) Significant scaling trend emerges primarily during the RL phase, suggesting that effective STTS capability is acquired predominantly through RL training.

We continue our analysis on conductivity in the anisotropic background by employing the D-brane probe technique, where the D-branes play the role of charge carriers. The DC and AC conductivity for massless charge carriers are obtained analytically, while interesting curves for the AC conductivity are also plotted. For massive charge carriers, we calculate the DC and AC conductivities in the dilute limit and we fix the parameters in the Einstein-Maxwell-dilaton theory so that the background exhibits the same scaling behaviors as those for real-world strange metals. The DC conductivity at finite density is also computed.

Discovering scaling laws for predicting model performance at scale is a fundamental and open-ended challenge, mostly reliant on slow, case specific human experimentation. To investigate the potential for LLMs to automate this process, we collect over 5,000 experiments from existing literature and curate seven diverse scaling law discovery tasks. While existing agents struggle to produce accurate law formulas, this paper introduces SLDAgent, an evolution-based agent that co-optimize the scaling law model and the parameters, enabling it to autonomously explore complex relationships between variables. For the first time, we demonstrates that SLDAgent can automatically discover laws that exhibit consistently more accurate extrapolation than their established, human-derived counterparts across all tasks. Through comprehensive analysis, we elucidate why these discovered laws are superior and verify their practical utility in both pretraining and finetuning applications. This work establishes a new paradigm for agentic scientific discovery, showing that AI systems can understand their own scaling behavior, and can contribute novel and practical knowledge back to the research community.

Large language models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks. However, existing approaches mainly rely on imitation learning and struggle to achieve effective test-time scaling. While reinforcement learning (RL) holds promise for enabling self-exploration and learning from feedback, recent attempts yield only modest improvements in complex reasoning. In this paper, we present T1 to scale RL by encouraging exploration and understand inference scaling. We first initialize the LLM using synthesized chain-of-thought data that integrates trial-and-error and self-verification. To scale RL training, we promote increased sampling diversity through oversampling. We further employ an entropy bonus as an auxiliary loss, alongside a dynamic anchor for regularization to facilitate reward optimization. We demonstrate that T1 with open LLMs as its base exhibits inference scaling behavior and achieves superior performance on challenging math reasoning benchmarks. For example, T1 with Qwen2.5-32B as the base model outperforms the recent Qwen QwQ-32B-Preview model on MATH500, AIME2024, and Omni-math-500. More importantly, we present a simple strategy to examine inference scaling, where increased inference budgets directly lead to T1's better performance without any additional verification. We will open-source the T1 models and the data used to train them at https://github.com/THUDM/T1.

We present MiroThinker v1.0, an open-source research agent designed to advance tool-augmented reasoning and information-seeking capabilities. Unlike previous agents that only scale up model size or context length, MiroThinker explores interaction scaling at the model level, systematically training the model to handle deeper and more frequent agent-environment interactions as a third dimension of performance improvement. Unlike LLM test-time scaling, which operates in isolation and risks degradation with longer reasoning chains, interactive scaling leverages environment feedback and external information acquisition to correct errors and refine trajectories. Through reinforcement learning, the model achieves efficient interaction scaling: with a 256K context window, it can perform up to 600 tool calls per task, enabling sustained multi-turn reasoning and complex real-world research workflows. Across four representative benchmarks-GAIA, HLE, BrowseComp, and BrowseComp-ZH-the 72B variant achieves up to 81.9%, 37.7%, 47.1%, and 55.6% accuracy respectively, surpassing previous open-source agents and approaching commercial counterparts such as GPT-5-high. Our analysis reveals that MiroThinker benefits from interactive scaling consistently: research performance improves predictably as the model engages in deeper and more frequent agent-environment interactions, demonstrating that interaction depth exhibits scaling behaviors analogous to model size and context length. These findings establish interaction scaling as a third critical dimension for building next-generation open research agents, complementing model capacity and context windows.

Test-time scaling has emerged as a transformative paradigm for enhancing the performance of large reasoning models, enabling dynamic allocation of computational resources during inference. However, as the landscape of reasoning models rapidly expands, a critical question remains: how can we systematically compare and evaluate the test-time scaling capabilities across different models? In this paper, we introduce ARISE (Adaptive Resolution-aware Scaling Evaluation), a novel metric specifically designed to assess the test-time scaling effectiveness of large reasoning models. Unlike existing evaluation approaches, ARISE incorporates two key innovations: (1) sample-level awareness that effectively penalizes negative scaling behaviors where increased computation leads to performance degradation, and (2) a dynamic sampling mechanism that mitigates the impact of accuracy fluctuations and token count instability on the final assessment. We conduct comprehensive experiments evaluating state-of-the-art reasoning models across diverse domains including mathematical reasoning, code generation, and agentic tasks. Our results demonstrate that ARISE provides a reliable and fine-grained measurement of test-time scaling capabilities, revealing significant variations in scaling efficiency across models. Notably, our evaluation identifies Claude Opus as exhibiting superior scaling characteristics compared to other contemporary reasoning models.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss decreases predictably as the model size increases, in line with established scaling law; yet no scaling law for task has been established and the task performances are far from predictable during scaling. Task performances typically show minor gains on small models until they improve dramatically once models exceed a size threshold, exemplifying the ``emergent abilities''. In this study, we discover that small models, although they exhibit minor performance, demonstrate critical and consistent task performance improvements that are not captured by conventional evaluation strategies due to insufficient measurement resolution. To measure such improvements, we introduce PassUntil, an evaluation strategy through massive sampling in the decoding phase. We conduct quantitative investigations into the scaling law of task performance. Firstly, a strict task scaling law is identified, enhancing the predictability of task performances. Remarkably, we are able to predict the performance of the 2.4B model on code generation with merely 0.05\% deviation before training starts. Secondly, underpinned by PassUntil, we observe concrete evidence of emergent abilities and ascertain that they are not in conflict with the continuity of performance improvement. Their semblance to break-through is that their scaling curve cannot be fitted by standard scaling law function. We then introduce a mathematical definition for the emergent abilities. Through the definition, we refute a prevalent ``multi-step reasoning hypothesis'' regarding the genesis of emergent abilities and propose a new hypothesis with a satisfying fit to the observed scaling curve.

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. This reproduces many observations about neural scaling laws. First, our model makes a prediction about why the scaling of performance with training time and with model size have different power law exponents. Consequently, the theory predicts an asymmetric compute-optimal scaling rule where the number of training steps are increased faster than model parameters, consistent with recent empirical observations. Second, it has been observed that early in training, networks converge to their infinite-width dynamics at a rate 1/width but at late time exhibit a rate width^{-c}, where c depends on the structure of the architecture and task. We show that our model exhibits this behavior. Lastly, our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning domains, however, where increasing the parameter count of a model often hurts its final performance. In this paper, we demonstrate that incorporating Mixture-of-Expert (MoE) modules, and in particular Soft MoEs (Puigcerver et al., 2023), into value-based networks results in more parameter-scalable models, evidenced by substantial performance increases across a variety of training regimes and model sizes. This work thus provides strong empirical evidence towards developing scaling laws for reinforcement learning.

Predictable behavior from scaling advanced AI systems is an extremely desirable property. Although a well-established literature exists on how pretraining performance scales, the literature on how particular downstream capabilities scale is significantly muddier. In this work, we take a step back and ask: why has predicting specific downstream capabilities with scale remained elusive? While many factors are certainly responsible, we identify a new factor that makes modeling scaling behavior on widely used multiple-choice question-answering benchmarks challenging. Using five model families and twelve well-established multiple-choice benchmarks, we show that downstream performance is computed from negative log likelihoods via a sequence of transformations that progressively degrade the statistical relationship between performance and scale. We then reveal the mechanism causing this degradation: downstream metrics require comparing the correct choice against a small number of specific incorrect choices, meaning accurately predicting downstream capabilities requires predicting not just how probability mass concentrates on the correct choice with scale, but also how probability mass fluctuates on specific incorrect choices with scale. We empirically study how probability mass on the correct choice co-varies with probability mass on incorrect choices with increasing compute, suggesting that scaling laws for incorrect choices might be achievable. Our work also explains why pretraining scaling laws are commonly regarded as more predictable than downstream capabilities and contributes towards establishing scaling-predictable evaluations of frontier AI models.

We study the scaling properties of avalanche activity in the two-dimensional Abelian sandpile model. Instead of the conventional avalanche size distribution, we analyze the site activity distribution, which measures how often a site participates in avalanches when grains are added across the lattice. Using numerical simulations for system sizes up to \(L = 160\), averaged over \(10^4\) configurations, we determine the probability distribution \(P(A, L)\) of site activities. The results show that \(P(A, L)\) follows a finite-size scaling form \[ P(A, L) \sim L^{-2} F\Big(A{L^2}\Big). \] For small values \(A \ll L^2\) the scaling function behaves as \[ F(u) \sim u^{-1/2}, \quad corresponding to \quad P(A) \sim 1{L}, \] while for large activities \(A \sim O(L^2)\) the distribution decays as \[ F(u) \sim \exp\big(-c_3 u - c_4 u^2\big). \] The crossover between these two regimes occurs at \[ A^* \sim 0.1 \, L^2, \] marking the threshold between typical and highly excitable sites. This characterization of local avalanche activity provides complementary information to the usual avalanche size statistics, highlighting how local regions serve as frequent conduits for critical dynamics. These results may help connect sandpile models to real-world self-organized critical systems where only partial local activity can be observed.

The deployment of ever-larger machine learning models reflects a growing consensus that the more expressive the modelx2013and the more data one has access tox2013the more one can improve performance. As models get deployed in a variety of real world scenarios, they inevitably face strategic environments. In this work, we consider the natural question of how the interplay of models and strategic interactions affects scaling laws. We find that strategic interactions can break the conventional view of scaling lawsx2013meaning that performance does not necessarily monotonically improve as models get larger and/ or more expressive (even with infinite data). We show the implications of this phenomenon in several contexts including strategic regression, strategic classification, and multi-agent reinforcement learning through examples of strategic environments in whichx2013by simply restricting the expressivity of one's model or policy classx2013one can achieve strictly better equilibrium outcomes. Motivated by these examples, we then propose a new paradigm for model-selection in games wherein an agent seeks to choose amongst different model classes to use as their action set in a game.

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~80 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.

As large language models (LLMs) continue to grow in size, distributed inference has become increasingly important. Model-parallel strategies must now efficiently scale not only across multiple GPUs but also across multiple nodes. In this work, we present a detailed performance study of multi-node distributed inference using LLMs on GPU-based supercomputers. We conduct experiments with several state-of-the-art inference engines alongside YALIS, a research-oriented prototype engine designed for controlled experimentation. We analyze the strong-scaling behavior of different model-parallel schemes and identify key bottlenecks. Since all-reduce operations are a common performance bottleneck, we develop NVRAR, a hierarchical all-reduce algorithm based on recursive doubling with NVSHMEM. NVRAR achieves up to 1.9x-3.6x lower latency than NCCL for message sizes between 128 KB and 2 MB on HPE Slingshot and InfiniBand interconnects. Integrated into YALIS, NVRAR achieves up to a 1.72x reduction in end-to-end batch latency for the Llama 3.1 405B model in multi-node decode-heavy workloads using tensor parallelism.

We introduce SuperClass, a super simple classification method for vision-language pre-training on image-text data. Unlike its contrastive counterpart CLIP who contrast with a text encoder, SuperClass directly utilizes tokenized raw text as supervised classification labels, without the need for additional text filtering or selection. Due to the absence of the text encoding as contrastive target, SuperClass does not require a text encoder and does not need to maintain a large batch size as CLIP does. SuperClass demonstrated superior performance on various downstream tasks, including classic computer vision benchmarks and vision language downstream tasks. We further explored the scaling behavior of SuperClass on model size, training length, or data size, and reported encouraging results and comparisons to CLIP. https://github.com/x-cls/superclass

Scaling data and compute is critical to the success of machine learning. However, scaling demands predictability: we want methods to not only perform well with more compute or data, but also have their performance be predictable from small-scale runs, without running the large-scale experiment. In this paper, we show that value-based off-policy RL methods are predictable despite community lore regarding their pathological behavior. First, we show that data and compute requirements to attain a given performance level lie on a Pareto frontier, controlled by the updates-to-data (UTD) ratio. By estimating this frontier, we can predict this data requirement when given more compute, and this compute requirement when given more data. Second, we determine the optimal allocation of a total resource budget across data and compute for a given performance and use it to determine hyperparameters that maximize performance for a given budget. Third, this scaling behavior is enabled by first estimating predictable relationships between hyperparameters, which is used to manage effects of overfitting and plasticity loss unique to RL. We validate our approach using three algorithms: SAC, BRO, and PQL on DeepMind Control, OpenAI gym, and IsaacGym, when extrapolating to higher levels of data, compute, budget, or performance.

We investigate the potential of large language models (LLMs) to serve as efficient simulators for agentic search tasks in reinforcement learning (RL), thereby reducing dependence on costly interactions with external search engines. To this end, we first quantify the intrinsic search capability of LLMs via structured prompting and repeated sampling, which we term Self-Search. Our results reveal that LLMs exhibit strong scaling behavior with respect to the inference budget, achieving high pass@k on question-answering benchmarks, including the challenging BrowseComp task. Building on these observations, we introduce Self-Search RL (SSRL), which enhances LLMs' Self-Search capability through format-based and rule-based rewards. SSRL enables models to iteratively refine their knowledge utilization internally, without requiring access to external tools. Empirical evaluations demonstrate that SSRL-trained policy models provide a cost-effective and stable environment for search-driven RL training, reducing reliance on external search engines and facilitating robust sim-to-real transfer. We draw the following conclusions: 1) LLMs possess world knowledge that can be effectively elicited to achieve high performance; 2) SSRL demonstrates the potential of leveraging internal knowledge to reduce hallucination; 3) SSRL-trained models integrate seamlessly with external search engines without additional effort. Our findings highlight the potential of LLMs to support more scalable RL agent training.

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we introduce Reinforcement Learning on Pre-Training data (RLPT), a new training-time scaling paradigm for optimizing LLMs. In contrast to prior approaches that scale training primarily through supervised learning, RLPT enables the policy to autonomously explore meaningful trajectories to learn from pre-training data and improve its capability through reinforcement learning (RL). While existing RL strategies such as reinforcement learning from human feedback (RLHF) and reinforcement learning with verifiable rewards (RLVR) rely on human annotation for reward construction, RLPT eliminates this dependency by deriving reward signals directly from pre-training data. Specifically, it adopts a next-segment reasoning objective, rewarding the policy for accurately predicting subsequent text segments conditioned on the preceding context. This formulation allows RL to be scaled on pre-training data, encouraging the exploration of richer trajectories across broader contexts and thereby fostering more generalizable reasoning skills. Extensive experiments on both general-domain and mathematical reasoning benchmarks across multiple models validate the effectiveness of RLPT. For example, when applied to Qwen3-4B-Base, RLPT yields absolute improvements of 3.0, 5.1, 8.1, 6.0, 6.6, and 5.3 on MMLU, MMLU-Pro, GPQA-Diamond, KOR-Bench, AIME24, and AIME25, respectively. The results further demonstrate favorable scaling behavior, suggesting strong potential for continued gains with more compute. In addition, RLPT provides a solid foundation, extending the reasoning boundaries of LLMs and enhancing RLVR performance.

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when selecting the best response from 256 random generations. The primary issue with the current base model is the difficulty in consistently eliciting its inherent mathematical capabilities. Notably, the accuracy for the first answer drops to 49.5% and 7.9% on the GSM8K and MATH benchmarks, respectively. We find that simply scaling up the SFT data can significantly enhance the reliability of generating correct answers. However, the potential for extensive scaling is constrained by the scarcity of publicly available math questions. To overcome this limitation, we employ synthetic data, which proves to be nearly as effective as real data and shows no clear saturation when scaled up to approximately one million samples. This straightforward approach achieves an accuracy of 82.6% on GSM8K and 40.6% on MATH using LLaMA-2 7B models, surpassing previous models by 14.2% and 20.8%, respectively. We also provide insights into scaling behaviors across different reasoning complexities and error types.

We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

This work is the first to openly reproduce the Reinforcement Learning from Human Feedback (RLHF) scaling behaviors reported in OpenAI's seminal TL;DR summarization work. We create an RLHF pipeline from scratch, enumerate over 20 key implementation details, and share key insights during the reproduction. Our RLHF-trained Pythia models demonstrate significant gains in response quality that scale with model size, with our 2.8B, 6.9B models outperforming OpenAI's released 1.3B checkpoint. We publicly release the trained model checkpoints and code to facilitate further research and accelerate progress in the field (https://github.com/vwxyzjn/summarize_from_feedback_details).

Scaling deep learning models has been at the heart of recent revolutions in language modelling and image generation. Practitioners have observed a strong relationship between model size, dataset size, and performance. However, structure-based architectures such as Graph Neural Networks (GNNs) are yet to show the benefits of scale mainly due to the lower efficiency of sparse operations, large data requirements, and lack of clarity about the effectiveness of various architectures. We address this drawback of GNNs by studying their scaling behavior. Specifically, we analyze message-passing networks, graph Transformers, and hybrid architectures on the largest public collection of 2D molecular graphs. For the first time, we observe that GNNs benefit tremendously from the increasing scale of depth, width, number of molecules, number of labels, and the diversity in the pretraining datasets, resulting in a 30.25% improvement when scaling to 1 billion parameters and 28.98% improvement when increasing size of dataset to eightfold. We further demonstrate strong finetuning scaling behavior on 38 tasks, outclassing previous large models. We hope that our work paves the way for an era where foundational GNNs drive pharmaceutical drug discovery.

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.

OpenAI's Sora highlights the potential of video generation for developing world models that adhere to fundamental physical laws. However, the ability of video generation models to discover such laws purely from visual data without human priors can be questioned. A world model learning the true law should give predictions robust to nuances and correctly extrapolate on unseen scenarios. In this work, we evaluate across three key scenarios: in-distribution, out-of-distribution, and combinatorial generalization. We developed a 2D simulation testbed for object movement and collisions to generate videos deterministically governed by one or more classical mechanics laws. This provides an unlimited supply of data for large-scale experimentation and enables quantitative evaluation of whether the generated videos adhere to physical laws. We trained diffusion-based video generation models to predict object movements based on initial frames. Our scaling experiments show perfect generalization within the distribution, measurable scaling behavior for combinatorial generalization, but failure in out-of-distribution scenarios. Further experiments reveal two key insights about the generalization mechanisms of these models: (1) the models fail to abstract general physical rules and instead exhibit "case-based" generalization behavior, i.e., mimicking the closest training example; (2) when generalizing to new cases, models are observed to prioritize different factors when referencing training data: color > size > velocity > shape. Our study suggests that scaling alone is insufficient for video generation models to uncover fundamental physical laws, despite its role in Sora's broader success. See our project page at https://phyworld.github.io

The rapid evolution of large language models (LLMs) has unlocked their capabilities in advanced reasoning tasks like mathematical problem-solving, code generation, and legal analysis. Central to this progress are inference-time reasoning algorithms, which refine outputs by exploring multiple solution paths, at the cost of increasing compute demands and response latencies. Existing serving systems fail to adapt to the scaling behaviors of these algorithms or the varying difficulty of queries, leading to inefficient resource use and unmet latency targets. We present Dynasor, a system that optimizes inference-time compute for LLM reasoning queries. Unlike traditional engines, Dynasor tracks and schedules requests within reasoning queries and uses Certaindex, a proxy that measures statistical reasoning progress based on model certainty, to guide compute allocation dynamically. Dynasor co-adapts scheduling with reasoning progress: it allocates more compute to hard queries, reduces compute for simpler ones, and terminates unpromising queries early, balancing accuracy, latency, and cost. On diverse datasets and algorithms, Dynasor reduces compute by up to 50% in batch processing and sustaining 3.3x higher query rates or 4.7x tighter latency SLOs in online serving.

Current vision-language generative models rely on expansive corpora of paired image-text data to attain optimal performance and generalization capabilities. However, automatically collecting such data (e.g. via large-scale web scraping) leads to low quality and poor image-text correlation, while human annotation is more accurate but requires significant manual effort and expense. We introduce ITIT (InTegrating Image Text): an innovative training paradigm grounded in the concept of cycle consistency which allows vision-language training on unpaired image and text data. ITIT is comprised of a joint image-text encoder with disjoint image and text decoders that enable bidirectional image-to-text and text-to-image generation in a single framework. During training, ITIT leverages a small set of paired image-text data to ensure its output matches the input reasonably well in both directions. Simultaneously, the model is also trained on much larger datasets containing only images or texts. This is achieved by enforcing cycle consistency between the original unpaired samples and the cycle-generated counterparts. For instance, it generates a caption for a given input image and then uses the caption to create an output image, and enforces similarity between the input and output images. Our experiments show that ITIT with unpaired datasets exhibits similar scaling behavior as using high-quality paired data. We demonstrate image generation and captioning performance on par with state-of-the-art text-to-image and image-to-text models with orders of magnitude fewer (only 3M) paired image-text data.

The Superficial Alignment Hypothesis posits that almost all of a language model's abilities and knowledge are learned during pre-training, while post-training is about giving a model the right style and format. We re-examine these claims by empirically studying the scaling behavior of post-training with increasing finetuning examples and evaluating them using objective task-specific standardized benchmarks. Through experiments with the Llama-3, Mistral, and Llama-2 model families of multiple sizes, we observe that, similar to the pre-training scaling laws, post-training task performance scales as a power law against the number of finetuning examples. This power law relationship holds across a broad array of capabilities, including mathematical reasoning, coding, instruction following, and multihop-reasoning. In addition, for tasks like math and multihop reasoning, we observe that a handful of examples merely align the model stylistically but do not saturate performance on the benchmarks. Model performance is instead correlated with its reasoning ability and it improves significantly with more examples, illustrating the need for holistic evaluation programs leveraging objective benchmarks in addition to measurement of alignment to human preferences. We also observe that language models are not necessarily limited to using knowledge learned during pre-training. With appropriate post-training, a model's ability to integrate new knowledge greatly improves on downstream tasks like multihop question-answering. Taken together, these results shed new light on the Superficial Alignment Hypothesis, suggesting that it is, at best, an over-simplification.

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

Diffusion models are the main driver of progress in image and video synthesis, but suffer from slow inference speed. Distillation methods, like the recently introduced adversarial diffusion distillation (ADD) aim to shift the model from many-shot to single-step inference, albeit at the cost of expensive and difficult optimization due to its reliance on a fixed pretrained DINOv2 discriminator. We introduce Latent Adversarial Diffusion Distillation (LADD), a novel distillation approach overcoming the limitations of ADD. In contrast to pixel-based ADD, LADD utilizes generative features from pretrained latent diffusion models. This approach simplifies training and enhances performance, enabling high-resolution multi-aspect ratio image synthesis. We apply LADD to Stable Diffusion 3 (8B) to obtain SD3-Turbo, a fast model that matches the performance of state-of-the-art text-to-image generators using only four unguided sampling steps. Moreover, we systematically investigate its scaling behavior and demonstrate LADD's effectiveness in various applications such as image editing and inpainting.

Recent generations of language models have introduced Large Reasoning Models (LRMs) that generate detailed thinking processes before providing answers. While these models demonstrate improved performance on reasoning benchmarks, their fundamental capabilities, scaling properties, and limitations remain insufficiently understood. Current evaluations primarily focus on established math and coding benchmarks, emphasizing final answer accuracy. However, this evaluation paradigm often suffers from contamination and does not provide insights into the reasoning traces. In this work, we systematically investigate these gaps with the help of controllable puzzle environments that allow precise manipulation of complexity while maintaining consistent logical structures. This setup enables the analysis of not only final answers but also the internal reasoning traces, offering insights into how LRMs think. Through extensive experiments, we show that LRMs face a complete accuracy collapse beyond certain complexities. Moreover, they exhibit a counterintuitive scaling limit: their reasoning effort increases with problem complexity up to a point, then declines despite having remaining token budget. By comparing LRMs with their standard LLM counterparts under same inference compute, we identify three performance regimes: (1) low-complexity tasks where standard models outperform LRMs, (2) medium-complexity tasks where LRMs demonstrates advantage, and (3) high-complexity tasks where both models face complete collapse. We found that LRMs have limitations in exact computation: they fail to use explicit algorithms and reason inconsistently across scales. We also investigate the reasoning traces in more depth, studying the patterns of explored solutions and analyzing the models' computational behavior, shedding light on their strengths, limitations, and raising questions about their reasoning capabilities.

This paper shows that masked autoencoders (MAE) are scalable self-supervised learners for computer vision. Our MAE approach is simple: we mask random patches of the input image and reconstruct the missing pixels. It is based on two core designs. First, we develop an asymmetric encoder-decoder architecture, with an encoder that operates only on the visible subset of patches (without mask tokens), along with a lightweight decoder that reconstructs the original image from the latent representation and mask tokens. Second, we find that masking a high proportion of the input image, e.g., 75%, yields a nontrivial and meaningful self-supervisory task. Coupling these two designs enables us to train large models efficiently and effectively: we accelerate training (by 3x or more) and improve accuracy. Our scalable approach allows for learning high-capacity models that generalize well: e.g., a vanilla ViT-Huge model achieves the best accuracy (87.8%) among methods that use only ImageNet-1K data. Transfer performance in downstream tasks outperforms supervised pre-training and shows promising scaling behavior.

Large language models (LLMs) have recently achieved impressive results in speech recognition across multiple modalities, including Auditory Speech Recognition (ASR), Visual Speech Recognition (VSR), and Audio-Visual Speech Recognition (AVSR). Despite this progress, current LLM-based approaches typically address each task independently, training separate models that raise computational and deployment resource use while missing potential cross-task synergies. They also rely on fixed-rate token compression, which restricts flexibility in balancing accuracy with efficiency. These limitations highlight the need for a unified framework that can support ASR, VSR, and AVSR while enabling elastic inference. To this end, we present Omni-AVSR, a unified audio-visual LLM that combines efficient multi-granularity training with parameter-efficient adaptation. Specifically, we adapt the matryoshka representation learning paradigm to efficiently train across multiple audio and visual granularities, reducing its inherent training resource use. Furthermore, we explore three LoRA-based strategies for adapting the backbone LLM, balancing shared and task-specific specialization. Experiments on LRS2 and LRS3 show that Omni-AVSR achieves comparable or superior accuracy to state-of-the-art baselines while training a single model at substantially lower training and deployment resource use. The model also remains robust under acoustic noise, and we analyze its scaling behavior as LLM size increases, providing insights into the trade-off between performance and efficiency.

Artificial intelligence (AI) systems, and Large Language Models (LLMs) in particular, are increasingly employed for creative tasks like scientific idea generation, constituting a form of generalization from training data unaddressed by existing conceptual frameworks. Despite its similarities to compositional generalization (CG), combinatorial creativity (CC) is an open-ended ability. Instead of evaluating for accuracy or correctness against fixed targets, which would contradict the open-ended nature of CC, we propose a theoretical framework and algorithmic task for evaluating outputs by their degrees of novelty and utility. From here, we make several important empirical contributions: (1) We obtain the first insights into the scaling behavior of creativity for LLMs. (2) We discover that, for fixed compute budgets, there exist optimal model depths and widths for creative ability. (3) We find that the ideation-execution gap, whereby LLMs excel at generating novel scientific ideas but struggle to ensure their practical feasibility, may be explained by a more fundamental novelty-utility tradeoff characteristic of creativity algorithms in general. Importantly, this tradeoff remains persistent even at scale, casting doubt on the long-term creative potential of LLMs in their current form. Together, our conceptual framework and empirical findings provide a foundation for understanding and improving creativity in modern AI models, bridging the gap between human and machine intelligence.

Sparse autoencoders (SAEs) are a promising technique for decomposing language model activations into interpretable linear features. However, current SAEs fall short of completely explaining model performance, resulting in "dark matter": unexplained variance in activations. This work investigates dark matter as an object of study in its own right. Surprisingly, we find that much of SAE dark matter--about half of the error vector itself and >90% of its norm--can be linearly predicted from the initial activation vector. Additionally, we find that the scaling behavior of SAE error norms at a per token level is remarkably predictable: larger SAEs mostly struggle to reconstruct the same contexts as smaller SAEs. We build on the linear representation hypothesis to propose models of activations that might lead to these observations, including postulating a new type of "introduced error"; these insights imply that the part of the SAE error vector that cannot be linearly predicted ("nonlinear" error) might be fundamentally different from the linearly predictable component. To validate this hypothesis, we empirically analyze nonlinear SAE error and show that 1) it contains fewer not yet learned features, 2) SAEs trained on it are quantitatively worse, 3) it helps predict SAE per-token scaling behavior, and 4) it is responsible for a proportional amount of the downstream increase in cross entropy loss when SAE activations are inserted into the model. Finally, we examine two methods to reduce nonlinear SAE error at a fixed sparsity: inference time gradient pursuit, which leads to a very slight decrease in nonlinear error, and linear transformations from earlier layer SAE outputs, which leads to a larger reduction.

Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on combined evidence from real-world observations, controlled experiments, and theoretical analysis, we demonstrate that task accuracy typically follows an inverted U-shaped curve with CoT length, where performance initially improves but eventually decreases as the number of CoT steps increases. With controlled experiments, we further uncover the scaling behaviors of the optimal CoT length: it increases with task difficulty but decreases with model capability, exposing an inherent simplicity bias where more capable models favor shorter, more efficient CoT reasoning. This bias is also evident in Reinforcement Learning (RL) training, where models gravitate towards shorter CoTs as their accuracy improves. To have a deep understanding of these dynamics, we establish a simple theoretical model that formally proves these phenomena, including the optimal length's scaling laws and the emergence of simplicity bias during RL. Guided by this framework, we demonstrate significant practical benefits from training with optimally-lengthed CoTs and employing length-aware filtering at inference. These findings offer both a principled understanding of the "overthinking" phenomenon and multiple practical guidelines for CoT calibration, enabling LLMs to achieve optimal reasoning performance with adaptive CoTs tailored to task complexity and model capability.

This paper introduces an approach for training o1-like RAG models that retrieve and reason over relevant information step by step before generating the final answer. Conventional RAG methods usually perform a single retrieval step before the generation process, which limits their effectiveness in addressing complex queries due to imperfect retrieval results. In contrast, our proposed method, CoRAG (Chain-of-Retrieval Augmented Generation), allows the model to dynamically reformulate the query based on the evolving state. To train CoRAG effectively, we utilize rejection sampling to automatically generate intermediate retrieval chains, thereby augmenting existing RAG datasets that only provide the correct final answer. At test time, we propose various decoding strategies to scale the model's test-time compute by controlling the length and number of sampled retrieval chains. Experimental results across multiple benchmarks validate the efficacy of CoRAG, particularly in multi-hop question answering tasks, where we observe more than 10 points improvement in EM score compared to strong baselines. On the KILT benchmark, CoRAG establishes a new state-of-the-art performance across a diverse range of knowledge-intensive tasks. Furthermore, we offer comprehensive analyses to understand the scaling behavior of CoRAG, laying the groundwork for future research aimed at developing factual and grounded foundation models.

We propose a novel approach to image generation by decomposing an image into a structured sequence, where each element in the sequence shares the same spatial resolution but differs in the number of unique tokens used, capturing different level of visual granularity. Image generation is carried out through our newly introduced Next Visual Granularity (NVG) generation framework, which generates a visual granularity sequence beginning from an empty image and progressively refines it, from global layout to fine details, in a structured manner. This iterative process encodes a hierarchical, layered representation that offers fine-grained control over the generation process across multiple granularity levels. We train a series of NVG models for class-conditional image generation on the ImageNet dataset and observe clear scaling behavior. Compared to the VAR series, NVG consistently outperforms it in terms of FID scores (3.30 -> 3.03, 2.57 ->2.44, 2.09 -> 2.06). We also conduct extensive analysis to showcase the capability and potential of the NVG framework. Our code and models will be released.

We empirically study autoregressive pre-training from videos. To perform our study, we construct a series of autoregressive video models, called Toto. We treat videos as sequences of visual tokens and train transformer models to autoregressively predict future tokens. Our models are pre-trained on a diverse dataset of videos and images comprising over 1 trillion visual tokens. We explore different architectural, training, and inference design choices. We evaluate the learned visual representations on a range of downstream tasks including image recognition, video classification, object tracking, and robotics. Our results demonstrate that, despite minimal inductive biases, autoregressive pre-training leads to competitive performance across all benchmarks. Finally, we find that scaling our video models results in similar scaling curves to those seen in language models, albeit with a different rate. More details at https://brjathu.github.io/toto/

Most transformer-based video encoders are limited to short temporal contexts due to their quadratic complexity. While various attempts have been made to extend this context, this has often come at the cost of both conceptual and computational complexity. We propose to instead re-purpose existing pre-trained video transformers by simply fine-tuning them to attend to memories derived non-parametrically from past activations. By leveraging redundancy reduction, our memory-consolidated vision transformer (MC-ViT) effortlessly extends its context far into the past and exhibits excellent scaling behavior when learning from longer videos. In doing so, MC-ViT sets a new state-of-the-art in long-context video understanding on EgoSchema, Perception Test, and Diving48, outperforming methods that benefit from orders of magnitude more parameters.

Recently, techniques such as explicit structured reasoning have demonstrated strong test-time scaling behavior by enforcing a separation between the model's internal "thinking" process and the final response. A key factor influencing answer quality in this setting is the length of the thinking stage. When the reasoning is too short, the model may fail to capture the complexity of the task. Conversely, when it is too long, the model may overthink, leading to unnecessary computation and degraded performance. This paper explores and exploits the underlying mechanisms by which LLMs understand and regulate the length of their reasoning during explicit thought processes. First, we show that LLMs encode their progress through the reasoning process and introduce an interactive progress bar visualization, which is then used to reveal insights on the model's planning dynamics. Second, we manipulate the internal progress encoding during inference to reduce unnecessary steps and generate a more concise and decisive chain of thoughts. Our empirical results demonstrate that this "overclocking" method mitigates overthinking, improves answer accuracy, and reduces inference latency. Our code is publicly available.

Large language model (LLM)-based agents increasingly rely on tool use to complete real-world tasks. While existing works evaluate the LLMs' tool use capability, they largely focus on the final answers yet overlook the detailed tool usage trajectory, i.e., whether tools are selected, parameterized, and ordered correctly. We introduce TRAJECT-Bench, a trajectory-aware benchmark to comprehensively evaluate LLMs' tool use capability through diverse tasks with fine-grained evaluation metrics. TRAJECT-Bench pairs high-fidelity, executable tools across practical domains with tasks grounded in production-style APIs, and synthesizes trajectories that vary in breadth (parallel calls) and depth (interdependent chains). Besides final accuracy, TRAJECT-Bench also reports trajectory-level diagnostics, including tool selection and argument correctness, and dependency/order satisfaction. Analyses reveal failure modes such as similar tool confusion and parameter-blind selection, and scaling behavior with tool diversity and trajectory length where the bottleneck of transiting from short to mid-length trajectories is revealed, offering actionable guidance for LLMs' tool use.

Analytical framework for predicting General Matrix Multiplication (GEMM) performance on modern GPUs, focusing on runtime, power consumption, and energy efficiency. Our study employs two approaches: a custom-implemented tiled matrix multiplication kernel for fundamental analysis, and NVIDIA's CUTLASS library for comprehensive performance data collection across advanced configurations. Using the NVIDIA RTX 4070 as our experimental platform, we developed a Random Forest-based prediction model with multi-output regression capability. Through analysis of both naive tiled matrix multiplication with varying tile sizes (1 to 32) and 16,128 CUTLASS GEMM operations across diverse configurations, we identified critical performance patterns related to matrix dimensions, thread block configurations, and memory access patterns. Our framework achieved exceptional accuracy with an R^2 score of 0.98 for runtime prediction (mean error 15.57%) and 0.78 for power prediction (median error 5.42%). The system successfully predicts performance across matrix sizes, demonstrating robust scaling behavior. Our results show that optimal tile size selection can improve performance by up to 3.2x while reducing power consumption by 22% compared to baseline configurations. Analysis of shared memory utilization and SM occupancy reveals that tile sizes of 16x16 achieve the best balance between parallelism and resource usage. The implementation of our framework, including prediction models and analysis tools, is available as an open-source project at GPPerf [https://github.com/pavlyhalim/GPPerf].

We are interested in learning scalable agents for reinforcement learning that can learn from large-scale, diverse sequential data similar to current large vision and language models. To this end, this paper presents masked decision prediction (MaskDP), a simple and scalable self-supervised pretraining method for reinforcement learning (RL) and behavioral cloning (BC). In our MaskDP approach, we employ a masked autoencoder (MAE) to state-action trajectories, wherein we randomly mask state and action tokens and reconstruct the missing data. By doing so, the model is required to infer masked-out states and actions and extract information about dynamics. We find that masking different proportions of the input sequence significantly helps with learning a better model that generalizes well to multiple downstream tasks. In our empirical study, we find that a MaskDP model gains the capability of zero-shot transfer to new BC tasks, such as single and multiple goal reaching, and it can zero-shot infer skills from a few example transitions. In addition, MaskDP transfers well to offline RL and shows promising scaling behavior w.r.t. to model size. It is amenable to data-efficient finetuning, achieving competitive results with prior methods based on autoregressive pretraining.

The advent of large-scale vision foundation models, pre-trained on diverse natural images, has marked a paradigm shift in computer vision. However, how the frontier vision foundation models' efficacies transfer to specialized domains remains such as medical imaging remains an open question. This report investigates whether DINOv3, a state-of-the-art self-supervised vision transformer (ViT) that features strong capability in dense prediction tasks, can directly serve as a powerful, unified encoder for medical vision tasks without domain-specific pre-training. To answer this, we benchmark DINOv3 across common medical vision tasks, including 2D/3D classification and segmentation on a wide range of medical imaging modalities. We systematically analyze its scalability by varying model sizes and input image resolutions. Our findings reveal that DINOv3 shows impressive performance and establishes a formidable new baseline. Remarkably, it can even outperform medical-specific foundation models like BiomedCLIP and CT-Net on several tasks, despite being trained solely on natural images. However, we identify clear limitations: The model's features degrade in scenarios requiring deep domain specialization, such as in Whole-Slide Pathological Images (WSIs), Electron Microscopy (EM), and Positron Emission Tomography (PET). Furthermore, we observe that DINOv3 does not consistently obey scaling law in the medical domain; performance does not reliably increase with larger models or finer feature resolutions, showing diverse scaling behaviors across tasks. Ultimately, our work establishes DINOv3 as a strong baseline, whose powerful visual features can serve as a robust prior for multiple complex medical tasks. This opens promising future directions, such as leveraging its features to enforce multiview consistency in 3D reconstruction.

One of the main challenges in optimal scaling of large language models (LLMs) is the prohibitive cost of hyperparameter tuning, particularly learning rate eta and batch size B. While techniques like muP (Yang et al., 2022) provide scaling rules for optimal eta transfer in the infinite model size limit, the optimal scaling behavior in the infinite data size limit remains unknown. We fill in this gap by observing for the first time an intricate dependence of optimal eta scaling on the pretraining token budget T, B and its relation to the critical batch size B_crit, which we measure to evolve as B_crit propto T. Furthermore, we show that the optimal batch size is positively correlated with B_crit: keeping it fixed becomes suboptimal over time even if learning rate is scaled optimally. Surprisingly, our results demonstrate that the observed optimal eta and B dynamics are preserved with muP model scaling, challenging the conventional view of B_crit dependence solely on loss value. Complementing optimality, we examine the sensitivity of loss to changes in learning rate, where we find the sensitivity to decrease with increase of T and to remain constant with muP model scaling. We hope our results make the first step towards a unified picture of the joint optimal data and model scaling.

Autoregressive transformers have revolutionized generative models in language processing and shown substantial promise in image and video generation. However, these models face significant challenges when extended to 3D generation tasks due to their reliance on next-token prediction to learn token sequences, which is incompatible with the unordered nature of 3D data. Instead of imposing an artificial order on 3D data, in this paper, we introduce G3PT, a scalable coarse-to-fine 3D generative model utilizing a cross-scale querying transformer. The key is to map point-based 3D data into discrete tokens with different levels of detail, naturally establishing a sequential relationship between different levels suitable for autoregressive modeling. Additionally, the cross-scale querying transformer connects tokens globally across different levels of detail without requiring an ordered sequence. Benefiting from this approach, G3PT features a versatile 3D generation pipeline that effortlessly supports diverse conditional structures, enabling the generation of 3D shapes from various types of conditions. Extensive experiments demonstrate that G3PT achieves superior generation quality and generalization ability compared to previous 3D generation methods. Most importantly, for the first time in 3D generation, scaling up G3PT reveals distinct power-law scaling behaviors.

Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pretraining on large-scale, carefully curated collections of real-world sequences. To allow for a sample-efficient pretraining of TSFMs, we propose CauKer, a novel algorithm designed to generate diverse, causally coherent synthetic time series with realistic trends, seasonality, and nonlinear interactions. CauKer combines Gaussian Process (GP) kernel composition with Structural Causal Models (SCM) to produce data for sample-efficient pretraining of state-of-the-art classification TSFMs having different architectures and following different pretraining approaches. Additionally, our experiments reveal that CauKer-generated datasets exhibit clear scaling laws for both dataset size (10K to 10M samples) and model capacity (1M to 783M parameters), unlike real-world datasets, which display irregular scaling behavior.

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the AdS/CFT correspondence by solving the Einstein-Abelian-Higgs model in an AdS_4 black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter.

In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example scaling strategies may include increasing model width, depth, resolution, etc. While various scaling strategies exist, their tradeoffs are not fully understood. Existing analysis typically focuses on the interplay of accuracy and flops (floating point operations). Yet, as we demonstrate, various scaling strategies affect model parameters, activations, and consequently actual runtime quite differently. In our experiments we show the surprising result that numerous scaling strategies yield networks with similar accuracy but with widely varying properties. This leads us to propose a simple fast compound scaling strategy that encourages primarily scaling model width, while scaling depth and resolution to a lesser extent. Unlike currently popular scaling strategies, which result in about O(s) increase in model activation w.r.t. scaling flops by a factor of s, the proposed fast compound scaling results in close to O(s) increase in activations, while achieving excellent accuracy. This leads to comparable speedups on modern memory-limited hardware (e.g., GPU, TPU). More generally, we hope this work provides a framework for analyzing and selecting scaling strategies under various computational constraints.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

Previous research observed accuracy degradation when replacing the attention softmax with a point-wise activation such as ReLU. In the context of vision transformers, we find that this degradation is mitigated when dividing by sequence length. Our experiments training small to large vision transformers on ImageNet-21k indicate that ReLU-attention can approach or match the performance of softmax-attention in terms of scaling behavior as a function of compute.

Contrastive pretraining on image-text pairs from the web is one of the most popular large-scale pretraining strategies for vision backbones, especially in the context of large multimodal models. At the same time, image captioning on this type of data is commonly considered an inferior pretraining strategy. In this paper, we perform a fair comparison of these two pretraining strategies, carefully matching training data, compute, and model capacity. Using a standard encoder-decoder transformer, we find that captioning alone is surprisingly effective: on classification tasks, captioning produces vision encoders competitive with contrastively pretrained encoders, while surpassing them on vision & language tasks. We further analyze the effect of the model architecture and scale, as well as the pretraining data on the representation quality, and find that captioning exhibits the same or better scaling behavior along these axes. Overall our results show that plain image captioning is a more powerful pretraining strategy than was previously believed.

Understanding functional representations within higher visual cortex is a fundamental question in computational neuroscience. While artificial neural networks pretrained on large-scale datasets exhibit striking representational alignment with human neural responses, learning image-computable models of visual cortex relies on individual-level, large-scale fMRI datasets. The necessity for expensive, time-intensive, and often impractical data acquisition limits the generalizability of encoders to new subjects and stimuli. BraInCoRL uses in-context learning to predict voxelwise neural responses from few-shot examples without any additional finetuning for novel subjects and stimuli. We leverage a transformer architecture that can flexibly condition on a variable number of in-context image stimuli, learning an inductive bias over multiple subjects. During training, we explicitly optimize the model for in-context learning. By jointly conditioning on image features and voxel activations, our model learns to directly generate better performing voxelwise models of higher visual cortex. We demonstrate that BraInCoRL consistently outperforms existing voxelwise encoder designs in a low-data regime when evaluated on entirely novel images, while also exhibiting strong test-time scaling behavior. The model also generalizes to an entirely new visual fMRI dataset, which uses different subjects and fMRI data acquisition parameters. Further, BraInCoRL facilitates better interpretability of neural signals in higher visual cortex by attending to semantically relevant stimuli. Finally, we show that our framework enables interpretable mappings from natural language queries to voxel selectivity.

Current methods for 3D scene reconstruction from sparse posed images employ intermediate 3D representations such as neural fields, voxel grids, or 3D Gaussians, to achieve multi-view consistent scene appearance and geometry. In this paper we introduce MVGD, a diffusion-based architecture capable of direct pixel-level generation of images and depth maps from novel viewpoints, given an arbitrary number of input views. Our method uses raymap conditioning to both augment visual features with spatial information from different viewpoints, as well as to guide the generation of images and depth maps from novel views. A key aspect of our approach is the multi-task generation of images and depth maps, using learnable task embeddings to guide the diffusion process towards specific modalities. We train this model on a collection of more than 60 million multi-view samples from publicly available datasets, and propose techniques to enable efficient and consistent learning in such diverse conditions. We also propose a novel strategy that enables the efficient training of larger models by incrementally fine-tuning smaller ones, with promising scaling behavior. Through extensive experiments, we report state-of-the-art results in multiple novel view synthesis benchmarks, as well as multi-view stereo and video depth estimation.

We present Hydra as an architectural proposal for hybrid long-context language models that combine conditional computation, long-context memory mechanisms, and sparse mixture-of-experts within an approximately 1.6B parameter design envelope. Hydra integrates a Mamba-style Structured State Space Model (SSM) backbone with intermittent sparse global attention, chunk-level MoE feed-forward routing, and dual (workspace plus factual PKM) memories. We formalize the component interfaces, give transparent parameter and complexity accounting, and outline a staged curriculum intended to stably activate the parts. We accompany the specification with illustrative toy-scale prototype measurements (tens of millions of parameters on synthetic data) whose sole purpose is to demonstrate implementation feasibility and qualitative scaling behaviors (for example, long-context throughput crossover and controllable expert routing), not to claim competitive full-scale performance. We explicitly delineate assumptions and open risks (training complexity, memory utilization, specialization dynamics) and position Hydra as a blueprint to stimulate empirical follow-up rather than a finished system. By combining SSM efficiency, selective sparse attention, MoE capacity, and learnable memory, Hydra sketches a path toward modular, input-adaptive long-context language models; validating end-task gains at target scale remains future work.

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to sim3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

Correlated structures are intimately connected to intriguing phenomena exhibited by a variety of disordered systems such as soft colloidal gels, bio-polymer networks and colloidal suspensions near a shear jamming transition. The universal critical behavior of these systems near the onset of rigidity is often described by traditional approaches as the coherent potential approximation - a versatile version of effective-medium theory that nevertheless have hitherto lacked key ingredients to describe disorder spatial correlations. Here we propose a multi-purpose generalization of the coherent potential approximation to describe the mechanical behavior of elastic networks with spatially-correlated disorder. We apply our theory to a simple rigidity-percolation model for colloidal gels and study the effects of correlations in both the critical point and the overall scaling behavior. We find that although the presence of spatial correlations (mimicking attractive interactions of gels) shifts the critical packing fraction to lower values, suggesting sub-isostatic behavior, the critical coordination number of the associated network remains isostatic. More importantly, we discuss how our theory can be employed to describe a large variety of systems with spatially-correlated disorder.

Implicit Neural Representations (INRs) have recently shown impressive results, but their fundamental capacity, implicit biases, and scaling behavior remain poorly understood. We investigate the performance of diverse INRs across a suite of 2D and 3D real and synthetic signals with varying effective bandwidth, as well as both overfitting and generalization tasks including tomography, super-resolution, and denoising. By stratifying performance according to model size as well as signal type and bandwidth, our results shed light on how different INR and grid representations allocate their capacity. We find that, for most tasks and signals, a simple regularized grid with interpolation trains faster and to higher quality than any INR with the same number of parameters. We also find limited settings where INRs outperform grids -- namely fitting signals with underlying lower-dimensional structure such as shape contours -- to guide future use of INRs towards the most advantageous applications. Code and synthetic signals used in our analysis are available at https://github.com/voilalab/INR-benchmark.

While AI agents have shown remarkable performance at various tasks, they still struggle with complex multi-modal applications, structured generation and strategic planning. Improvements via standard fine-tuning is often impractical, as solving agentic tasks usually relies on black box API access without control over model parameters. Inference-time methods such as Best-of-N (BON) sampling offer a simple yet effective alternative to improve performance. However, BON lacks iterative feedback integration mechanism. Hence, we propose Iterative Agent Decoding (IAD) which combines iterative refinement with dynamic candidate evaluation and selection guided by a verifier. IAD differs in how feedback is designed and integrated, specifically optimized to extract maximal signal from reward scores. We conduct a detailed comparison of baselines across key metrics on Sketch2Code, Text2SQL, and Webshop where IAD consistently outperforms baselines, achieving 3--6% absolute gains on Sketch2Code and Text2SQL (with and without LLM judges) and 8--10% gains on Webshop across multiple metrics. To better understand the source of IAD's gains, we perform controlled experiments to disentangle the effect of adaptive feedback from stochastic sampling, and find that IAD's improvements are primarily driven by verifier-guided refinement, not merely sampling diversity. We also show that both IAD and BON exhibit inference-time scaling with increased compute when guided by an optimal verifier. Our analysis highlights the critical role of verifier quality in effective inference-time optimization and examines the impact of noisy and sparse rewards on scaling behavior. Together, these findings offer key insights into the trade-offs and principles of effective inference-time optimization.

The advancement of large Vision-Language-Action (VLA) models has significantly improved robotic manipulation in terms of language-guided task execution and generalization to unseen scenarios. While existing VLAs adapted from pretrained large Vision-Language-Models (VLM) have demonstrated promising generalizability, their task performance is still unsatisfactory as indicated by the low tasks success rates in different environments. In this paper, we present a new advanced VLA architecture derived from VLM. Unlike previous works that directly repurpose VLM for action prediction by simple action quantization, we propose a omponentized VLA architecture that has a specialized action module conditioned on VLM output. We systematically study the design of the action module and demonstrates the strong performance enhancement with diffusion action transformers for action sequence modeling, as well as their favorable scaling behaviors. We also conduct comprehensive experiments and ablation studies to evaluate the efficacy of our models with varied designs. The evaluation on 5 robot embodiments in simulation and real work shows that our model not only significantly surpasses existing VLAs in task performance and but also exhibits remarkable adaptation to new robots and generalization to unseen objects and backgrounds. It exceeds the average success rates of OpenVLA which has similar model size (7B) with ours by over 35% in simulated evaluation and 55% in real robot experiments. It also outperforms the large RT-2-X model (55B) by 18% absolute success rates in simulation. Code and models can be found on our project page (https://cogact.github.io/).

Artificial intelligence (AI) methods have become critical in scientific applications to help accelerate scientific discovery. Large language models (LLMs) are being considered as a promising approach to address some of the challenging problems because of their superior generalization capabilities across domains. The effectiveness of the models and the accuracy of the applications is contingent upon their efficient execution on the underlying hardware infrastructure. Specialized AI accelerator hardware systems have recently become available for accelerating AI applications. However, the comparative performance of these AI accelerators on large language models has not been previously studied. In this paper, we systematically study LLMs on multiple AI accelerators and GPUs and evaluate their performance characteristics for these models. We evaluate these systems with (i) a micro-benchmark using a core transformer block, (ii) a GPT- 2 model, and (iii) an LLM-driven science use case, GenSLM. We present our findings and analyses of the models' performance to better understand the intrinsic capabilities of AI accelerators. Furthermore, our analysis takes into account key factors such as sequence lengths, scaling behavior, sparsity, and sensitivity to gradient accumulation steps.

We introduce LaViLa, a new approach to learning video-language representations by leveraging Large Language Models (LLMs). We repurpose pre-trained LLMs to be conditioned on visual input, and finetune them to create automatic video narrators. Our auto-generated narrations offer a number of advantages, including dense coverage of long videos, better temporal synchronization of the visual information and text, and much higher diversity of text. The video-text embedding learned contrastively with these additional auto-generated narrations outperforms the previous state-of-the-art on multiple first-person and third-person video tasks, both in zero-shot and finetuned setups. Most notably, LaViLa obtains an absolute gain of 10.1% on EGTEA classification and 5.9% Epic-Kitchens-100 multi-instance retrieval benchmarks. Furthermore, LaViLa trained with only half the narrations from the Ego4D dataset outperforms baseline models trained on the full set, and shows positive scaling behavior on increasing pre-training data and model size.

Recently DeepSeek R1 has shown that reinforcement learning (RL) can substantially improve the reasoning capabilities of Large Language Models (LLMs) through a simple yet effective design. The core of R1 lies in its rule-based reward formulation, which leverages tasks with deterministic ground-truth answers to enable precise and stable reward computation. In the visual domain, we similarly observe that a wide range of visual understanding tasks are inherently equipped with well-defined ground-truth annotations. This property makes them naturally compatible with rule-based reward mechanisms. Motivated by this observation, we investigate the extension of R1-style reinforcement learning to Vision-Language Models (VLMs), aiming to enhance their visual reasoning capabilities. To this end, we develop VLM-R1, a dedicated framework designed to harness RL for improving VLMs' performance on general vision-language tasks. Using this framework, we further explore the feasibility of applying RL to visual domain. Experimental results indicate that the RL-based model not only delivers competitive performance on visual understanding tasks but also surpasses Supervised Fine-Tuning (SFT) in generalization ability. Furthermore, we conduct comprehensive ablation studies that uncover a series of noteworthy insights, including the presence of reward hacking in object detection, the emergence of the "OD aha moment", the impact of training data quality, and the scaling behavior of RL across different model sizes. Through these analyses, we aim to deepen the understanding of how reinforcement learning enhances the capabilities of vision-language models, and we hope our findings and open-source contributions will support continued progress in the vision-language RL community. Our code and model are available at https://github.com/om-ai-lab/VLM-R1

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at https://inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.

The performance of embodied agents has been shown to improve by increasing model parameters, dataset size, and compute. This has been demonstrated in domains from robotics to video games, when generative learning objectives on offline datasets (pre-training) are used to model an agent's behavior (imitation learning) or their environment (world modeling). This paper characterizes the role of scale in these tasks more precisely. Going beyond the simple intuition that `bigger is better', we show that the same types of power laws found in language modeling (e.g. between loss and optimal model size), also arise in world modeling and imitation learning. However, the coefficients of these laws are heavily influenced by the tokenizer, task \& architecture -- this has important implications on the optimal sizing of models and data.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Kaplan et al. and Hoffmann et al. developed influential scaling laws for the optimal model size as a function of the compute budget, but these laws yield substantially different predictions. We explain the discrepancy by reproducing the Kaplan scaling law on two datasets (OpenWebText2 and RefinedWeb) and identifying three factors causing the difference: last layer computational cost, warmup duration, and scale-dependent optimizer tuning. With these factors corrected, we obtain excellent agreement with the Hoffmann et al. (i.e., "Chinchilla") scaling law. Counter to a hypothesis of Hoffmann et al., we find that careful learning rate decay is not essential for the validity of their scaling law. As a secondary result, we derive scaling laws for the optimal learning rate and batch size, finding that tuning the AdamW beta_2 parameter is essential at lower batch sizes.

The current paradigm of test-time scaling relies on generating long reasoning traces ("thinking" more) before producing a response. In agent problems that require interaction, this can be done by generating thinking traces before acting in the world. However, this process does not allow agents to acquire new information from the environment or adapt their behavior over time. In this work, we propose to scale test-time interaction, an untapped dimension of test-time scaling that increases the agent's interaction horizon to enable running rich behaviors such as exploration, backtracking, and dynamic re-planning within a single rollout. To demonstrate the promise of this scaling dimension, we study the domain of web agents. We first show that even prompting-based interaction scaling without any training can improve task success on web benchmarks non-trivially. Building on this, we introduce TTI (Test-Time Interaction), a curriculum-based online reinforcement learning (RL) approach that trains agents by adaptively adjusting their rollout lengths. Using a Gemma 3 12B model, TTI produces state-of-the-art open-source, open-data web agents on WebVoyager and WebArena benchmarks. We further show that TTI enables agents to balance exploration and exploitation adaptively. Our results establish interaction scaling as a powerful, complementary axis to scaling per-step compute, offering new avenues for training adaptive agents.

Scaling laws are typically fit using a family of models with a narrow range of frozen hyper-parameter choices. In this work we study scaling laws using a wide range of architecture and hyper-parameter choices, and highlight their impact on resulting prescriptions. As a primary artifact of our research, we release the Gemstones: the most comprehensive open-source scaling law dataset to date, consisting of over 4000 checkpoints from transformers with up to 2 billion parameters; these models have been trained with different learning rates, cooldown schedules, and architectural shapes. Our checkpoints enable more complex studies of scaling, such as a law that predicts language modeling performance as a function of model width and depth. By examining the various facets of our model suite, we find that the prescriptions of scaling laws can be highly sensitive to the experimental design process and the specific model checkpoints used during fitting. Code: https://github.com/mcleish7/gemstone-scaling-laws

Language models have been shown to exhibit positive scaling, where performance improves as models are scaled up in terms of size, compute, or data. In this work, we introduce NeQA, a dataset consisting of questions with negation in which language models do not exhibit straightforward positive scaling. We show that this task can exhibit inverse scaling, U-shaped scaling, or positive scaling, and the three scaling trends shift in this order as we use more powerful prompting methods or model families. We hypothesize that solving NeQA depends on two subtasks: question answering (task 1) and negation understanding (task 2). We find that task 1 has linear scaling, while task 2 has sigmoid-shaped scaling with an emergent transition point, and composing these two scaling trends yields the final scaling trend of NeQA. Our work reveals and provides a way to analyze the complex scaling trends of language models.

Emergent properties have been widely adopted as a term to describe behavior not present in smaller models but observed in larger models. Recent work suggests that the trade-off incurred by quantization is also an emergent property, with sharp drops in performance in models over 6B parameters. In this work, we ask "are quantization cliffs in performance solely a factor of scale?" Against a backdrop of increased research focus on why certain emergent properties surface at scale, this work provides a useful counter-example. We posit that it is possible to optimize for a quantization friendly training recipe that suppresses large activation magnitude outliers. Here, we find that outlier dimensions are not an inherent product of scale, but rather sensitive to the optimization conditions present during pre-training. This both opens up directions for more efficient quantization, and poses the question of whether other emergent properties are inherent or can be altered and conditioned by optimization and architecture design choices. We successfully quantize models ranging in size from 410M to 52B with minimal degradation in performance.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with scaling laws. Unlike pre-training, We find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing scaling laws fail to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our rectified scaling law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection.

Neural scaling laws (NSL) refer to the phenomenon where model performance improves with scale. Sharma & Kaplan analyzed NSL using approximation theory and predict that MSE losses decay as N^{-alpha}, alpha=4/d, where N is the number of model parameters, and d is the intrinsic input dimension. Although their theory works well for some cases (e.g., ReLU networks), we surprisingly find that a simple 1D problem y=x^2 manifests a different scaling law (alpha=1) from their predictions (alpha=4). We opened the neural networks and found that the new scaling law originates from lottery ticket ensembling: a wider network on average has more "lottery tickets", which are ensembled to reduce the variance of outputs. We support the ensembling mechanism by mechanistically interpreting single neural networks, as well as studying them statistically. We attribute the N^{-1} scaling law to the "central limit theorem" of lottery tickets. Finally, we discuss its potential implications for large language models and statistical physics-type theories of learning.

Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can be used to accelerate model development. In this work, we perform such an empirical investigation across a wide range of language understanding tasks, starting from models with as few as 10K parameters, and evaluate downstream performance across 9 language understanding tasks. We find that scaling laws emerge at finetuning time in some NLP tasks, and that they can also be exploited for debugging convergence when training large models. Moreover, for tasks where scaling laws exist, they can be used to predict the performance of larger models, which enables effective model selection. However, revealing scaling laws requires careful hyperparameter tuning and multiple runs for the purpose of uncertainty estimation, which incurs additional overhead, partially offsetting the computational benefits.

In studies of transferable learning, scaling laws are obtained for various important foundation models to predict their properties and performance at larger scales. We show here how scaling law derivation can also be used for model and dataset comparison, allowing to decide which procedure is to be preferred for pre-training. For the first time, full scaling laws based on dense measurements across a wide span of model and samples seen scales are derived for two important language-vision learning procedures, CLIP and MaMMUT, that use either contrastive only or contrastive and captioning text generative loss. Ensuring sufficient prediction accuracy for held out points, we use derived scaling laws to compare both models, obtaining evidence for MaMMUT's stronger improvement with scale and better sample efficiency than standard CLIP. To strengthen validity of the comparison, we show scaling laws for various downstream tasks, classification, retrieval, and segmentation, and for different open datasets, DataComp, DFN and Re-LAION, observing consistently the same trends. We show that comparison can also be performed when deriving scaling laws with a constant learning rate schedule, reducing compute cost. Accurate derivation of scaling laws provides thus means to perform model and dataset comparison across scale spans, avoiding misleading conclusions based on measurements from single reference scales only, paving the road for systematic comparison and improvement of open foundation models and datasets for their creation. We release all the pre-trained models with their intermediate checkpoints, including openMaMMUT-L/14, which achieves 80.3% zero-shot ImageNet-1k accuracy, trained on 12.8B samples from DataComp-1.4B. Code for reproducing experiments in the paper and raw experiments data can be found at https://github.com/LAION-AI/scaling-laws-for-comparison.

Foundation models have shown impressive adaptation and scalability in supervised and self-supervised learning problems, but so far these successes have not fully translated to reinforcement learning (RL). In this work, we demonstrate that training an RL agent at scale leads to a general in-context learning algorithm that can adapt to open-ended novel embodied 3D problems as quickly as humans. In a vast space of held-out environment dynamics, our adaptive agent (AdA) displays on-the-fly hypothesis-driven exploration, efficient exploitation of acquired knowledge, and can successfully be prompted with first-person demonstrations. Adaptation emerges from three ingredients: (1) meta-reinforcement learning across a vast, smooth and diverse task distribution, (2) a policy parameterised as a large-scale attention-based memory architecture, and (3) an effective automated curriculum that prioritises tasks at the frontier of an agent's capabilities. We demonstrate characteristic scaling laws with respect to network size, memory length, and richness of the training task distribution. We believe our results lay the foundation for increasingly general and adaptive RL agents that perform well across ever-larger open-ended domains.

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of model pre-training, ultimately contributing to the success of large language models such as GPT-4, Llama and Gemini. However, the original scaling law paper by OpenAI did not disclose the complete details necessary to derive the precise scaling law formulas, and their conclusions are only based on models containing up to 1.5 billion parameters. Though some subsequent works attempt to unveil these details and scale to larger models, they often neglect the training dependency of important factors such as the learning rate, context length and batch size, leading to their failure to establish a reliable formula for predicting the test loss trajectory. In this technical report, we confirm that the scaling law formulations proposed in the original OpenAI paper remain valid when scaling the model size up to 33 billion, but the constant coefficients in these formulas vary significantly with the experiment setup. We meticulously identify influential factors and provide transparent, step-by-step instructions to estimate all constant terms in scaling-law formulas by training on models with only 1M~60M parameters. Using these estimated formulas, we showcase the capability to accurately predict various attributes for models with up to 33B parameters before their training, including (1) the minimum possible test loss; (2) the minimum required training steps and processed tokens to achieve a specific loss; (3) the critical batch size with an optimal time/computation trade-off at any loss value; and (4) the complete test loss trajectory with arbitrary batch size.

As AI model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data. In this paper we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the large language model Llama2.

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would like a deeper understanding of the relationships between training set size, computational scale, and model accuracy improvements to advance the state-of-the-art. This paper presents a large scale empirical characterization of generalization error and model size growth as training sets grow. We introduce a methodology for this measurement and test four machine learning domains: machine translation, language modeling, image processing, and speech recognition. Our empirical results show power-law generalization error scaling across a breadth of factors, resulting in power-law exponents---the "steepness" of the learning curve---yet to be explained by theoretical work. Further, model improvements only shift the error but do not appear to affect the power-law exponent. We also show that model size scales sublinearly with data size. These scaling relationships have significant implications on deep learning research, practice, and systems. They can assist model debugging, setting accuracy targets, and decisions about data set growth. They can also guide computing system design and underscore the importance of continued computational scaling.

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

The Earth's atmosphere is an aerosol, it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition, and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number, St. We show that near the critical value of the Stokes number, St_c, the amount of deposition has the unusual scaling law of exp(-1/(St-St_c)^{1/2}). The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time for the particle to reach the surface of the cylinder varying as 1/(St-St_c)^{1/2}, together with the distance away from the stagnation point (perpendicular to the flow direction) increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the amount of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination.

Prior studies on the emergence in large models have primarily focused on how the functional capabilities of large language models (LLMs) scale with model size. Our research, however, transcends this traditional paradigm, aiming to deepen our understanding of the emergence within LLMs by placing a special emphasis not just on the model size but more significantly on the complex behavior of neuron interactions during the training process. By introducing the concepts of "self-organization" and "multifractal analysis," we explore how neuron interactions dynamically evolve during training, leading to "emergence," mirroring the phenomenon in natural systems where simple micro-level interactions give rise to complex macro-level behaviors. To quantitatively analyze the continuously evolving interactions among neurons in large models during training, we propose the Neuron-based Multifractal Analysis (NeuroMFA). Utilizing NeuroMFA, we conduct a comprehensive examination of the emergent behavior in LLMs through the lens of both model size and training process, paving new avenues for research into the emergence in large models.

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization (muP) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading muP transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as eta/lambda with an approximately invariant shape; under width scaling d, we observe that the top singular value scales approximately as eta/lambdacdot d^{0.75}. Combining this observation with the muP learning-rate rule eta_2propto d^{-1} for matrix-like parameters implies an empirical weight-decay scaling rule lambda_2propto d that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at eta_1=Theta_d(1) and lambda_1=0, this yields zero-shot transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend muP beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

Scaling laws are useful guides for developing language models, but there are still gaps between current scaling studies and how language models are ultimately trained and evaluated. For instance, scaling is usually studied in the compute-optimal training regime (i.e., "Chinchilla optimal" regime); however, in practice, models are often over-trained to reduce inference costs. Moreover, scaling laws mostly predict loss on next-token prediction, but ultimately models are compared based on downstream task performance. In this paper, we address both shortcomings. To do so, we create a testbed of 104 models with 0.011B to 6.9B parameters trained with various numbers of tokens on three data distributions. First, we investigate scaling in the over-trained regime. We fit scaling laws that extrapolate in both the number of model parameters and the ratio of training tokens to parameters. This enables us to predict the validation loss of a 1.4B parameter, 900B token run (i.e., 32times over-trained) and a 6.9B parameter, 138B token runx2014each from experiments that take 300times less compute. Second, we relate the perplexity of a language model to its downstream task performance via a power law. We use this law to predict top-1 error averaged over downstream tasks for the two aforementioned models using experiments that take 20times less compute. Our experiments are available at https://github.com/mlfoundations/scaling.

Representations from transformer-based unidirectional language models are known to be effective at predicting brain responses to natural language. However, most studies comparing language models to brains have used GPT-2 or similarly sized language models. Here we tested whether larger open-source models such as those from the OPT and LLaMA families are better at predicting brain responses recorded using fMRI. Mirroring scaling results from other contexts, we found that brain prediction performance scales log-linearly with model size from 125M to 30B parameter models, with ~15% increased encoding performance as measured by correlation with a held-out test set across 3 subjects. Similar log-linear behavior was observed when scaling the size of the fMRI training set. We also characterized scaling for acoustic encoding models that use HuBERT, WavLM, and Whisper, and we found comparable improvements with model size. A noise ceiling analysis of these large, high-performance encoding models showed that performance is nearing the theoretical maximum for brain areas such as the precuneus and higher auditory cortex. These results suggest that increasing scale in both models and data will yield incredibly effective models of language processing in the brain, enabling better scientific understanding as well as applications such as decoding.

Climbing grades are used to classify a climbing route based on its perceived difficulty, and have come to play a central role in the sport of rock climbing. Recently, the first statistically rigorous method for estimating climbing grades from whole-history ascent data was described, based on the dynamic Bradley-Terry model for games between players of time-varying ability. In this paper, we implement inference under the whole-history rating model using Markov chain Monte Carlo and apply the method to a curated data set made up of climbers who climb regularly. We use these data to get an estimate of the model's fundamental scale parameter m, which defines the proportional increase in difficulty associated with an increment of grade. We show that the data conform to assumptions that the climbing grade scale is a logarithmic scale of difficulty, like decibels or stellar magnitude. We estimate that an increment in Ewbank, French and UIAA climbing grade systems corresponds to 2.1, 2.09 and 2.13 times increase in difficulty respectively, assuming a logistic model of probability of success as a function of grade. Whereas we find that the Vermin scale for bouldering (V-grade scale) corresponds to a 3.17 increase in difficulty per grade increment. In addition, we highlight potential connections between the logarithmic properties of climbing grade scales and the psychophysical laws of Weber and Fechner.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

Computer-use agents (CUAs) hold promise for automating everyday digital tasks, but their unreliability and high variance hinder their application to long-horizon, complex tasks. We introduce Behavior Best-of-N (bBoN), a method that scales over agents by generating multiple rollouts and selecting among them using behavior narratives that describe the agents' rollouts. It enables both wide exploration and principled trajectory selection, substantially improving robustness and success rates. On OSWorld, our bBoN scaling method establishes a new state of the art (SoTA) at 69.9%, significantly outperforming prior methods and approaching human-level performance at 72%, with comprehensive ablations validating key design choices. We further demonstrate strong generalization results to different operating systems on WindowsAgentArena and AndroidWorld. Crucially, our results highlight the unreasonable effectiveness of scaling CUAs, when you do it right: effective scaling requires structured trajectory understanding and selection, and bBoN provides a practical framework to achieve this.

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model -- a joint generative data model and random feature model -- that captures this neural scaling phenomenology. By solving this model in the dual limit of large training set size and large number of parameters, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws, (ii) the way nonlinear feature maps, such as those provided by neural networks, enable scaling laws when trained on these datasets, (iii) the optimality of the equiparameterization scaling of training sets and parameters, and (iv) whether such scaling laws can break down and how they behave when they do. Key findings are the manner in which the power laws that occur in the statistics of natural datasets are extended by nonlinear random feature maps and then translated into power-law scalings of the test loss and how the finite extent of the data's spectral power law causes the model's performance to plateau.

Alternatives to backpropagation have long been studied to better understand how biological brains may learn. Recently, they have also garnered interest as a way to train neural networks more efficiently. By relaxing constraints inherent to backpropagation (e.g., symmetric feedforward and feedback weights, sequential updates), these methods enable promising prospects, such as local learning. However, the tradeoffs between different methods in terms of final task performance, convergence speed, and ultimately compute and data requirements are rarely outlined. In this work, we use scaling laws to study the ability of Direct Feedback Alignment~(DFA) to train causal decoder-only Transformers efficiently. Scaling laws provide an overview of the tradeoffs implied by a modeling decision, up to extrapolating how it might transfer to increasingly large models. We find that DFA fails to offer more efficient scaling than backpropagation: there is never a regime for which the degradation in loss incurred by using DFA is worth the potential reduction in compute budget. Our finding comes at variance with previous beliefs in the alternative training methods community, and highlights the need for holistic empirical approaches to better understand modeling decisions.

Many studies on scaling laws consider basic factors such as model size, model shape, dataset size, and compute power. These factors are easily tunable and represent the fundamental elements of any machine learning setup. But researchers have also employed more complex factors to estimate the test error and generalization performance with high predictability. These factors are generally specific to the domain or application. For example, feature diversity was primarily used for promoting syn-to-real transfer by Chen et al. (2021). With numerous scaling factors defined in previous works, it would be interesting to investigate how these factors may affect overall generalization performance in the context of self-supervised learning with CNN models. How do individual factors promote generalization, which includes varying depth, width, or the number of training epochs with early stopping? For example, does higher feature diversity result in higher accuracy held in complex settings other than a syn-to-real transfer? How do these factors depend on each other? We found that the last layer is the most diversified throughout the training. However, while the model's test error decreases with increasing epochs, its diversity drops. We also discovered that diversity is directly related to model width.

In recent years, foundational models have revolutionized the fields of language and vision, demonstrating remarkable abilities in understanding and generating complex data; however, similar advances in user behavior modeling have been limited, largely due to the complexity of behavioral data and the challenges involved in capturing intricate temporal and contextual relationships in user activities. To address this, we propose BehaveGPT, a foundational model designed specifically for large-scale user behavior prediction. Leveraging transformer-based architecture and a novel pretraining paradigm, BehaveGPT is trained on vast user behavior datasets, allowing it to learn complex behavior patterns and support a range of downstream tasks, including next behavior prediction, long-term generation, and cross-domain adaptation. Our approach introduces the DRO-based pretraining paradigm tailored for user behavior data, which improves model generalization and transferability by equitably modeling both head and tail behaviors. Extensive experiments on real-world datasets demonstrate that BehaveGPT outperforms state-of-the-art baselines, achieving more than a 10% improvement in macro and weighted recall, showcasing its ability to effectively capture and predict user behavior. Furthermore, we measure the scaling law in the user behavior domain for the first time on the Honor dataset, providing insights into how model performance scales with increased data and parameter sizes.

As we scale to more massive machine learning models, the frequent synchronization demands inherent in data-parallel approaches create significant slowdowns, posing a critical challenge to further scaling. Recent work develops an approach (DiLoCo) that relaxes synchronization demands without compromising model quality. However, these works do not carefully analyze how DiLoCo's behavior changes with model size. In this work, we study the scaling law behavior of DiLoCo when training LLMs under a fixed compute budget. We focus on how algorithmic factors, including number of model replicas, hyperparameters, and token budget affect training in ways that can be accurately predicted via scaling laws. We find that DiLoCo scales both predictably and robustly with model size. When well-tuned, DiLoCo scales better than data-parallel training with model size, and can outperform data-parallel training even at small model sizes. Our results showcase a more general set of benefits of DiLoCo than previously documented, including increased optimal batch sizes, improved downstream generalization with scale, and improved evaluation loss for a fixed token budget.

In the realm of large language models (LLMs), enhancing instruction-following capability often involves curating expansive training data. This is achieved through two primary schemes: i) Scaling-Inputs: Amplifying (input, output) pairs per task instruction, aiming for better instruction adherence. ii) Scaling Input-Free Tasks: Enlarging tasks, each composed of an (instruction, output) pair (without requiring a separate input anymore). However, LLMs under Scaling-Inputs tend to be overly sensitive to inputs, leading to misinterpretation or non-compliance with instructions. Conversely, Scaling Input-Free Tasks demands a substantial number of tasks but is less effective in instruction following when dealing with instances in Scaling-Inputs. This work introduces MUFFIN, a new scheme of instruction-following dataset curation. Specifically, we automatically Scale Tasks per Input by diversifying these tasks with various input facets. Experimental results across four zero-shot benchmarks, spanning both Scaling-Inputs and Scaling Input-Free Tasks schemes, reveal that LLMs, at various scales, trained on MUFFIN generally demonstrate superior instruction-following capabilities compared to those trained on the two aforementioned schemes.

Large foundation models are typically trained on data from multiple domains, with the data mixture--the proportion of each domain used--playing a critical role in model performance. The standard approach to selecting this mixture relies on trial and error, which becomes impractical for large-scale pretraining. We propose a systematic method to determine the optimal data mixture for any target domain using scaling laws. Our approach accurately predicts the loss of a model of size N trained with D tokens and a specific domain weight vector h. We validate the universality of these scaling laws by demonstrating their predictive power in three distinct and large-scale settings: large language model (LLM), native multimodal model (NMM), and large vision models (LVM) pretraining. We further show that these scaling laws can extrapolate to new data mixtures and across scales: their parameters can be accurately estimated using a few small-scale training runs, and used to estimate the performance at larger scales and unseen domain weights. The scaling laws allow to derive the optimal domain weights for any target domain under a given training budget (N,D), providing a principled alternative to costly trial-and-error methods.

Large language model (LLM) scaling laws are empirical formulas that estimate changes in model quality as a result of increasing parameter count and training data. However, these formulas, including the popular DeepMind Chinchilla scaling laws, neglect to include the cost of inference. We modify the Chinchilla scaling laws to calculate the optimal LLM parameter count and pre-training data size to train and deploy a model of a given quality and inference demand. We conduct our analysis both in terms of a compute budget and real-world costs and find that LLM researchers expecting reasonably large inference demand (~1B requests) should train models smaller and longer than Chinchilla-optimal.

Recent work claims that large language models display emergent abilities, abilities not present in smaller-scale models that are present in larger-scale models. What makes emergent abilities intriguing is two-fold: their sharpness, transitioning seemingly instantaneously from not present to present, and their unpredictability, appearing at seemingly unforeseeable model scales. Here, we present an alternative explanation for emergent abilities: that for a particular task and model family, when analyzing fixed model outputs, emergent abilities appear due to the researcher's choice of metric rather than due to fundamental changes in model behavior with scale. Specifically, nonlinear or discontinuous metrics produce apparent emergent abilities, whereas linear or continuous metrics produce smooth, continuous predictable changes in model performance. We present our alternative explanation in a simple mathematical model, then test it in three complementary ways: we (1) make, test and confirm three predictions on the effect of metric choice using the InstructGPT/GPT-3 family on tasks with claimed emergent abilities; (2) make, test and confirm two predictions about metric choices in a meta-analysis of emergent abilities on BIG-Bench; and (3) show to choose metrics to produce never-before-seen seemingly emergent abilities in multiple vision tasks across diverse deep networks. Via all three analyses, we provide evidence that alleged emergent abilities evaporate with different metrics or with better statistics, and may not be a fundamental property of scaling AI models.

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all widths, a process known as feature learning. Here, we show that feature learning is achieved by scaling the spectral norm of weight matrices and their updates like texttt{fan-out/fan-in}, in contrast to widely used but heuristic scalings based on Frobenius norm and entry size. Our spectral scaling analysis also leads to an elementary derivation of maximal update parametrization. All in all, we aim to provide the reader with a solid conceptual understanding of feature learning in neural networks.

Scaling recommendation models into large recommendation models has become one of the most widely discussed topics. Recent efforts focus on components beyond the scaling embedding dimension, as it is believed that scaling embedding may lead to performance degradation. Although there have been some initial observations on embedding, the root cause of their non-scalability remains unclear. Moreover, whether performance degradation occurs across different types of models and datasets is still an unexplored area. Regarding the effect of embedding dimensions on performance, we conduct large-scale experiments across 10 datasets with varying sparsity levels and scales, using 4 representative classical architectures. We surprisingly observe two novel phenomenon: double-peak and logarithmic. For the former, as the embedding dimension increases, performance first improves, then declines, rises again, and eventually drops. For the latter, it exhibits a perfect logarithmic curve. Our contributions are threefold. First, we discover two novel phenomena when scaling collaborative filtering models. Second, we gain an understanding of the underlying causes of the double-peak phenomenon. Lastly, we theoretically analyze the noise robustness of collaborative filtering models, with results matching empirical observations.

Scaling laws have emerged as important components of large language model (LLM) training as they can predict performance gains through scale, and provide guidance on important hyper-parameter choices that would otherwise be expensive. LLMs also rely on large, high-quality training datasets, like those sourced from (sometimes sensitive) user data. Training models on this sensitive user data requires careful privacy protections like differential privacy (DP). However, the dynamics of DP training are significantly different, and consequently their scaling laws are not yet fully understood. In this work, we establish scaling laws that accurately model the intricacies of DP LLM training, providing a complete picture of the compute-privacy-utility tradeoffs and the optimal training configurations in many settings.

We study reinforcement learning for global decision-making in the presence of many local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the rewards of both the global and the local agents. Such problems find many applications, e.g. demand response, EV charging, queueing, etc. In this setting, scalability has been a long-standing challenge due to the size of the state/action space which can be exponential in the number of agents. This work proposes the SUB-SAMPLE-Q algorithm where the global agent subsamples kleq n local agents to compute an optimal policy in time that is only exponential in k, providing an exponential speedup from standard methods that are exponential in n. We show that the learned policy converges to the optimal policy in the order of O(1/k+epsilon_{k,m}) as the number of sub-sampled agents k increases, where epsilon_{k,m} is the Bellman noise. We also conduct numerical simulations in a demand-response setting and a queueing setting.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Generalist imitation learning policies trained on large datasets show great promise for solving diverse manipulation tasks. However, to ensure generalization to different conditions, policies need to be trained with data collected across a large set of environmental factor variations (e.g., camera pose, table height, distractors) - a prohibitively expensive undertaking, if done exhaustively. We introduce a principled method for deciding what data to collect and how much to collect for each factor by constructing factored scaling curves (FSC), which quantify how policy performance varies as data scales along individual or paired factors. These curves enable targeted data acquisition for the most influential factor combinations within a given budget. We evaluate the proposed method through extensive simulated and real-world experiments, across both training-from-scratch and fine-tuning settings, and show that it boosts success rates in real-world tasks in new environments by up to 26% over existing data-collection strategies. We further demonstrate how factored scaling curves can effectively guide data collection using an offline metric, without requiring real-world evaluation at scale.

Scaling up the size of vision models has been the de facto standard to obtain more powerful visual representations. In this work, we discuss the point beyond which larger vision models are not necessary. First, we demonstrate the power of Scaling on Scales (S^2), whereby a pre-trained and frozen smaller vision model (e.g., ViT-B or ViT-L), run over multiple image scales, can outperform larger models (e.g., ViT-H or ViT-G) on classification, segmentation, depth estimation, Multimodal LLM (MLLM) benchmarks, and robotic manipulation. Notably, S^2 achieves state-of-the-art performance in detailed understanding of MLLM on the V* benchmark, surpassing models such as GPT-4V. We examine the conditions under which S^2 is a preferred scaling approach compared to scaling on model size. While larger models have the advantage of better generalization on hard examples, we show that features of larger vision models can be well approximated by those of multi-scale smaller models. This suggests most, if not all, of the representations learned by current large pre-trained models can also be obtained from multi-scale smaller models. Our results show that a multi-scale smaller model has comparable learning capacity to a larger model, and pre-training smaller models with S^2 can match or even exceed the advantage of larger models. We release a Python package that can apply S^2 on any vision model with one line of code: https://github.com/bfshi/scaling_on_scales.

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

FP8 formats are gaining popularity to boost the computational efficiency for training and inference of large deep learning models. Their main challenge is that a careful choice of scaling is needed to prevent degradation due to the reduced dynamic range compared to higher-precision formats. Although there exists ample literature about selecting such scalings for INT formats, this critical aspect has yet to be addressed for FP8. This paper presents a methodology to select the scalings for FP8 linear layers, based on dynamically updating per-tensor scales for the weights, gradients and activations. We apply this methodology to train and validate large language models of the type of GPT and Llama 2 using FP8, for model sizes ranging from 111M to 70B. To facilitate the understanding of the FP8 dynamics, our results are accompanied by plots of the per-tensor scale distribution for weights, activations and gradients during both training and inference.

Robot manipulation has seen tremendous progress in recent years, with imitation learning policies enabling successful performance of dexterous and hard-to-model tasks. Concurrently, scaling data and model size has led to the development of capable language and vision foundation models, motivating large-scale efforts to create general-purpose robot foundation models. While these models have garnered significant enthusiasm and investment, meaningful evaluation of real-world performance remains a challenge, limiting both the pace of development and inhibiting a nuanced understanding of current capabilities. In this paper, we rigorously evaluate multitask robot manipulation policies, referred to as Large Behavior Models (LBMs), by extending the Diffusion Policy paradigm across a corpus of simulated and real-world robot data. We propose and validate an evaluation pipeline to rigorously analyze the capabilities of these models with statistical confidence. We compare against single-task baselines through blind, randomized trials in a controlled setting, using both simulation and real-world experiments. We find that multi-task pretraining makes the policies more successful and robust, and enables teaching complex new tasks more quickly, using a fraction of the data when compared to single-task baselines. Moreover, performance predictably increases as pretraining scale and diversity grows. Project page: https://toyotaresearchinstitute.github.io/lbm1/

Novel computer vision architectures monopolize the spotlight, but the impact of the model architecture is often conflated with simultaneous changes to training methodology and scaling strategies. Our work revisits the canonical ResNet (He et al., 2015) and studies these three aspects in an effort to disentangle them. Perhaps surprisingly, we find that training and scaling strategies may matter more than architectural changes, and further, that the resulting ResNets match recent state-of-the-art models. We show that the best performing scaling strategy depends on the training regime and offer two new scaling strategies: (1) scale model depth in regimes where overfitting can occur (width scaling is preferable otherwise); (2) increase image resolution more slowly than previously recommended (Tan & Le, 2019). Using improved training and scaling strategies, we design a family of ResNet architectures, ResNet-RS, which are 1.7x - 2.7x faster than EfficientNets on TPUs, while achieving similar accuracies on ImageNet. In a large-scale semi-supervised learning setup, ResNet-RS achieves 86.2% top-1 ImageNet accuracy, while being 4.7x faster than EfficientNet NoisyStudent. The training techniques improve transfer performance on a suite of downstream tasks (rivaling state-of-the-art self-supervised algorithms) and extend to video classification on Kinetics-400. We recommend practitioners use these simple revised ResNets as baselines for future research.

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

Scaling laws play an instrumental role in the sustainable improvement in model quality. Unfortunately, recommendation models to date do not exhibit such laws similar to those observed in the domain of large language models, due to the inefficiencies of their upscaling mechanisms. This limitation poses significant challenges in adapting these models to increasingly more complex real-world datasets. In this paper, we propose an effective network architecture based purely on stacked factorization machines, and a synergistic upscaling strategy, collectively dubbed Wukong, to establish a scaling law in the domain of recommendation. Wukong's unique design makes it possible to capture diverse, any-order of interactions simply through taller and wider layers. We conducted extensive evaluations on six public datasets, and our results demonstrate that Wukong consistently outperforms state-of-the-art models quality-wise. Further, we assessed Wukong's scalability on an internal, large-scale dataset. The results show that Wukong retains its superiority in quality over state-of-the-art models, while holding the scaling law across two orders of magnitude in model complexity, extending beyond 100 Gflop or equivalently up to GPT-3/LLaMa-2 scale of total training compute, where prior arts fall short.

Developing AI agents to autonomously manipulate graphical user interfaces is a long challenging task. Recent advances in data scaling law inspire us to train computer-use agents with a scaled instruction set, yet using behavior cloning to train agents still requires immense high-quality trajectories. To meet the scalability need, we designed STEVE, a step verification pipeline for computer-use agent training. First, we establish a large instruction set for computer-use agents and collect trajectory data with some suboptimal agents. GPT-4o is used to verify the correctness of each step in the trajectories based on the screens before and after the action execution, assigning each step with a binary label. Last, we adopt the Kahneman and Tversky Optimization to optimize the agent from the binary stepwise labels. Extensive experiments manifest that our agent outperforms supervised finetuning by leveraging both positive and negative actions within a trajectory. Also, STEVE enables us to train a 7B vision-language model as a computer-use agent, achieving leading performance in the challenging live desktop environment WinAgentArena with great efficiency at a reduced cost. Code and data: https://github.com/FanbinLu/STEVE.

It is commonly believed that scaling language models should commit a significant space or time cost, by increasing the parameters (parameter scaling) or output tokens (inference-time scaling). We introduce the third and more inference-efficient scaling paradigm: increasing the model's parallel computation during both training and inference time. We apply P diverse and learnable transformations to the input, execute forward passes of the model in parallel, and dynamically aggregate the P outputs. This method, namely parallel scaling (ParScale), scales parallel computation by reusing existing parameters and can be applied to any model structure, optimization procedure, data, or task. We theoretically propose a new scaling law and validate it through large-scale pre-training, which shows that a model with P parallel streams is similar to scaling the parameters by O(log P) while showing superior inference efficiency. For example, ParScale can use up to 22times less memory increase and 6times less latency increase compared to parameter scaling that achieves the same performance improvement. It can also recycle an off-the-shelf pre-trained model into a parallelly scaled one by post-training on a small amount of tokens, further reducing the training budget. The new scaling law we discovered potentially facilitates the deployment of more powerful models in low-resource scenarios, and provides an alternative perspective for the role of computation in machine learning.

Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many large language models in deployment. However, autoregressive models rely on myopic temperature scaling that greedily optimizes the next token. To address this, we propose Long Horizon Temperature Scaling (LHTS), a novel approach for sampling from temperature-scaled joint distributions. LHTS is compatible with all likelihood-based models, and optimizes for the long-horizon likelihood of samples. We derive a temperature-dependent LHTS objective, and show that fine-tuning a model on a range of temperatures produces a single model capable of generation with a controllable long-horizon temperature parameter. We experiment with LHTS on image diffusion models and character/language autoregressive models, demonstrating advantages over myopic temperature scaling in likelihood and sample quality, and showing improvements in accuracy on a multiple choice analogy task by 10%.

As language models (LMs) scale, they develop many novel behaviors, good and bad, exacerbating the need to evaluate how they behave. Prior work creates evaluations with crowdwork (which is time-consuming and expensive) or existing data sources (which are not always available). Here, we automatically generate evaluations with LMs. We explore approaches with varying amounts of human effort, from instructing LMs to write yes/no questions to making complex Winogender schemas with multiple stages of LM-based generation and filtering. Crowdworkers rate the examples as highly relevant and agree with 90-100% of labels, sometimes more so than corresponding human-written datasets. We generate 154 datasets and discover new cases of inverse scaling where LMs get worse with size. Larger LMs repeat back a dialog user's preferred answer ("sycophancy") and express greater desire to pursue concerning goals like resource acquisition and goal preservation. We also find some of the first examples of inverse scaling in RL from Human Feedback (RLHF), where more RLHF makes LMs worse. For example, RLHF makes LMs express stronger political views (on gun rights and immigration) and a greater desire to avoid shut down. Overall, LM-written evaluations are high-quality and let us quickly discover many novel LM behaviors.

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.

Data scaling has revolutionized fields like natural language processing and computer vision, providing models with remarkable generalization capabilities. In this paper, we investigate whether similar data scaling laws exist in robotics, particularly in robotic manipulation, and whether appropriate data scaling can yield single-task robot policies that can be deployed zero-shot for any object within the same category in any environment. To this end, we conduct a comprehensive empirical study on data scaling in imitation learning. By collecting data across numerous environments and objects, we study how a policy's generalization performance changes with the number of training environments, objects, and demonstrations. Throughout our research, we collect over 40,000 demonstrations and execute more than 15,000 real-world robot rollouts under a rigorous evaluation protocol. Our findings reveal several intriguing results: the generalization performance of the policy follows a roughly power-law relationship with the number of environments and objects. The diversity of environments and objects is far more important than the absolute number of demonstrations; once the number of demonstrations per environment or object reaches a certain threshold, additional demonstrations have minimal effect. Based on these insights, we propose an efficient data collection strategy. With four data collectors working for one afternoon, we collect sufficient data to enable the policies for two tasks to achieve approximately 90% success rates in novel environments with unseen objects.

Vision-language models (VLMs) are trained for thousands of GPU hours on carefully curated web datasets. In recent times, data curation has gained prominence with several works developing strategies to retain 'high-quality' subsets of 'raw' scraped data. For instance, the LAION public dataset retained only 10% of the total crawled data. However, these strategies are typically developed agnostic of the available compute for training. In this paper, we first demonstrate that making filtering decisions independent of training compute is often suboptimal: the limited high-quality data rapidly loses its utility when repeated, eventually requiring the inclusion of 'unseen' but 'lower-quality' data. To address this quality-quantity tradeoff (QQT), we introduce neural scaling laws that account for the non-homogeneous nature of web data, an angle ignored in existing literature. Our scaling laws (i) characterize the differing 'utility' of various quality subsets of web data; (ii) account for how utility diminishes for a data point at its 'nth' repetition; and (iii) formulate the mutual interaction of various data pools when combined, enabling the estimation of model performance on a combination of multiple data pools without ever jointly training on them. Our key message is that data curation cannot be agnostic of the total compute that a model will be trained for. Our scaling laws allow us to curate the best possible pool for achieving top performance on Datacomp at various compute budgets, carving out a pareto-frontier for data curation. Code is available at https://github.com/locuslab/scaling_laws_data_filtering.

Preserving training dynamics across batch sizes is an important tool for practical machine learning as it enables the trade-off between batch size and wall-clock time. This trade-off is typically enabled by a scaling rule, for example, in stochastic gradient descent, one should scale the learning rate linearly with the batch size. Another important tool for practical machine learning is the model Exponential Moving Average (EMA), which is a model copy that does not receive gradient information, but instead follows its target model with some momentum. This model EMA can improve the robustness and generalization properties of supervised learning, stabilize pseudo-labeling, and provide a learning signal for Self-Supervised Learning (SSL). Prior works have treated the model EMA separately from optimization, leading to different training dynamics across batch sizes and lower model performance. In this work, we provide a scaling rule for optimization in the presence of model EMAs and demonstrate its validity across a range of architectures, optimizers, and data modalities. We also show the rule's validity where the model EMA contributes to the optimization of the target model, enabling us to train EMA-based pseudo-labeling and SSL methods at small and large batch sizes. For SSL, we enable training of BYOL up to batch size 24,576 without sacrificing performance, optimally a 6times wall-clock time reduction.

In recent years, language models have drastically grown in size, and the abilities of these models have been shown to improve with scale. The majority of recent scaling laws studies focused on high-compute high-parameter count settings, leaving the question of when these abilities begin to emerge largely unanswered. In this paper, we investigate whether the effects of pre-training can be observed when the problem size is reduced, modeling a smaller, reduced-vocabulary language. We show the benefits of pre-training with masked language modeling (MLM) objective in models as small as 1.25M parameters, and establish a strong correlation between pre-training perplexity and downstream performance (GLUE benchmark). We examine downscaling effects, extending scaling laws to models as small as ~1M parameters. At this scale, we observe a break of the power law for compute-optimal models and show that the MLM loss does not scale smoothly with compute-cost (FLOPs) below 2.2 times 10^{15} FLOPs. We also find that adding layers does not always benefit downstream performance.

Reasoning reinforcement learning (RL) has recently revealed a new scaling effect: test-time scaling. Thinking models such as R1 and o1 improve their reasoning accuracy at test time as the length of the reasoning context increases. However, compared with training-time scaling, test-time scaling is fundamentally limited by the limited context length of base models, which remains orders of magnitude smaller than the amount of tokens consumed during training. We revisit test-time enhancement techniques through the lens of scaling effect and introduce a unified framework of multi-dimensional test-time scaling to extend the capacity of test-time reasoning. Beyond conventional context-length scaling, we consider two additional dimensions: batch scaling, where accuracy improves with parallel sampling, and turn scaling, where iterative self-refinement enhances reasoning quality. Building on this perspective, we propose 3D test-time scaling, which integrates context, batch, and turn scaling. We show that: (1) each dimension demonstrates a test-time scaling effect, but with a bounded capacity; (2) combining all three dimensions substantially improves the reasoning performance of challenging testbeds, including IOI, IMO, and CPHO, and further benefits from human preference feedback; and (3) the human-in-the-loop framework naturally extends to a more open-ended domain, i.e., embodied learning, which enables the design of humanoid control behaviors.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

When using Large Language Models (LLMs) to support Knowledge Graph Engineering (KGE), one of the first indications when searching for an appropriate model is its size. According to the scaling laws, larger models typically show higher capabilities. However, in practice, resource costs are also an important factor and thus it makes sense to consider the ratio between model performance and costs. The LLM-KG-Bench framework enables the comparison of LLMs in the context of KGE tasks and assesses their capabilities of understanding and producing KGs and KG queries. Based on a dataset created in an LLM-KG-Bench run covering 26 open state-of-the-art LLMs, we explore the model size scaling laws specific to KGE tasks. In our analyses, we assess how benchmark scores evolve between different model size categories. Additionally, we inspect how the general score development of single models and families of models correlates to their size. Our analyses revealed that, with a few exceptions, the model size scaling laws generally also apply to the selected KGE tasks. However, in some cases, plateau or ceiling effects occurred, i.e., the task performance did not change much between a model and the next larger model. In these cases, smaller models could be considered to achieve high cost-effectiveness. Regarding models of the same family, sometimes larger models performed worse than smaller models of the same family. These effects occurred only locally. Hence it is advisable to additionally test the next smallest and largest model of the same family.

Recent work has shown that deep reinforcement learning agents have difficulty in effectively using their network parameters. We leverage prior insights into the advantages of sparse training techniques and demonstrate that gradual magnitude pruning enables agents to maximize parameter effectiveness. This results in networks that yield dramatic performance improvements over traditional networks and exhibit a type of "scaling law", using only a small fraction of the full network parameters.

Humans regularly engage in analogical thinking, relating personal experiences to current situations (X is analogous to Y because of Z). Analogical thinking allows humans to solve problems in creative ways, grasp difficult concepts, and articulate ideas more effectively. Can language models (LMs) do the same? To answer this question, we propose ANALOBENCH, a benchmark to determine analogical reasoning ability in LMs. Our benchmarking approach focuses on aspects of this ability that are common among humans: (i) recalling related experiences from a large amount of information, and (ii) applying analogical reasoning to complex and lengthy scenarios. We test a broad collection of proprietary models (e.g., GPT family, Claude V2) and open source models such as LLaMA2. As in prior results, scaling up LMs results in some performance boosts. Surprisingly, scale offers minimal gains when, (i) analogies involve lengthy scenarios, or (ii) recalling relevant scenarios from a large pool of information, a process analogous to finding a needle in a haystack. We hope these observations encourage further research in this field.

Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of 2 times 10^4 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen real world chaotic systems, and nonlinear resonance patterns in cross-channel attention heads. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.

Pioneering advancements in large language model-powered agents have underscored the design pattern of multi-agent collaboration, demonstrating that collective intelligence can surpass the capabilities of each individual. Inspired by the neural scaling law, which posits that increasing neurons leads to emergent abilities, this study investigates whether a similar principle applies to increasing agents in multi-agent collaboration. Technically, we propose multi-agent collaboration networks (MacNet), which utilize directed acyclic graphs to organize agents and streamline their interactive reasoning via topological ordering, with solutions derived from their dialogues. Extensive experiments show that MacNet consistently outperforms baseline models, enabling effective agent collaboration across various network topologies and supporting cooperation among more than a thousand agents. Notably, we observed a small-world collaboration phenomenon, where topologies resembling small-world properties achieved superior performance. Additionally, we identified a collaborative scaling law, indicating that normalized solution quality follows a logistic growth pattern as scaling agents, with collaborative emergence occurring much earlier than previously observed instances of neural emergence. The code and data will be available at https://github.com/OpenBMB/ChatDev.

Diffusion models offer impressive controllability for image tasks, primarily through noise predictions that encode task-specific information and classifier-free guidance enabling adjustable scaling. This scaling mechanism implicitly defines a ``scaling space'' whose potential for fine-grained semantic manipulation remains underexplored. We investigate this space, starting with inversion-based editing where the difference between conditional/unconditional noise predictions carries key semantic information. Our core contribution stems from a Fourier analysis of noise predictions, revealing that its low- and high-frequency components evolve differently throughout diffusion. Based on this insight, we introduce FreSca, a straightforward method that applies guidance scaling independently to different frequency bands in the Fourier domain. FreSca demonstrably enhances existing image editing methods without retraining. Excitingly, its effectiveness extends to image understanding tasks such as depth estimation, yielding quantitative gains across multiple datasets.

Scaling laws research has focused overwhelmingly on English -- yet the most prominent AI models explicitly serve billions of international users. In this work, we undertake the largest multilingual scaling laws study to date, totaling 774 multilingual training experiments, spanning 10M-8B model parameters, 400+ training languages and 48 evaluation languages. We introduce the Adaptive Transfer Scaling Law (ATLAS) for both monolingual and multilingual pretraining, which outperforms existing scaling laws' out-of-sample generalization often by more than 0.3 R^2. Our analyses of the experiments shed light on multilingual learning dynamics, transfer properties between languages, and the curse of multilinguality. First, we derive a cross-lingual transfer matrix, empirically measuring mutual benefit scores between 38 x 38=1444 language pairs. Second, we derive a language-agnostic scaling law that reveals how to optimally scale model size and data when adding languages without sacrificing performance. Third, we identify the computational crossover points for when to pretrain from scratch versus finetune from multilingual checkpoints. We hope these findings provide the scientific foundation for democratizing scaling laws across languages, and enable practitioners to efficiently scale models -- beyond English-first AI.

The Maximal Update Parametrization (muP) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-muP, which improves upon muP by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: muP ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-muP models reaching a lower loss than comparable muP models and working out-of-the-box in FP8.

Widely used language models (LMs) are typically built by scaling up a two-stage training pipeline: a pre-training stage that uses a very large, diverse dataset of text and a fine-tuning (sometimes, 'alignment') stage that uses targeted examples or other specifications of desired behaviors. While it has been hypothesized that knowledge and skills come from pre-training, and fine-tuning mostly filters this knowledge and skillset, this intuition has not been extensively tested. To aid in doing so, we introduce a novel technique for decoupling the knowledge and skills gained in these two stages, enabling a direct answer to the question, "What would happen if we combined the knowledge learned by a large model during pre-training with the knowledge learned by a small model during fine-tuning (or vice versa)?" Using an RL-based framework derived from recent developments in learning from human preferences, we introduce emulated fine-tuning (EFT), a principled and practical method for sampling from a distribution that approximates (or 'emulates') the result of pre-training and fine-tuning at different scales. Our experiments with EFT show that scaling up fine-tuning tends to improve helpfulness, while scaling up pre-training tends to improve factuality. Beyond decoupling scale, we show that EFT enables test-time adjustment of competing behavioral traits like helpfulness and harmlessness without additional training. Finally, a special case of emulated fine-tuning, which we call LM up-scaling, avoids resource-intensive fine-tuning of large pre-trained models by ensembling them with small fine-tuned models, essentially emulating the result of fine-tuning the large pre-trained model. Up-scaling consistently improves helpfulness and factuality of instruction-following models in the Llama, Llama-2, and Falcon families, without additional hyperparameters or training.

Over the past few years, the size of language models has grown exponentially, as has the computational cost to train these large models. This rapid growth has motivated researchers to develop new techniques aimed at enhancing the efficiency of the training process. Despite these advancements, optimally predicting the model size or allocating optimal resources remains a challenge. Several efforts have addressed the challenge by proposing different scaling laws, but almost all of them are architecture-specific (dense or sparse). In this work we revisit existing scaling laws and propose a generalized scaling law to provide a unified framework that is applicable to both dense and sparse large language models. We evaluate and compare our proposed scaling law with existing scaling laws to demonstrate its effectiveness.

The realization that complex systems such as ecological communities can collapse or shift regimes suddenly and without rapid external forcing poses a serious challenge to our understanding and management of the natural world. The potential to identify early warning signals that would allow researchers and managers to predict such events before they happen has therefore been an invaluable discovery that offers a way forward in spite of such seemingly unpredictable behavior. Research into early warning signals has demonstrated that it is possible to define and detect such early warning signals in advance of a transition in certain contexts. Here we describe the pattern emerging as research continues to explore just how far we can generalize these results. A core of examples emerges that shares three properties: the phenomenon of rapid regime shifts, a pattern of 'critical slowing down' that can be used to detect the approaching shift, and a mechanism of bifurcation driving the sudden change. As research has expanded beyond these core examples, it is becoming clear that not all systems that show regime shifts exhibit critical slowing down, or vice versa. Even when systems exhibit critical slowing down, statistical detection is a challenge. We review the literature that explores these edge cases and highlight the need for (a) new early warning behaviors that can be used in cases where rapid shifts do not exhibit critical slowing down, (b) the development of methods to identify which behavior might be an appropriate signal when encountering a novel system; bearing in mind that a positive indication for some systems is a negative indication in others, and (c) statistical methods that can distinguish between signatures of early warning behaviors and noise.

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model scale provides compelling evidence that larger models are also more capable models. However, scaling up models under the constraints of hardware and infrastructure is no easy feat, and rapidly becomes a hard and expensive engineering problem. We investigate ways to tentatively cheat scaling laws, and train larger models for cheaper. We emulate an increase in effective parameters, using efficient approximations: either by doping the models with frozen random parameters, or by using fast structured transforms in place of dense linear layers. We find that the scaling relationship between test loss and compute depends only on the actual number of trainable parameters; scaling laws cannot be deceived by spurious parameters.

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.

Self-supervised learning aims to learn representations from the data itself without explicit manual supervision. Existing efforts ignore a crucial aspect of self-supervised learning - the ability to scale to large amount of data because self-supervision requires no manual labels. In this work, we revisit this principle and scale two popular self-supervised approaches to 100 million images. We show that by scaling on various axes (including data size and problem 'hardness'), one can largely match or even exceed the performance of supervised pre-training on a variety of tasks such as object detection, surface normal estimation (3D) and visual navigation using reinforcement learning. Scaling these methods also provides many interesting insights into the limitations of current self-supervised techniques and evaluations. We conclude that current self-supervised methods are not 'hard' enough to take full advantage of large scale data and do not seem to learn effective high level semantic representations. We also introduce an extensive benchmark across 9 different datasets and tasks. We believe that such a benchmark along with comparable evaluation settings is necessary to make meaningful progress. Code is at: https://github.com/facebookresearch/fair_self_supervision_benchmark.

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: Investing more computational resources (optimally) leads to better performance, and even predictably so; neural scaling laws have been derived that accurately forecast the performance of a network for a desired level of compute. This leads to the notion of a "compute-optimal" model, i.e. a model that allocates a given level of compute during training optimally to maximise performance. In this work, we extend the concept of optimality by allowing for an "adaptive" model, i.e. a model that can change its shape during the course of training. By allowing the shape to adapt, we can optimally traverse between the underlying scaling laws, leading to a significant reduction in the required compute to reach a given target performance. We focus on vision tasks and the family of Vision Transformers, where the patch size as well as the width naturally serve as adaptive shape parameters. We demonstrate that, guided by scaling laws, we can design compute-optimal adaptive models that beat their "static" counterparts.

Scaling up language models has been shown to predictably improve performance and sample efficiency on a wide range of downstream tasks. This paper instead discusses an unpredictable phenomenon that we refer to as emergent abilities of large language models. We consider an ability to be emergent if it is not present in smaller models but is present in larger models. Thus, emergent abilities cannot be predicted simply by extrapolating the performance of smaller models. The existence of such emergence implies that additional scaling could further expand the range of capabilities of language models.

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

Uncovering early-stage metrics that reflect final model performance is one core principle for large-scale pretraining. The existing scaling law demonstrates the power-law correlation between pretraining loss and training flops, which serves as an important indicator of the current training state for large language models. However, this principle only focuses on the model's compression properties on the training data, resulting in an inconsistency with the ability improvements on the downstream tasks. Some follow-up works attempted to extend the scaling-law to more complex metrics (such as hyperparameters), but still lacked a comprehensive analysis of the dynamic differences among various capabilities during pretraining. To address the aforementioned limitations, this paper undertakes a comprehensive comparison of model capabilities at various pretraining intermediate checkpoints. Through this analysis, we confirm that specific downstream metrics exhibit similar training dynamics across models of different sizes, up to 67 billion parameters. In addition to our core findings, we've reproduced Amber and OpenLLaMA, releasing their intermediate checkpoints. This initiative offers valuable resources to the research community and facilitates the verification and exploration of LLM pretraining by open-source researchers. Besides, we provide empirical summaries, including performance comparisons of different models and capabilities, and tuition of key metrics for different training phases. Based on these findings, we provide a more user-friendly strategy for evaluating the optimization state, offering guidance for establishing a stable pretraining process.

A fairly reliable trend in deep reinforcement learning is that the performance scales with the number of parameters, provided a complimentary scaling in amount of training data. As the appetite for large models increases, it is imperative to address, sooner than later, the potential problem of running out of high-quality demonstrations. In this case, instead of collecting only new data via costly human demonstrations or risking a simulation-to-real transfer with uncertain effects, it would be beneficial to leverage vast amounts of readily-available low-quality data. Since classical control algorithms such as behavior cloning or temporal difference learning cannot be used on reward-free or action-free data out-of-the-box, this solution warrants novel training paradigms for continuous control. We propose a simple algorithm called Diffused Value Function (DVF), which learns a joint multi-step model of the environment-robot interaction dynamics using a diffusion model. This model can be efficiently learned from state sequences (i.e., without access to reward functions nor actions), and subsequently used to estimate the value of each action out-of-the-box. We show how DVF can be used to efficiently capture the state visitation measure for multiple controllers, and show promising qualitative and quantitative results on challenging robotics benchmarks.

Scaling has been critical in improving model performance and generalization in machine learning. It involves how a model's performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in other areas, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations. The dominant paradigm here is to incorporate many physical domain constraints into the model, such as rotational equivariance. We contend that these complex constraints inhibit the scaling ability of NNIPs, and are likely to lead to performance plateaus in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling strategies. Our findings indicate that scaling the model through attention mechanisms is efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency--at least 10x faster inference, 5x less memory usage--compared to existing NNIPs. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). We emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept for developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

While the field of Quality-Diversity (QD) has grown into a distinct branch of stochastic optimization, a few problems, in particular locomotion and navigation tasks, have become de facto standards. Are such benchmarks sufficient? Are they representative of the key challenges faced by QD algorithms? Do they provide the ability to focus on one particular challenge by properly disentangling it from others? Do they have much predictive power in terms of scalability and generalization? Existing benchmarks are not standardized, and there is currently no MNIST equivalent for QD. Inspired by recent works on Reinforcement Learning benchmarks, we argue that the identification of challenges faced by QD methods and the development of targeted, challenging, scalable but affordable benchmarks is an important step. As an initial effort, we identify three problems that are challenging in sparse reward settings, and propose associated benchmarks: (1) Behavior metric bias, which can result from the use of metrics that do not match the structure of the behavior space. (2) Behavioral Plateaus, with varying characteristics, such that escaping them would require adaptive QD algorithms and (3) Evolvability Traps, where small variations in genotype result in large behavioral changes. The environments that we propose satisfy the properties listed above.

Diffusion transformers (DiT) have already achieved appealing synthesis and scaling properties in content recreation, e.g., image and video generation. However, scaling laws of DiT are less explored, which usually offer precise predictions regarding optimal model size and data requirements given a specific compute budget. Therefore, experiments across a broad range of compute budgets, from 1e17 to 6e18 FLOPs are conducted to confirm the existence of scaling laws in DiT for the first time. Concretely, the loss of pretraining DiT also follows a power-law relationship with the involved compute. Based on the scaling law, we can not only determine the optimal model size and required data but also accurately predict the text-to-image generation loss given a model with 1B parameters and a compute budget of 1e21 FLOPs. Additionally, we also demonstrate that the trend of pre-training loss matches the generation performances (e.g., FID), even across various datasets, which complements the mapping from compute to synthesis quality and thus provides a predictable benchmark that assesses model performance and data quality at a reduced cost.

Autonomous agents driven by Large Language Models (LLMs) have revolutionized reasoning and problem-solving but remain static after training, unable to grow with experience as intelligent beings do during deployment. We introduce Forward Learning with EXperience (FLEX), a gradient-free learning paradigm that enables LLM agents to continuously evolve through accumulated experience. Specifically, FLEX cultivates scalable and inheritable evolution by constructing a structured experience library through continual reflection on successes and failures during interaction with the environment. FLEX delivers substantial improvements on mathematical reasoning, chemical retrosynthesis, and protein fitness prediction (up to 23% on AIME25, 10% on USPTO50k, and 14% on ProteinGym). We further identify a clear scaling law of experiential growth and the phenomenon of experience inheritance across agents, marking a step toward scalable and inheritable continuous agent evolution. Project Page: https://flex-gensi-thuair.github.io.

Test-time scaling (TTS) has demonstrated remarkable success in enhancing large language models, yet its application to next-token prediction (NTP) autoregressive (AR) image generation remains largely uncharted. Existing TTS approaches for visual AR (VAR), which rely on frequent partial decoding and external reward models, are ill-suited for NTP-based image generation due to the inherent incompleteness of intermediate decoding results. To bridge this gap, we introduce ScalingAR, the first TTS framework specifically designed for NTP-based AR image generation that eliminates the need for early decoding or auxiliary rewards. ScalingAR leverages token entropy as a novel signal in visual token generation and operates at two complementary scaling levels: (i) Profile Level, which streams a calibrated confidence state by fusing intrinsic and conditional signals; and (ii) Policy Level, which utilizes this state to adaptively terminate low-confidence trajectories and dynamically schedule guidance for phase-appropriate conditioning strength. Experiments on both general and compositional benchmarks show that ScalingAR (1) improves base models by 12.5% on GenEval and 15.2% on TIIF-Bench, (2) efficiently reduces visual token consumption by 62.0% while outperforming baselines, and (3) successfully enhances robustness, mitigating performance drops by 26.0% in challenging scenarios.

Scaling up the model size and computation has brought consistent performance improvements in supervised learning. However, this lesson often fails to apply to reinforcement learning (RL) because training the model on non-stationary data easily leads to overfitting and unstable optimization. In response, we introduce SimbaV2, a novel RL architecture designed to stabilize optimization by (i) constraining the growth of weight and feature norm by hyperspherical normalization; and (ii) using a distributional value estimation with reward scaling to maintain stable gradients under varying reward magnitudes. Using the soft actor-critic as a base algorithm, SimbaV2 scales up effectively with larger models and greater compute, achieving state-of-the-art performance on 57 continuous control tasks across 4 domains. The code is available at https://dojeon-ai.github.io/SimbaV2.

The leakage of benchmark data into the training data has emerged as a significant challenge for evaluating the capabilities of large language models (LLMs). In this work, we challenge the common assumption that small-scale contamination renders benchmark evaluations invalid. First, we experimentally quantify the magnitude of benchmark overfitting based on scaling along three dimensions: The number of model parameters (up to 1.6B), the number of times an example is seen (up to 144), and the number of training tokens (up to 40B). If model and data follow the Chinchilla scaling laws, minor contamination indeed leads to overfitting. At the same time, even 144 times of contamination can be forgotten if the training data is scaled beyond five times Chinchilla, a regime characteristic of many modern LLMs. Continual pre-training of OLMo-7B corroborates these results. Next, we study the impact of the weight decay parameter on example forgetting, showing that empirical forgetting occurs faster than the cumulative weight decay. This allows us to gauge the degree of example forgetting in large-scale training runs, indicating that many LLMs, including Lllama 3 405B, have forgotten the data seen at the beginning of training.

Does continued scaling of large language models (LLMs) yield diminishing returns? Real-world value often stems from the length of task an agent can complete. We start this work by observing the simple but counterintuitive fact that marginal gains in single-step accuracy can compound into exponential improvements in the length of a task a model can successfully complete. Then, we argue that failures of LLMs when simple tasks are made longer arise from mistakes in execution, rather than an inability to reason. We propose isolating execution capability, by explicitly providing the knowledge and plan needed to solve a long-horizon task. We find that larger models can correctly execute significantly more turns even when small models have 100\% single-turn accuracy. We observe that the per-step accuracy of models degrades as the number of steps increases. This is not just due to long-context limitations -- curiously, we observe a self-conditioning effect -- models become more likely to make mistakes when the context contains their errors from prior turns. Self-conditioning does not reduce by just scaling the model size. In contrast, recent thinking models do not self-condition, and can also execute much longer tasks in a single turn. We conclude by benchmarking frontier thinking models on the length of task they can execute in a single turn. Overall, by focusing on the ability to execute, we hope to reconcile debates on how LLMs can solve complex reasoning problems yet fail at simple tasks when made longer, and highlight the massive benefits of scaling model size and sequential test-time compute for long-horizon tasks.

The scaling hypothesis motivates the expansion of models past trillions of parameters as a path towards better performance. Recent significant developments, such as GPT-3, have been driven by this conjecture. However, as models scale-up, training them efficiently with backpropagation becomes difficult. Because model, pipeline, and data parallelism distribute parameters and gradients over compute nodes, communication is challenging to orchestrate: this is a bottleneck to further scaling. In this work, we argue that alternative training methods can mitigate these issues, and can inform the design of extreme-scale training hardware. Indeed, using a synaptically asymmetric method with a parallelizable backward pass, such as Direct Feedback Alignement, communication needs are drastically reduced. We present a photonic accelerator for Direct Feedback Alignment, able to compute random projections with trillions of parameters. We demonstrate our system on benchmark tasks, using both fully-connected and graph convolutional networks. Our hardware is the first architecture-agnostic photonic co-processor for training neural networks. This is a significant step towards building scalable hardware, able to go beyond backpropagation, and opening new avenues for deep learning.

We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps (s): $L(s) = L_0 + Acdot S_1^{-alpha} - Ccdot S_2 Where S_1 is forward area and S_2$ is learning rate annealing area. This formulation takes into account two factors: (1) The forward scaling defined as typical scaling law, and (2) the additional loss drop brought by LR annealing. Therefore, this formulation can describe the full loss curve at each step, rather than the single loss point at the end of training. Applying the scaling law with LR annealing and fitting only one or two training curves, we can accurately predict the loss of language model training at any given step and across any learning rate scheduler (LRS). Furthermore, this equation accurately describes the dynamics during training process, and provides a theoretical verification and explanation for numerous experimental findings of previous studies, particularly those focusing on LR schedule and LR annealing. The resulting insights, also serve as a guide for researchers to select critical LRS in advance by prediction using our equation. Most significantly, since all the points in a full training curve follow the equation, we can achieve accurate loss prediction at any given step across any learning rate scheduler, while expending less than 1\% of the computational cost required by the chinchilla scaling law to fit language modeling loss. This approach extremely democratizes scaling law fitting and predicting in developing large language models.

This paper describes an AI agent that plays the popular first-person-shooter (FPS) video game `Counter-Strike; Global Offensive' (CSGO) from pixel input. The agent, a deep neural network, matches the performance of the medium difficulty built-in AI on the deathmatch game mode, whilst adopting a humanlike play style. Unlike much prior work in games, no API is available for CSGO, so algorithms must train and run in real-time. This limits the quantity of on-policy data that can be generated, precluding many reinforcement learning algorithms. Our solution uses behavioural cloning - training on a large noisy dataset scraped from human play on online servers (4 million frames, comparable in size to ImageNet), and a smaller dataset of high-quality expert demonstrations. This scale is an order of magnitude larger than prior work on imitation learning in FPS games.

Language model pretraining with next token prediction has proved effective for scaling compute but is limited to the amount of available training data. Scaling reinforcement learning (RL) unlocks a new axis for the continued improvement of artificial intelligence, with the promise that large language models (LLMs) can scale their training data by learning to explore with rewards. However, prior published work has not produced competitive results. In light of this, we report on the training practice of Kimi k1.5, our latest multi-modal LLM trained with RL, including its RL training techniques, multi-modal data recipes, and infrastructure optimization. Long context scaling and improved policy optimization methods are key ingredients of our approach, which establishes a simplistic, effective RL framework without relying on more complex techniques such as Monte Carlo tree search, value functions, and process reward models. Notably, our system achieves state-of-the-art reasoning performance across multiple benchmarks and modalities -- e.g., 77.5 on AIME, 96.2 on MATH 500, 94-th percentile on Codeforces, 74.9 on MathVista -- matching OpenAI's o1. Moreover, we present effective long2short methods that use long-CoT techniques to improve short-CoT models, yielding state-of-the-art short-CoT reasoning results -- e.g., 60.8 on AIME, 94.6 on MATH500, 47.3 on LiveCodeBench -- outperforming existing short-CoT models such as GPT-4o and Claude Sonnet 3.5 by a large margin (up to +550%).

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Attention-based neural networks such as the Vision Transformer (ViT) have recently attained state-of-the-art results on many computer vision benchmarks. Scale is a primary ingredient in attaining excellent results, therefore, understanding a model's scaling properties is a key to designing future generations effectively. While the laws for scaling Transformer language models have been studied, it is unknown how Vision Transformers scale. To address this, we scale ViT models and data, both up and down, and characterize the relationships between error rate, data, and compute. Along the way, we refine the architecture and training of ViT, reducing memory consumption and increasing accuracy of the resulting models. As a result, we successfully train a ViT model with two billion parameters, which attains a new state-of-the-art on ImageNet of 90.45% top-1 accuracy. The model also performs well for few-shot transfer, for example, reaching 84.86% top-1 accuracy on ImageNet with only 10 examples per class.