Daily Papers

By utilizing more computational resources at test-time, large language models (LLMs) can improve without additional training. One common strategy uses verifiers to evaluate candidate outputs. In this work, we propose a novel scaling dimension for test-time compute: scaling the number of verifiers. We introduce Multi-Agent Verification (MAV) as a test-time compute paradigm that combines multiple verifiers to improve performance. We propose using Aspect Verifiers (AVs), off-the-shelf LLMs prompted to verify different aspects of outputs, as one possible choice for the verifiers in a MAV system. AVs are a convenient building block for MAV since they can be easily combined without additional training. Moreover, we introduce BoN-MAV, a simple multi-agent verification algorithm that combines best-of-n sampling with multiple verifiers. BoN-MAV demonstrates stronger scaling patterns than self-consistency and reward model verification, and we demonstrate both weak-to-strong generalization, where combining weak verifiers improves even stronger LLMs, and self-improvement, where the same base model is used to both generate and verify outputs. Our results establish scaling the number of verifiers as a promising new dimension for improving language model performance at test-time.

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.

Large language models (LLMs) with enormous pre-training tokens and parameter amounts emerge abilities, including math reasoning, code generation, and instruction following. These abilities are further enhanced by supervised fine-tuning (SFT). The open-source community has studied on ad-hoc SFT for each ability, while proprietary LLMs are versatile for all abilities. It is important to investigate how to unlock them with multiple abilities via SFT. In this study, we specifically focus on the data composition between mathematical reasoning, code generation, and general human-aligning abilities during SFT. From a scaling perspective, we investigate the relationship between model abilities and various factors including data amounts, data composition ratio, model parameters, and SFT strategies. Our experiments reveal that different abilities exhibit different scaling patterns, and larger models generally show superior performance with the same amount of data. Mathematical reasoning and code generation improve as data amounts increase consistently, while the general ability is enhanced with about a thousand samples and improves slowly. We find data composition results in various abilities improvements with low data amounts, while conflicts of abilities with high data amounts. Our experiments further show that composition data amount impacts performance, while the influence of composition ratio is insignificant. Regarding the SFT strategies, we evaluate sequential learning multiple abilities are prone to catastrophic forgetting. Our proposed Dual-stage Mixed Fine-tuning (DMT) strategy learns specialized abilities first and then learns general abilities with a small amount of specialized data to prevent forgetting, offering a promising solution to learn multiple abilities with different scaling patterns.

Continued pre-training of small language models offers a promising path for domain adaptation with limited computational resources. I've investigated this approach within educational domains, evaluating it as a resource-efficient alternative to training models from scratch. Using a 125M parameter model, I demonstrate significant performance improvements through incremental training on 400 million tokens, followed by further training to reach 1 billion tokens. My approach includes comprehensive data preprocessing, memory-optimized training configurations, and benchmark-based evaluation. Results show notable gains in knowledge-intensive tasks (MMLU +8.1%) and contextual understanding (HellaSwag +7.6%), while revealing educational domain specialization trade-offs. I analyze token efficiency, catastrophic forgetting mitigation strategies, and scaling patterns. My findings suggest that thoughtful preprocessing and training methodologies enable meaningful improvements in language model capabilities even with constrained computational resources, opening pathways for domain-specific adaptation of smaller language models.

Recent advances in large multimodal models have leveraged image-based tools with reinforcement learning to tackle visual problems. However, existing open-source approaches often exhibit monotonous reasoning patterns and allow only a limited number of interaction turns, making them inadequate for difficult tasks that require trial-and-error exploration. In this work, we address this limitation by scaling up tool-based interactions and introduce Mini-o3, a system that executes deep, multi-turn reasoning -- spanning tens of steps -- and achieves state-of-the-art performance on challenging visual search tasks. Our recipe for reproducing OpenAI o3-style behaviors comprises three key components. First, we construct the Visual Probe Dataset, a collection of thousands of challenging visual search problems designed for exploratory reasoning. Second, we develop an iterative data collection pipeline to obtain cold-start trajectories that exhibit diverse reasoning patterns, including depth-first search, trial-and-error, and goal maintenance. Third, we propose an over-turn masking strategy that prevents penalization of over-turn responses (those that hit the maximum number of turns) during reinforcement learning, thereby balancing training-time efficiency with test-time scalability. Despite training with an upper bound of only six interaction turns, our model generates trajectories that naturally scale to tens of turns at inference time, with accuracy improving as the number of turns increases. Extensive experiments demonstrate that Mini-o3 produces rich reasoning patterns and deep thinking paths, effectively solving challenging visual search problems.

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.

Motivated by scaling laws in language modeling that demonstrate how test loss scales as a power law with model and dataset sizes, we find that similar laws exist in preference modeling. We propose World Preference Modeling$ (WorldPM) to emphasize this scaling potential, where World Preference embodies a unified representation of human preferences. In this paper, we collect preference data from public forums covering diverse user communities, and conduct extensive training using 15M-scale data across models ranging from 1.5B to 72B parameters. We observe distinct patterns across different evaluation metrics: (1) Adversarial metrics (ability to identify deceptive features) consistently scale up with increased training data and base model size; (2) Objective metrics (objective knowledge with well-defined answers) show emergent behavior in larger language models, highlighting WorldPM's scalability potential; (3) Subjective metrics (subjective preferences from a limited number of humans or AI) do not demonstrate scaling trends. Further experiments validate the effectiveness of WorldPM as a foundation for preference fine-tuning. Through evaluations on 7 benchmarks with 20 subtasks, we find that WorldPM broadly improves the generalization performance across human preference datasets of varying sizes (7K, 100K and 800K samples), with performance gains exceeding 5% on many key subtasks. Integrating WorldPM into our internal RLHF pipeline, we observe significant improvements on both in-house and public evaluation sets, with notable gains of 4% to 8% in our in-house evaluations.

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.

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.

How do large language models (LLMs) develop and evolve over the course of training? How do these patterns change as models scale? To answer these questions, we introduce Pythia, a suite of 16 LLMs all trained on public data seen in the exact same order and ranging in size from 70M to 12B parameters. We provide public access to 154 checkpoints for each one of the 16 models, alongside tools to download and reconstruct their exact training dataloaders for further study. We intend Pythia to facilitate research in many areas, and we present several case studies including novel results in memorization, term frequency effects on few-shot performance, and reducing gender bias. We demonstrate that this highly controlled setup can be used to yield novel insights toward LLMs and their training dynamics. Trained models, analysis code, training code, and training data can be found at https://github.com/EleutherAI/pythia.

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.

Neural network scaling has been critical for improving the model quality in many real-world machine learning applications with vast amounts of training data and compute. Although this trend of scaling is affirmed to be a sure-fire approach for better model quality, there are challenges on the path such as the computation cost, ease of programming, and efficient implementation on parallel devices. GShard is a module composed of a set of lightweight annotation APIs and an extension to the XLA compiler. It provides an elegant way to express a wide range of parallel computation patterns with minimal changes to the existing model code. GShard enabled us to scale up multilingual neural machine translation Transformer model with Sparsely-Gated Mixture-of-Experts beyond 600 billion parameters using automatic sharding. We demonstrate that such a giant model can efficiently be trained on 2048 TPU v3 accelerators in 4 days to achieve far superior quality for translation from 100 languages to English compared to the prior art.

Language models have demonstrated remarkable capabilities in reasoning tasks through test-time scaling techniques like best-of-N sampling and tree search. However, these approaches often demand substantial computational resources, creating a critical trade-off between performance and efficiency. We introduce STAND (STochastic Adaptive N-gram Drafting), a novel model-free speculative decoding approach that leverages the inherent redundancy in reasoning trajectories to achieve significant acceleration without compromising accuracy. Our analysis reveals that reasoning paths frequently reuse similar reasoning patterns, enabling efficient model-free token prediction without requiring separate draft models. By introducing stochastic drafting and preserving probabilistic information through a memory-efficient logit-based N-gram module, combined with optimized Gumbel-Top-K sampling and data-driven tree construction, STAND significantly improves token acceptance rates. Extensive evaluations across multiple models and reasoning tasks (AIME-2024, GPQA-Diamond, and LiveCodeBench) demonstrate that STAND reduces inference latency by 60-65% compared to standard autoregressive decoding while maintaining accuracy. Furthermore, STAND outperforms state-of-the-art speculative decoding methods by 14-28% in throughput and shows strong performance even in single-trajectory scenarios, reducing inference latency by 48-58%. As a model-free approach, STAND can be applied to any existing language model without additional training, being a powerful plug-and-play solution for accelerating language model reasoning.

Reinforcement Learning from Human Feedback (RLHF) has been crucial to the recent success of Large Language Models (LLMs), however, it is often a complex and brittle process. In the classical RLHF framework, a reward model is first trained to represent human preferences, which is in turn used by an online reinforcement learning (RL) algorithm to optimize the LLM. A prominent issue with such methods is reward over-optimization or reward hacking, where performance as measured by the learned proxy reward model increases, but true quality plateaus or even deteriorates. Direct Alignment Algorithms (DDAs) like Direct Preference Optimization have emerged as alternatives to the classical RLHF pipeline by circumventing the reward modeling phase. However, although DAAs do not use a separate proxy reward model, they still commonly deteriorate from over-optimization. While the so-called reward hacking phenomenon is not well-defined for DAAs, we still uncover similar trends: at higher KL budgets, DAA algorithms exhibit similar degradation patterns to their classic RLHF counterparts. In particular, we find that DAA methods deteriorate not only across a wide range of KL budgets but also often before even a single epoch of the dataset is completed. Through extensive empirical experimentation, this work formulates and formalizes the reward over-optimization or hacking problem for DAAs and explores its consequences across objectives, training regimes, and model scales.

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

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.

Vision-Language-Action (VLA) models have recently emerged as a powerful paradigm for robotic manipulation. Despite substantial progress enabled by large-scale pretraining and supervised fine-tuning (SFT), these models face two fundamental challenges: (i) the scarcity and high cost of large-scale human-operated robotic trajectories required for SFT scaling, and (ii) limited generalization to tasks involving distribution shift. Recent breakthroughs in Large Reasoning Models (LRMs) demonstrate that reinforcement learning (RL) can dramatically enhance step-by-step reasoning capabilities, raising a natural question: Can RL similarly improve the long-horizon step-by-step action planning of VLA? In this work, we introduce SimpleVLA-RL, an efficient RL framework tailored for VLA models. Building upon veRL, we introduce VLA-specific trajectory sampling, scalable parallelization, multi-environment rendering, and optimized loss computation. When applied to OpenVLA-OFT, SimpleVLA-RL achieves SoTA performance on LIBERO and even outperforms pi_0 on RoboTwin 1.0\&2.0 with the exploration-enhancing strategies we introduce. SimpleVLA-RL not only reduces dependence on large-scale data and enables robust generalization, but also remarkably surpasses SFT in real-world tasks. Moreover, we identify a novel phenomenon ``pushcut'' during RL training, wherein the policy discovers previously unseen patterns beyond those seen in the previous training process. Github: https://github.com/PRIME-RL/SimpleVLA-RL

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.

Vision-language models (VLMs) trained via reinforcement learning with verifiable reward (RLVR) have shown notable progress in scaling test-time compute effectively. In this work, we investigate how synthesized RL data can further improve RLVR. To this end, we propose SynthRL-a scalable and guaranteed pipeline for automatic data scaling in reasoning-oriented RL training. SynthRL comprises three key stages: (1) selecting seed questions with appropriate distribution, (2) augmenting them into more challenging variants while preserving the original answers, and (3) a guaranteed verification stage that ensures near-perfect correctness and difficulty enhancement. Our empirical experiments demonstrate SynthRL's scalability and effectiveness. When applied to the MMK12 dataset, SynthRL synthesizes over 3.3K additional verifiable, challenging questions from approximately 8K seed samples. Models trained with our synthesized data achieve consistent gains across five out-of-domain visual math reasoning benchmarks, with a significant improvement over baseline models trained on seed data alone. Notably, detailed analysis reveals that the gains are more pronounced on the most challenging evaluation samples, highlighting SynthRL's effectiveness in eliciting deeper and more complex reasoning patterns.

We construct evaluation tasks where extending the reasoning length of Large Reasoning Models (LRMs) deteriorates performance, exhibiting an inverse scaling relationship between test-time compute and accuracy. Our evaluation tasks span four categories: simple counting tasks with distractors, regression tasks with spurious features, deduction tasks with constraint tracking, and advanced AI risks. We identify five distinct failure modes when models reason for longer: 1) Claude models become increasingly distracted by irrelevant information; 2) OpenAI o-series models resist distractors but overfit to problem framings; 3) models shift from reasonable priors to spurious correlations; 4) all models show difficulties in maintaining focus on complex deductive tasks; and 5) extended reasoning may amplify concerning behaviors, with Claude Sonnet 4 showing increased expressions of self-preservation. These findings suggest that while test-time compute scaling remains promising for improving model capabilities, it may inadvertently reinforce problematic reasoning patterns. Our results demonstrate the importance of evaluating models across diverse reasoning lengths to identify and address these failure modes in LRMs.

Recent advances in text-based large language models (LLMs), particularly in the GPT series and the o1 model, have demonstrated the effectiveness of scaling both training-time and inference-time compute. However, current state-of-the-art TTS systems leveraging LLMs are often multi-stage, requiring separate models (e.g., diffusion models after LLM), complicating the decision of whether to scale a particular model during training or testing. This work makes the following contributions: First, we explore the scaling of train-time and inference-time compute for speech synthesis. Second, we propose a simple framework Llasa for speech synthesis that employs a single-layer vector quantizer (VQ) codec and a single Transformer architecture to fully align with standard LLMs such as Llama. Our experiments reveal that scaling train-time compute for Llasa consistently improves the naturalness of synthesized speech and enables the generation of more complex and accurate prosody patterns. Furthermore, from the perspective of scaling inference-time compute, we employ speech understanding models as verifiers during the search, finding that scaling inference-time compute shifts the sampling modes toward the preferences of specific verifiers, thereby improving emotional expressiveness, timbre consistency, and content accuracy. In addition, we released the checkpoint and training code for our TTS model (1B, 3B, 8B) and codec model publicly available.

Training a high-quality deep neural network requires choosing suitable hyperparameters, which is a non-trivial and expensive process. Current works try to automatically optimize or design principles of hyperparameters, such that they can generalize to diverse unseen scenarios. However, most designs or optimization methods are agnostic to the choice of network structures, and thus largely ignore the impact of neural architectures on hyperparameters. In this work, we precisely characterize the dependence of initializations and maximal learning rates on the network architecture, which includes the network depth, width, convolutional kernel size, and connectivity patterns. By pursuing every parameter to be maximally updated with the same mean squared change in pre-activations, we can generalize our initialization and learning rates across MLPs (multi-layer perception) and CNNs (convolutional neural network) with sophisticated graph topologies. We verify our principles with comprehensive experiments. More importantly, our strategy further sheds light on advancing current benchmarks for architecture design. A fair comparison of AutoML algorithms requires accurate network rankings. However, we demonstrate that network rankings can be easily changed by better training networks in benchmarks with our architecture-aware learning rates and initialization.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Test-time scaling has emerged as a prominent research direction in machine learning, enabling models to enhance their expressive capabilities during inference.Transformers, renowned for striking a delicate balance between efficiency and expressiveness, have benefited from test-time scaling techniques that leverage an expanding key-value (KV) cache to significantly improve performance.In this paper, we introduce a novel state-based approach to test-time scaling, which we term state tuning, tailored to the RNN-based RWKV-7 model.By exploiting the unique strengths of RWKV-7, our method achieves state-of-the-art performance on the target task without altering the model's pre-trained weights. Our approach centers on three key innovations. First, we develop an observer framework that allows a smaller model to replicate and learn the state dynamics of the RWKV-7 model. Second, we employ a kernel method to dynamically upscale the state size, enhancing the model's capacity to capture intricate patterns. Third, we integrate Decorrelated Backpropagation (DBP) to optimize the upscaled state matrix, thereby improving convergence and expressivity. By tuning only the state matrix, we demonstrate that a smaller model can outperform larger models on the given task. This method preserves the efficiency of the original RWKV-7 architecture while harnessing the power of test-time scaling to deliver superior results. Our findings underscore the potential of state tuning as an effective strategy for advancing model performance in resource-constrained settings. Our code is https://github.com/TorchRWKV/flash-linear-attention.

The success of ChatGPT has recently attracted numerous efforts to replicate it, with instruction-tuning strategies being a key factor in achieving remarkable results. Instruction-tuning not only significantly enhances the model's performance and generalization but also makes the model's generated results more consistent with human speech patterns. However current research rarely studies the impact of different amounts of instruction data on model performance, especially in the real-world use cases. In this paper we explore the performance of large language models based on instruction tuning across different scales of instruction data. An evaluation dataset consisting of 12 major online use cases is constructed in the experiment. With Bloomz-7B1-mt as the base model, the results show that 1) merely increasing the amount of instruction data leads to continuous improvement in tasks such as open-ended generation, 2) in tasks such as math and code, the model performance curve remains quite flat while increasing data size. We further analyze the possible causes of these phenomena and propose potential future research directions such as effectively selecting high-quality training data, scaling base models and training methods specialized for hard tasks. We will release our training and evaluation datasets, as well as model checkpoints.

Large Reasoning Models (LRMs) demonstrate exceptional capability in tackling complex mathematical, logical, and coding tasks by leveraging extended Chain-of-Thought (CoT) reasoning. Test-time scaling methods, such as prolonging CoT with explicit token-level exploration, can push LRMs' accuracy boundaries, but they incur significant decoding overhead. A key inefficiency source is LRMs often generate redundant thinking CoTs, which demonstrate clear structured overthinking and underthinking patterns. Inspired by human cognitive reasoning processes and numerical optimization theories, we propose TrimR, a verifier-based, training-free, efficient framework for dynamic CoT compression to trim reasoning and enhance test-time scaling, explicitly tailored for production-level deployment. Our method employs a lightweight, pretrained, instruction-tuned verifier to detect and truncate redundant intermediate thoughts of LRMs without any LRM or verifier fine-tuning. We present both the core algorithm and asynchronous online system engineered for high-throughput industrial applications. Empirical evaluations on Ascend NPUs and vLLM show that our framework delivers substantial gains in inference efficiency under large-batch workloads. In particular, on the four MATH500, AIME24, AIME25, and GPQA benchmarks, the reasoning runtime of Pangu Pro MoE, Pangu-R-38B, QwQ-32B, and DeepSeek-R1-Distill-Qwen-32B is improved by up to 70% with negligible impact on accuracy.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Frequent itemset mining is a popular data mining technique. Apriori, Eclat, and FP-Growth are among the most common algorithms for frequent itemset mining. Considerable research has been performed to compare the relative performance between these three algorithms, by evaluating the scalability of each algorithm as the dataset size increases. While scalability as data size increases is important, previous papers have not examined the performance impact of similarly sized datasets that contain different itemset characteristics. This paper explores the effects that two dataset characteristics can have on the performance of these three frequent itemset algorithms. To perform this empirical analysis, a dataset generator is created to measure the effects of frequent item density and the maximum transaction size on performance. The generated datasets contain the same number of rows. This provides some insight into dataset characteristics that are conducive to each algorithm. The results of this paper's research demonstrate Eclat and FP-Growth both handle increases in maximum transaction size and frequent itemset density considerably better than the Apriori algorithm. This paper explores the effects that two dataset characteristics can have on the performance of these three frequent itemset algorithms. To perform this empirical analysis, a dataset generator is created to measure the effects of frequent item density and the maximum transaction size on performance. The generated datasets contain the same number of rows. This provides some insight into dataset characteristics that are conducive to each algorithm. The results of this paper's research demonstrate Eclat and FP-Growth both handle increases in maximum transaction size and frequent itemset density considerably better than the Apriori algorithm.

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.

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 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.

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.

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.

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.

Mathematical researchers, especially those in early-career positions, face critical decisions about topic specialization with limited information about the collaborative environments of different research areas. The aim of this paper is to study how the popularity of a research topic is associated with the structure of that topic's collaboration network, as observed by a suite of measures capturing organizational structure at several scales. We apply these measures to 1,938 algorithmically discovered topics across 121,391 papers sourced from arXiv metadata during the period 2020--2025. Our analysis, which controls for the confounding effects of network size, reveals a structural dichotomy--we find that popular topics organize into modular "schools of thought," while niche topics maintain hierarchical core-periphery structures centered around established experts. This divide is not an artifact of scale, but represents a size-independent structural pattern correlated with popularity. We also document a "constraint reversal": after controlling for size, researchers in popular fields face greater structural constraints on collaboration opportunities, contrary to conventional expectations. Our findings suggest that topic selection is an implicit choice between two fundamentally different collaborative environments, each with distinct implications for a researcher's career. To make these structural patterns transparent to the research community, we developed the Math Research Compass (https://mathresearchcompass.com), an interactive platform providing data on topic popularity and collaboration patterns across mathematical topics.

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.

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.

Visualizing multiple time series presents fundamental tradeoffs between scalability and visual clarity. Time series capture the behavior of many large-scale real-world processes, from stock market trends to urban activities. Users often gain insights by visualizing them as line charts, juxtaposing or superposing multiple time series to compare them and identify trends and patterns. However, existing representations struggle with scalability: when covering long time spans, leading to visual clutter from too many small multiples or overlapping lines. We propose TiVy, a new algorithm that summarizes time series using sequential patterns. It transforms the series into a set of symbolic sequences based on subsequence visual similarity using Dynamic Time Warping (DTW), then constructs a disjoint grouping of similar subsequences based on the frequent sequential patterns. The grouping result, a visual summary of time series, provides uncluttered superposition with fewer small multiples. Unlike common clustering techniques, TiVy extracts similar subsequences (of varying lengths) aligned in time. We also present an interactive time series visualization that renders large-scale time series in real-time. Our experimental evaluation shows that our algorithm (1) extracts clear and accurate patterns when visualizing time series data, (2) achieves a significant speed-up (1000X) compared to a straightforward DTW clustering. We also demonstrate the efficiency of our approach to explore hidden structures in massive time series data in two usage scenarios.

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.

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.

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.

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.

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.

Due to the unsupervised nature of anomaly detection, the key to fueling deep models is finding supervisory signals. Different from current reconstruction-guided generative models and transformation-based contrastive models, we devise novel data-driven supervision for tabular data by introducing a characteristic -- scale -- as data labels. By representing varied sub-vectors of data instances, we define scale as the relationship between the dimensionality of original sub-vectors and that of representations. Scales serve as labels attached to transformed representations, thus offering ample labeled data for neural network training. This paper further proposes a scale learning-based anomaly detection method. Supervised by the learning objective of scale distribution alignment, our approach learns the ranking of representations converted from varied subspaces of each data instance. Through this proxy task, our approach models inherent regularities and patterns within data, which well describes data "normality". Abnormal degrees of testing instances are obtained by measuring whether they fit these learned patterns. Extensive experiments show that our approach leads to significant improvement over state-of-the-art generative/contrastive anomaly detection methods.

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.

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.

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.

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.

Sparse attention can effectively mitigate the significant memory and throughput demands of Large Language Models (LLMs) in long contexts. Existing methods typically employ a uniform sparse attention mask, applying the same sparse pattern across different attention heads and input lengths. However, this uniform approach fails to capture the diverse attention patterns inherent in LLMs, ignoring their distinct accuracy-latency trade-offs. To address this challenge, we propose the Mixture of Attention (MoA), which automatically tailors distinct sparse attention configurations to different heads and layers. MoA constructs and navigates a search space of various attention patterns and their scaling rules relative to input sequence lengths. It profiles the model, evaluates potential configurations, and pinpoints the optimal sparse attention compression plan. MoA adapts to varying input sizes, revealing that some attention heads expand their focus to accommodate longer sequences, while other heads consistently concentrate on fixed-length local contexts. Experiments show that MoA increases the effective context length by 3.9times with the same average attention span, boosting retrieval accuracy by 1.5-7.1times over the uniform-attention baseline across Vicuna-7B, Vicuna-13B, and Llama3-8B models. Moreover, MoA narrows the capability gaps between sparse and dense models, reducing the maximum relative performance drop from 9%-36% to within 5% across two long-context understanding benchmarks. MoA achieves a 1.2-1.4times GPU memory reduction and boosts decode throughput by 5.5-6.7 times for 7B and 13B dense models on a single GPU, with minimal impact on performance.

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

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.

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.

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.

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for Sudoku, and matrix factorization. Concretely, we train diffusion models with an architecture tailored to the problem specification. This problem specification should contain a graphical model describing relationships between variables, and often benefits from explicit representation of subcomputations. Permutation invariances can also be exploited. Across a diverse set of experiments we improve the scaling relationship between problem dimension and our model's performance, in terms of both training time and final accuracy. Our code can be found at https://github.com/plai-group/gsdm.

Mixture of Experts (MoE) LLMs, characterized by their sparse activation patterns, offer a promising approach to scaling language models while avoiding proportionally increasing the inference cost. However, their large parameter sizes present deployment challenges in resource-constrained environments with limited GPU memory capacity, as GPU memory is often insufficient to accommodate the full set of model weights. Consequently, typical deployments rely on CPU-GPU hybrid execution: the GPU handles compute-intensive GEMM operations, while the CPU processes the relatively lightweight attention mechanism. This setup introduces a key challenge: how to effectively optimize resource utilization across CPU and GPU? Prior work has designed system optimizations based on performance models with limited scope. Specifically, such models do not capture the complex interactions between hardware properties and system execution mechanisms. Therefore, previous approaches neither identify nor achieve the hardware limit. This paper presents MoE-Lens, a high-throughput MoE LLM inference system designed through holistic performance modeling for resource-constrained environments. Our performance model thoroughly analyzes various fundamental system components, including CPU memory capacity, GPU compute power, and workload characteristics, to understand the theoretical performance upper bound of MoE inference. Furthermore, it captures the system execution mechanisms to identify the key hardware bottlenecks and accurately predict the achievable throughput. Informed by our performance model, MoE-Lens introduces an inference system approaching hardware limits. Evaluated on diverse MoE models and datasets, MoE-Lens outperforms the state-of-the-art solution by 4.6x on average (up to 25.5x), with our theoretical model predicting performance with an average 94% accuracy.

We propose a self-supervised method for learning motion-focused video representations. Existing approaches minimize distances between temporally augmented videos, which maintain high spatial similarity. We instead propose to learn similarities between videos with identical local motion dynamics but an otherwise different appearance. We do so by adding synthetic motion trajectories to videos which we refer to as tubelets. By simulating different tubelet motions and applying transformations, such as scaling and rotation, we introduce motion patterns beyond what is present in the pretraining data. This allows us to learn a video representation that is remarkably data-efficient: our approach maintains performance when using only 25% of the pretraining videos. Experiments on 10 diverse downstream settings demonstrate our competitive performance and generalizability to new domains and fine-grained actions.

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.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

This paper is not motivated to seek innovation within the attention mechanism. Instead, it focuses on overcoming the existing trade-offs between accuracy and efficiency within the context of point cloud processing, leveraging the power of scale. Drawing inspiration from recent advances in 3D large-scale representation learning, we recognize that model performance is more influenced by scale than by intricate design. Therefore, we present Point Transformer V3 (PTv3), which prioritizes simplicity and efficiency over the accuracy of certain mechanisms that are minor to the overall performance after scaling, such as replacing the precise neighbor search by KNN with an efficient serialized neighbor mapping of point clouds organized with specific patterns. This principle enables significant scaling, expanding the receptive field from 16 to 1024 points while remaining efficient (a 3x increase in processing speed and a 10x improvement in memory efficiency compared with its predecessor, PTv2). PTv3 attains state-of-the-art results on over 20 downstream tasks that span both indoor and outdoor scenarios. Further enhanced with multi-dataset joint training, PTv3 pushes these results to a higher level.

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.

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.

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.

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.

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.

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.

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.

Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets will be released.

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%.

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.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Scaling laws predict that the performance of large language models improves with increasing model size and data size. In practice, pre-training has been relying on massive web crawls, using almost all data sources publicly available on the internet so far. However, this pool of natural data does not grow at the same rate as the compute supply. Furthermore, the availability of high-quality texts is even more limited: data filtering pipelines often remove up to 99% of the initial web scrapes to achieve state-of-the-art. To address the "data wall" of pre-training scaling, our work explores ways to transform and recycle data discarded in existing filtering processes. We propose REWIRE, REcycling the Web with guIded REwrite, a method to enrich low-quality documents so that they could become useful for training. This in turn allows us to increase the representation of synthetic data in the final pre-training set. Experiments at 1B, 3B and 7B scales of the DCLM benchmark show that mixing high-quality raw texts and our rewritten texts lead to 1.0, 1.3 and 2.5 percentage points improvement respectively across 22 diverse tasks, compared to training on only filtered web data. Training on the raw-synthetic data mix is also more effective than having access to 2x web data. Through further analysis, we demonstrate that about 82% of the mixed in texts come from transforming lower-quality documents that would otherwise be discarded. REWIRE also outperforms related approaches of generating synthetic data, including Wikipedia-style paraphrasing, question-answer synthesizing and knowledge extraction. These results suggest that recycling web texts holds the potential for being a simple and effective approach for scaling pre-training data.

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 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

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 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.

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.

We introduce a pattern mining framework that operates on semi-structured datasets and exploits the dichotomy between outcomes. Our approach takes advantage of constraint reasoning to find sequential patterns that occur frequently and exhibit desired properties. This allows the creation of novel pattern embeddings that are useful for knowledge extraction and predictive modeling. Finally, we present an application on customer intent prediction from digital clickstream data. Overall, we show that pattern embeddings play an integrator role between semi-structured data and machine learning models, improve the performance of the downstream task and retain interpretability.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

While many capabilities of language models (LMs) improve with increased training budget, the influence of scale on hallucinations is not yet fully understood. Hallucinations come in many forms, and there is no universally accepted definition. We thus focus on studying only those hallucinations where a correct answer appears verbatim in the training set. To fully control the training data content, we construct a knowledge graph (KG)-based dataset, and use it to train a set of increasingly large LMs. We find that for a fixed dataset, larger and longer-trained LMs hallucinate less. However, hallucinating on leq5% of the training data requires an order of magnitude larger model, and thus an order of magnitude more compute, than Hoffmann et al. (2022) reported was optimal. Given this costliness, we study how hallucination detectors depend on scale. While we see detector size improves performance on fixed LM's outputs, we find an inverse relationship between the scale of the LM and the detectability of its hallucinations.

Deep learning has solved a problem that as little as five years ago was thought by many to be intractable - the automatic recognition of patterns in data; and it can do so with accuracy that often surpasses human beings. It has solved problems beyond the realm of traditional, hand-crafted machine learning algorithms and captured the imagination of practitioners trying to make sense out of the flood of data that now inundates our society. As public awareness of the efficacy of DL increases so does the desire to make use of it. But even for highly trained professionals it can be daunting to approach the rapidly increasing body of knowledge produced by experts in the field. Where does one start? How does one determine if a particular model is applicable to their problem? How does one train and deploy such a network? A primer on the subject can be a good place to start. With that in mind, we present an overview of some of the key multilayer ANNs that comprise DL. We also discuss some new automatic architecture optimization protocols that use multi-agent approaches. Further, since guaranteeing system uptime is becoming critical to many computer applications, we include a section on using neural networks for fault detection and subsequent mitigation. This is followed by an exploratory survey of several application areas where DL has emerged as a game-changing technology: anomalous behavior detection in financial applications or in financial time-series forecasting, predictive and prescriptive analytics, medical image processing and analysis and power systems research. The thrust of this review is to outline emerging areas of application-oriented research within the DL community as well as to provide a reference to researchers seeking to use it in their work for what it does best: statistical pattern recognition with unparalleled learning capacity with the ability to scale with information.

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.

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.

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.

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.

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.

Neural collapse (NC) is a phenomenon observed in classification tasks where top-layer representations collapse into their class means, which become equinorm, equiangular and aligned with the classifiers. These behaviors -- associated with generalization and robustness -- would manifest under specific conditions: models are trained towards zero loss, with noise-free labels belonging to balanced classes, which do not outnumber the model's hidden dimension. Recent studies have explored NC in the absence of one or more of these conditions to extend and capitalize on the associated benefits of ideal geometries. Language modeling presents a curious frontier, as training by token prediction constitutes a classification task where none of the conditions exist: the vocabulary is imbalanced and exceeds the embedding dimension; different tokens might correspond to similar contextual embeddings; and large language models (LLMs) in particular are typically only trained for a few epochs. This paper empirically investigates the impact of scaling the architectures and training of causal language models (CLMs) on their progression towards NC. We find that NC properties that develop with scaling are linked to generalization. Moreover, there is evidence of some relationship between NC and generalization independent of scale. Our work therefore underscores the generality of NC as it extends to the novel and more challenging setting of language modeling. Downstream, we seek to inspire further research on the phenomenon to deepen our understanding of LLMs -- and neural networks at large -- and improve existing architectures based on NC-related properties.

In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied, then the associated stochastic processes and their local times also converge. The metric-entropy condition can be checked by applying volume estimates of balls. Whilst similar results have been proved previously, the approach of this article is more widely applicable. Indeed, we recover various known conclusions for scaling limits of some deterministic self-similar fractal graphs, critical Galton-Watson trees, the critical Erdos-R\'enyi random graph and the configuration model (in the latter two cases, we prove for the first time the convergence of the models with respect to the resistance metric and also, for the configuration model, we overcome an error in the existing proof of local time convergence). Moreover, we derive new ones for scaling limits of uniform spanning trees and random recursive fractals. The metric-entropy condition also implies convergence of associated Gaussian processes.

Language exhibits a fractal structure in its information-theoretic complexity (i.e. bits per token), with self-similarity across scales and long-range dependence (LRD). In this work, we investigate whether large language models (LLMs) can replicate such fractal characteristics and identify conditions-such as temperature setting and prompting method-under which they may fail. Moreover, we find that the fractal parameters observed in natural language are contained within a narrow range, whereas those of LLMs' output vary widely, suggesting that fractal parameters might prove helpful in detecting a non-trivial portion of LLM-generated texts. Notably, these findings, and many others reported in this work, are robust to the choice of the architecture; e.g. Gemini 1.0 Pro, Mistral-7B and Gemma-2B. We also release a dataset comprising of over 240,000 articles generated by various LLMs (both pretrained and instruction-tuned) with different decoding temperatures and prompting methods, along with their corresponding human-generated texts. We hope that this work highlights the complex interplay between fractal properties, prompting, and statistical mimicry in LLMs, offering insights for generating, evaluating and detecting synthetic texts.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their algorithmic reasoning capabilities in realistic parameter regimes is lacking. We investigate this question in terms of the network's depth, width, and number of extra tokens for algorithm execution. Our novel representational hierarchy separates 9 algorithmic reasoning problems into classes solvable by transformers in different realistic parameter scaling regimes. We prove that logarithmic depth is necessary and sufficient for tasks like graph connectivity, while single-layer transformers with small embedding dimensions can solve contextual retrieval tasks. We also support our theoretical analysis with ample empirical evidence using the GraphQA benchmark. These results show that transformers excel at many graph reasoning tasks, even outperforming specialized graph neural networks.

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.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

We study the fractal structure of language, aiming to provide a precise formalism for quantifying properties that may have been previously suspected but not formally shown. We establish that language is: (1) self-similar, exhibiting complexities at all levels of granularity, with no particular characteristic context length, and (2) long-range dependent (LRD), with a Hurst parameter of approximately H=0.70. Based on these findings, we argue that short-term patterns/dependencies in language, such as in paragraphs, mirror the patterns/dependencies over larger scopes, like entire documents. This may shed some light on how next-token prediction can lead to a comprehension of the structure of text at multiple levels of granularity, from words and clauses to broader contexts and intents. We also demonstrate that fractal parameters improve upon perplexity-based bits-per-byte (BPB) in predicting downstream performance. We hope these findings offer a fresh perspective on language and the mechanisms underlying the success of LLMs.

Graph mining workloads aim to extract structural properties of a graph by exploring its subgraph structures. General purpose graph mining systems provide a generic runtime to explore subgraph structures of interest with the help of user-defined functions that guide the overall exploration process. However, the state-of-the-art graph mining systems remain largely oblivious to the shape (or pattern) of the subgraphs that they mine. This causes them to: (a) explore unnecessary subgraphs; (b) perform expensive computations on the explored subgraphs; and, (c) hold intermediate partial subgraphs in memory; all of which affect their overall performance. Furthermore, their programming models are often tied to their underlying exploration strategies, which makes it difficult for domain users to express complex mining tasks. In this paper, we develop Peregrine, a pattern-aware graph mining system that directly explores the subgraphs of interest while avoiding exploration of unnecessary subgraphs, and simultaneously bypassing expensive computations throughout the mining process. We design a pattern-based programming model that treats "graph patterns" as first class constructs and enables Peregrine to extract the semantics of patterns, which it uses to guide its exploration. Our evaluation shows that Peregrine outperforms state-of-the-art distributed and single machine graph mining systems, and scales to complex mining tasks on larger graphs, while retaining simplicity and expressivity with its "pattern-first" programming approach.

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.

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learning rate along with its scheduling, we systematically investigate the impact of scale on CBS. Then we fit scaling laws with respect to model and data sizes to decouple their effects. Overall, our results demonstrate that CBS scales primarily with data size rather than model size, a finding we justify theoretically through the analysis of infinite-width limits of neural networks and infinite-dimensional least squares regression. Of independent interest, we highlight the importance of common hyper-parameter choices and strategies for studying large-scale pre-training beyond fixed training durations.

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.

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.

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

Contemporary intelligent systems incorporate software components, including machine learning components. As they grow in complexity and data volume such machine learning systems face unique quality challenges like scalability and performance. To overcome them, engineers may often use specific architectural patterns, however their impact on ML systems is difficult to quantify. The effect of software architecture on traditional systems is well studied, however more work is needed in the area of machine learning systems. This study proposes a framework for quantitative assessment of architectural patterns in ML systems, focusing on scalability and performance metrics for cost-effective CPU-based inference. We integrate these metrics into a systematic evaluation process for selection of architectural patterns and demonstrate its application through a case study. The approach shown in the paper should enable software architects to objectively analyze and select optimal patterns, addressing key challenges in ML system design.

We classify and re-examine some of the current approaches to improve the performance-computes trade-off of language models, including (1) non-causal models (such as masked language models), (2) extension of batch length with efficient attention, (3) recurrence, (4) conditional computation and (5) retrieval. We identify some limitations (1) - (4) suffer from. For example, (1) currently struggles with open-ended text generation with the output loosely constrained by the input as well as performing general textual tasks like GPT-2/3 due to its need for a specific fine-tuning dataset. (2) and (3) do not improve the prediction of the first sim 10^3 tokens. Scaling up a model size (e.g. efficiently with (4)) still results in poor performance scaling for some tasks. We argue (5) would resolve many of these limitations, and it can (a) reduce the amount of supervision and (b) efficiently extend the context over the entire training dataset and the entire past of the current sample. We speculate how to modify MARGE to perform unsupervised causal modeling that achieves (b) with the retriever jointly trained.

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.

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.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

Seminal research in the field of graph neural networks (GNNs) has revealed a direct correspondence between the expressive capabilities of GNNs and the k-dimensional Weisfeiler-Leman (kWL) test, a widely-recognized method for verifying graph isomorphism. This connection has reignited interest in comprehending the specific graph properties effectively distinguishable by the kWL test. A central focus of research in this field revolves around determining the least dimensionality k, for which kWL can discern graphs with different number of occurrences of a pattern graph P. We refer to such a least k as the WL-dimension of this pattern counting problem. This inquiry traditionally delves into two distinct counting problems related to patterns: subgraph counting and induced subgraph counting. Intriguingly, despite their initial appearance as separate challenges with seemingly divergent approaches, both of these problems are interconnected components of a more comprehensive problem: "graph motif parameters". In this paper, we provide a precise characterization of the WL-dimension of labeled graph motif parameters. As specific instances of this result, we obtain characterizations of the WL-dimension of the subgraph counting and induced subgraph counting problem for every labeled pattern P. We additionally demonstrate that in cases where the kWL test distinguishes between graphs with varying occurrences of a pattern P, the exact number of occurrences of P can be computed uniformly using only local information of the last layer of a corresponding GNN. We finally delve into the challenge of recognizing the WL-dimension of various graph parameters. We give a polynomial time algorithm for determining the WL-dimension of the subgraph counting problem for given pattern P, answering an open question from previous work.

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.

While Large Language Models require more and more data to train and scale, rather than looking for any data to acquire, we should consider what types of tasks are more likely to benefit from data scaling. We should be intentional in our data acquisition. We argue that the topology of data itself informs which tasks to prioritize in data scaling, and shapes the development of the next generation of compute paradigms for tasks where data scaling is inefficient, or even insufficient.

Data profiling is an essential process in modern data-driven industries. One of its critical components is the discovery and validation of complex statistics, including functional dependencies, data constraints, association rules, and others. However, most existing data profiling systems that focus on complex statistics do not provide proper integration with the tools used by contemporary data scientists. This creates a significant barrier to the adoption of these tools in the industry. Moreover, existing systems were not created with industrial-grade workloads in mind. Finally, they do not aim to provide descriptive explanations, i.e. why a given pattern is not found. It is a significant issue as it is essential to understand the underlying reasons for a specific pattern's absence to make informed decisions based on the data. Because of that, these patterns are effectively rest in thin air: their application scope is rather limited, they are rarely used by the broader public. At the same time, as we are going to demonstrate in this presentation, complex statistics can be efficiently used to solve many classic data quality problems. Desbordante is an open-source data profiler that aims to close this gap. It is built with emphasis on industrial application: it is efficient, scalable, resilient to crashes, and provides explanations. Furthermore, it provides seamless Python integration by offloading various costly operations to the C++ core, not only mining. In this demonstration, we show several scenarios that allow end users to solve different data quality problems. Namely, we showcase typo detection, data deduplication, and data anomaly detection scenarios.

Pretraining data of large language models composes multiple domains (e.g., web texts, academic papers, codes), whose mixture proportions crucially impact the competence of outcome models. While existing endeavors rely on heuristics or qualitative strategies to tune the proportions, we discover the quantitative predictability of model performance regarding the mixture proportions in function forms, which we refer to as the data mixing laws. Fitting such functions on sample mixtures unveils model performance on unseen mixtures before actual runs, thus guiding the selection of an ideal data mixture. Furthermore, we propose nested use of the scaling laws of training steps, model sizes, and our data mixing law to enable predicting the performance of large models trained on massive data under various mixtures with only small-scale training. Moreover, experimental results verify that our method effectively optimizes the training mixture of a 1B model trained for 100B tokens in RedPajama, reaching a performance comparable to the one trained for 48% more steps on the default mixture. Extending the application of data mixing laws to continual training accurately predicts the critical mixture proportion that avoids catastrophic forgetting and outlooks the potential for dynamic data schedules

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.

Scaling laws are powerful tools to predict the performance of large language models. However, current scaling laws fall short of accounting for inference costs. In this work, we first show that model architecture affects inference latency, where models of the same size can have up to 3.5x difference in latency. To tackle this challenge, we modify the Chinchilla scaling laws to co-optimize the model parameter count, the number of training tokens, and the model architecture. Due to the reason that models of similar training loss exhibit gaps in downstream evaluation, we also propose a novel method to train inference-efficient models based on the revised scaling laws. We perform extensive empirical studies to fit and evaluate our inference-aware scaling laws. We vary model parameters from 80M to 1B, training tokens from 1.6B to 30B, and model shapes, training a total of 63 models. Guided by our inference-efficient scaling law and model selection method, we release the Morph-1B model, which improves inference latency by 1.8x while maintaining accuracy on downstream tasks compared to open-source models, pushing the Pareto frontier of accuracy-latency tradeoff.

We apply a complex network approach to analyse the time series of five solar parameters, and propose an strategy to predict the number of sunspots for the next solar maximum, and when will this maximum will occur. The approach is based on the Visibility Graph (VG) algorithm, and a slightly modified version of it, the Horizontal Visibility Graph (HVG), which map a time series into a complex network. Various network metrics exhibit either an exponential or a scale-free behavior, and we find that the evolution of the characteristic decay exponents is consistent with variations of the sunspots number along solar cycles. During solar minimum, the sunspots number and the solar index time series have characteristic decay exponents that correlate well with the next maximum sunspots number, suggesting that they may be good precursors of the intensity of the next solar maximum. Based on this observation, we find that, based on current data, the algorithm predicts a number of 179 sunspots for cycle 25. Combining this with the Hathaway function, adjusted to yield such maximum sunspots number, we find that the maximum for solar cycle 25 will occur in December 2024/January 2025.

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.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by 1/depth (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

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.

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy "graph tracing" task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

Finding evidence for human opinion and behavior at scale is a challenging task, often requiring an understanding of sophisticated thought patterns among vast online communities found on social media. For example, studying how gun ownership is related to the perception of Freedom, requires a retrieval system that can operate at scale over social media posts, while dealing with two key challenges: (1) identifying abstract concept instances, (2) which can be instantiated differently across different communities. To address these, we introduce ConceptCarve, an evidence retrieval framework that utilizes traditional retrievers and LLMs to dynamically characterize the search space during retrieval. Our experiments show that ConceptCarve surpasses traditional retrieval systems in finding evidence within a social media community. It also produces an interpretable representation of the evidence for that community, which we use to qualitatively analyze complex thought patterns that manifest differently across the communities.

Full-complexity Earth system models (ESMs) are computationally very expensive, limiting their use in exploring the climate outcomes of multiple emission pathways. More efficient emulators that approximate ESMs can directly map emissions onto climate outcomes, and benchmarks are being used to evaluate their accuracy on standardized tasks and datasets. We investigate a popular benchmark in data-driven climate emulation, ClimateBench, on which deep learning-based emulators are currently achieving the best performance. We implement a linear regression-based emulator, akin to pattern scaling, and find that it outperforms the incumbent 100M-parameter deep learning foundation model, ClimaX, on 3 out of 4 regionally-resolved surface-level climate variables. While emulating surface temperature is expected to be predominantly linear, this result is surprising for emulating precipitation. We identify that this outcome is a result of high levels of internal variability in the benchmark targets. To address internal variability, we update the benchmark targets with ensemble averages from the MPI-ESM1.2-LR model that contain 50 instead of 3 climate simulations per emission pathway. Using the new targets, we show that linear pattern scaling continues to be more accurate on temperature, but can be outperformed by a deep learning-based model for emulating precipitation. We publish our code, data, and an interactive tutorial at github.com/blutjens/climate-emulator.

We introduce MONSTER-the MONash Scalable Time Series Evaluation Repository-a collection of large datasets for time series classification. The field of time series classification has benefitted from common benchmarks set by the UCR and UEA time series classification repositories. However, the datasets in these benchmarks are small, with median sizes of 217 and 255 examples, respectively. In consequence they favour a narrow subspace of models that are optimised to achieve low classification error on a wide variety of smaller datasets, that is, models that minimise variance, and give little weight to computational issues such as scalability. Our hope is to diversify the field by introducing benchmarks using larger datasets. We believe that there is enormous potential for new progress in the field by engaging with the theoretical and practical challenges of learning effectively from larger quantities of data.

We consider the Similarity Sketching problem: Given a universe [u] = {0,ldots, u-1} we want a random function S mapping subsets Asubseteq [u] into vectors S(A) of size t, such that the Jaccard similarity J(A,B) = |Acap B|/|Acup B| between sets A and B is preserved. More precisely, define X_i = [S(A)[i] = S(B)[i]] and X = sum_{iin [t]} X_i. We want E[X_i]=J(A,B), and we want X to be strongly concentrated around E[X] = t cdot J(A,B) (i.e. Chernoff-style bounds). This is a fundamental problem which has found numerous applications in data mining, large-scale classification, computer vision, similarity search, etc. via the classic MinHash algorithm. The vectors S(A) are also called sketches. Strong concentration is critical, for often we want to sketch many sets B_1,ldots,B_n so that we later, for a query set A, can find (one of) the most similar B_i. It is then critical that no B_i looks much more similar to A due to errors in the sketch. The seminal ttimesMinHash algorithm uses t random hash functions h_1,ldots, h_t, and stores left ( min_{ain A} h_1(A),ldots, min_{ain A} h_t(A) right ) as the sketch of A. The main drawback of MinHash is, however, its O(tcdot |A|) running time, and finding a sketch with similar properties and faster running time has been the subject of several papers. (continued...)

Artefact descriptions are the primary carriers of engineering design knowledge that is both an outcome and a driver of the design process. While an artefact could be described in different connotations, the design process requires a description to embody engineering design knowledge, which is expressed in the text through intricate placement of entities and relationships. As large-language models learn from all kinds of text merely as a sequence of characters/tokens, these are yet to generate text that embodies explicit engineering design facts. Existing ontological design theories are less likely to guide the large-language models whose applications are currently limited to ideation and learning purposes. In this article, we explicate engineering design knowledge as knowledge graphs from a large sample of 33,881 patent documents. We examine the constituents of these knowledge graphs to understand the linguistic and structural basis of engineering design knowledge. In terms of linguistic basis, we observe that entities and relationships could be generalised to 64 and 24 linguistic syntaxes. While relationships mainly capture attributes ('of'), structure ('in', 'with'), purpose ('to', 'for'), hierarchy ('include'), exemplification ('such as'), and behaviour ('to', 'from'), the hierarchical relationships could specifically be identified using 75 unique syntaxes. To understand the structural basis, we draw inspiration from various studies on biological/ecological networks and discover motifs from patent knowledge graphs. We identify four 3-node and four 4-node patterns that could further be converged and simplified into sequence [->...->], aggregation [->...<-], and hierarchy [<-...->]. Expected to guide large-language model based design tools, we propose few regulatory precepts for concretising abstract entities and relationships within subgraphs, while explicating hierarchical structures.

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.

A research division plays an important role of driving innovation in an organization. Drawing insights, following trends, keeping abreast of new research, and formulating strategies are increasingly becoming more challenging for both researchers and executives as the amount of information grows in both velocity and volume. In this paper we present a use case of how a corporate research community, IBM Research, utilizes Semantic Web technologies to induce a unified Knowledge Graph from both structured and textual data obtained by integrating various applications used by the community related to research projects, academic papers, datasets, achievements and recognition. In order to make the Knowledge Graph more accessible to application developers, we identified a set of common patterns for exploiting the induced knowledge and exposed them as APIs. Those patterns were born out of user research which identified the most valuable use cases or user pain points to be alleviated. We outline two distinct scenarios: recommendation and analytics for business use. We will discuss these scenarios in detail and provide an empirical evaluation on entity recommendation specifically. The methodology used and the lessons learned from this work can be applied to other organizations facing similar challenges.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.

Scaling laws guide the development of large language models (LLMs) by offering estimates for the optimal balance of model size, tokens, and compute. More recently, loss-to-loss scaling laws that relate losses across pretraining datasets and downstream tasks have emerged as a powerful tool for understanding and improving LLM performance. In this work, we investigate which factors most strongly influence loss-to-loss scaling. Our experiments reveal that the pretraining data and tokenizer determine the scaling trend. In contrast, model size, optimization hyperparameters, and even significant architectural differences, such as between transformer-based models like Llama and state-space models like Mamba, have limited impact. Consequently, practitioners should carefully curate suitable pretraining datasets for optimal downstream performance, while architectures and other settings can be freely optimized for training efficiency.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series analytical tasks. This survey provides a comprehensive overview of the current state of the art pre-trained foundation models, introducing a novel taxonomy to categorize them across several dimensions. Specifically, we classify models by their architecture design, distinguishing between those leveraging patch-based representations and those operating directly on raw sequences. The taxonomy further includes whether the models provide probabilistic or deterministic predictions, and whether they are designed to work with univariate time series or can handle multivariate time series out of the box. Additionally, the taxonomy encompasses model scale and complexity, highlighting differences between lightweight architectures and large-scale foundation models. A unique aspect of this survey is its categorization by the type of objective function employed during training phase. By synthesizing these perspectives, this survey serves as a resource for researchers and practitioners, providing insights into current trends and identifying promising directions for future research in transformer-based time series modeling.

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.

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been extensively used in the most diverse types of problems, also motivating some respective generalizations. The present work addresses further generalizations of this index, including its modification into a coincidence index capable of accounting also for the level of relative interiority between the two compared entities, as well as respective extensions for sets in continuous vector spaces, the generalization to multiset addition, densities and generic scalar fields, as well as a means to quantify the joint interdependence between two random variables. The also interesting possibility to take into account more than two sets has also been addressed, including the description of an index capable of quantifying the level of chaining between three structures. Several of the described and suggested eneralizations have been illustrated with respect to numeric case examples. It is also posited that these indices can play an important role while analyzing and integrating datasets in modeling approaches and pattern recognition activities, including as a measurement of clusters similarity or separation and as a resource for representing and analyzing complex networks.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 442 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting.

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.

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.

As large language models increase in capability, researchers have started to conduct surveys of all kinds on these models with varying scientific motivations. In this work, we examine what we can learn from a model's survey responses on the basis of the well-established American Community Survey (ACS) by the U.S. Census Bureau. Evaluating more than a dozen different models, varying in size from a few hundred million to ten billion parameters, hundreds of thousands of times each on questions from the ACS, we systematically establish two dominant patterns. First, smaller models have a significant position and labeling bias, for example, towards survey responses labeled with the letter "A". This A-bias diminishes, albeit slowly, as model size increases. Second, when adjusting for this labeling bias through randomized answer ordering, models still do not trend toward US population statistics or those of any cognizable population. Rather, models across the board trend toward uniformly random aggregate statistics over survey responses. This pattern is robust to various different ways of prompting the model, including what is the de-facto standard. Our findings demonstrate that aggregate statistics of a language model's survey responses lack the signals found in human populations. This absence of statistical signal cautions about the use of survey responses from large language models at present time.

Because large language models are expensive to pretrain on different datasets, using smaller-scale experiments to decide on data is crucial for reducing costs. Which benchmarks and methods of making decisions from observed performance at small scale most accurately predict the datasets that yield the best large models? To empower open exploration of this question, we release models, data, and evaluations in DataDecide -- the most extensive open suite of models over differences in data and scale. We conduct controlled pretraining experiments across 25 corpora with differing sources, deduplication, and filtering up to 100B tokens, model sizes up to 1B parameters, and 3 random seeds. We find that the ranking of models at a single, small size (e.g., 150M parameters) is a strong baseline for predicting best models at our larger target scale (1B) (~80% of com parisons correct). No scaling law methods among 8 baselines exceed the compute-decision frontier of single-scale predictions, but DataDecide can measure improvement in future scaling laws. We also identify that using continuous likelihood metrics as proxies in small experiments makes benchmarks including MMLU, ARC, HellaSwag, MBPP, and HumanEval >80% predictable at the target 1B scale with just 0.01% of the compute.

Time series models face significant challenges in scaling to handle large and complex datasets, akin to the scaling achieved by large language models (LLMs). The unique characteristics of time series data and the computational demands of model scaling necessitate innovative approaches. While researchers have explored various architectures such as Transformers, LSTMs, and GRUs to address these challenges, we propose a novel solution using RWKV-7, which incorporates meta-learning into its state update mechanism. By integrating RWKV-7's time mix and channel mix components into the transformer-based time series model Timer, we achieve a substantial performance improvement of approximately 1.13 to 43.3x and a 4.5x reduction in training time with 1/23 parameters, all while utilizing fewer parameters. Our code and model weights are publicly available for further research and development at https://github.com/Alic-Li/BlackGoose_Rimer.

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.

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.

Large language model pre-training has become increasingly expensive, with most practitioners relying on scaling laws to allocate compute budgets for model size and training tokens, commonly referred to as Compute-Optimal or Chinchilla Optimal. In this paper, we hypothesize a new scaling law that suggests model performance depends mostly on the amount of compute spent for transformer-based models, independent of the specific allocation to model size and dataset size. Using this unified scaling law, we predict that (a) for inference efficiency, training should prioritize smaller model sizes and larger training datasets, and (b) assuming the exhaustion of available web datasets, scaling the model size might be the only way to further improve model performance.

Analyzing both temporal and spatial patterns for an accurate forecasting model for financial time series forecasting is a challenge due to the complex nature of temporal-spatial dynamics: time series from different locations often have distinct patterns; and for the same time series, patterns may vary as time goes by. Inspired by the successful applications of deep learning, we propose a new model to resolve the issues of forecasting household leverage in China. Our solution consists of multiple RNN-based layers and an attention layer: each RNN-based layer automatically learns the temporal pattern of a specific series with multivariate exogenous series, and then the attention layer learns the spatial correlative weight and obtains the global representations simultaneously. The results show that the new approach can capture the temporal-spatial dynamics of household leverage well and get more accurate and solid predictive results. More, the simulation also studies show that clustering and choosing correlative series are necessary to obtain accurate forecasting results.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

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.

In diffusion models, UNet is the most popular network backbone, since its long skip connects (LSCs) to connect distant network blocks can aggregate long-distant information and alleviate vanishing gradient. Unfortunately, UNet often suffers from unstable training in diffusion models which can be alleviated by scaling its LSC coefficients smaller. However, theoretical understandings of the instability of UNet in diffusion models and also the performance improvement of LSC scaling remain absent yet. To solve this issue, we theoretically show that the coefficients of LSCs in UNet have big effects on the stableness of the forward and backward propagation and robustness of UNet. Specifically, the hidden feature and gradient of UNet at any layer can oscillate and their oscillation ranges are actually large which explains the instability of UNet training. Moreover, UNet is also provably sensitive to perturbed input, and predicts an output distant from the desired output, yielding oscillatory loss and thus oscillatory gradient. Besides, we also observe the theoretical benefits of the LSC coefficient scaling of UNet in the stableness of hidden features and gradient and also robustness. Finally, inspired by our theory, we propose an effective coefficient scaling framework ScaleLong that scales the coefficients of LSC in UNet and better improves the training stability of UNet. Experimental results on four famous datasets show that our methods are superior to stabilize training and yield about 1.5x training acceleration on different diffusion models with UNet or UViT backbones. Code: https://github.com/sail-sg/ScaleLong

Hidden Markov Models (HMMs) are foundational tools for modeling sequential data with latent Markovian structure, yet fitting them to real-world data remains computationally challenging. In this work, we show that pre-trained large language models (LLMs) can effectively model data generated by HMMs via in-context learning (ICL)x2013their ability to infer patterns from examples within a prompt. On a diverse set of synthetic HMMs, LLMs achieve predictive accuracy approaching the theoretical optimum. We uncover novel scaling trends influenced by HMM properties, and offer theoretical conjectures for these empirical observations. We also provide practical guidelines for scientists on using ICL as a diagnostic tool for complex data. On real-world animal decision-making tasks, ICL achieves competitive performance with models designed by human experts. To our knowledge, this is the first demonstration that ICL can learn and predict HMM-generated sequencesx2013an advance that deepens our understanding of in-context learning in LLMs and establishes its potential as a powerful tool for uncovering hidden structure in complex scientific data.

Large language models can solve new tasks without task-specific fine-tuning. This ability, also known as in-context learning (ICL), is considered an emergent ability and is primarily seen in large language models with billions of parameters. This study investigates if such emergent properties are strictly tied to model size or can be demonstrated by smaller models trained on reduced-scale data. To explore this, we simplify pre-training data and pre-train 36 causal language models with parameters varying from 1 million to 165 million parameters. We show that models trained on this simplified pre-training data demonstrate enhanced zero-shot capabilities across various tasks in simplified language, achieving performance comparable to that of pre-trained models six times larger on unrestricted language. This suggests that downscaling the language allows zero-shot learning capabilities to emerge in models with limited size. Additionally, we find that these smaller models pre-trained on simplified data demonstrate a power law relationship between the evaluation loss and the three scaling factors: compute, dataset size, and model size.

Data pruning algorithms are commonly used to reduce the memory and computational cost of the optimization process. Recent empirical results reveal that random data pruning remains a strong baseline and outperforms most existing data pruning methods in the high compression regime, i.e., where a fraction of 30% or less of the data is kept. This regime has recently attracted a lot of interest as a result of the role of data pruning in improving the so-called neural scaling laws; in [Sorscher et al.], the authors showed the need for high-quality data pruning algorithms in order to beat the sample power law. In this work, we focus on score-based data pruning algorithms and show theoretically and empirically why such algorithms fail in the high compression regime. We demonstrate ``No Free Lunch" theorems for data pruning and present calibration protocols that enhance the performance of existing pruning algorithms in this high compression regime using randomization.

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

Scaling the amount of compute used to train language models has dramatically improved their capabilities. However, when it comes to inference, we often limit the amount of compute to only one attempt per problem. Here, we explore inference compute as another axis for scaling by increasing the number of generated samples. Across multiple tasks and models, we observe that coverage - the fraction of problems solved by any attempt - scales with the number of samples over four orders of magnitude. In domains like coding and formal proofs, where all answers can be automatically verified, these increases in coverage directly translate into improved performance. When we apply repeated sampling to SWE-bench Lite, the fraction of issues solved with DeepSeek-V2-Coder-Instruct increases from 15.9% with one sample to 56% with 250 samples, outperforming the single-attempt state-of-the-art of 43% which uses more capable frontier models. Moreover, using current API pricing, amplifying the cheaper DeepSeek model with five samples is more cost-effective and solves more issues than paying a premium for one sample from GPT-4o or Claude 3.5 Sonnet. Interestingly, the relationship between coverage and the number of samples is often log-linear and can be modelled with an exponentiated power law, suggesting the existence of inference-time scaling laws. Finally, we find that identifying correct samples out of many generations remains an important direction for future research in domains without automatic verifiers. When solving math word problems from GSM8K and MATH, coverage with Llama-3 models grows to over 95% with 10,000 samples. However, common methods to pick correct solutions from a sample collection, such as majority voting or reward models, plateau beyond several hundred samples and fail to fully scale with the sample budget.

Every data selection method inherently has a target. In practice, these targets often emerge implicitly through benchmark-driven iteration: researchers develop selection strategies, train models, measure benchmark performance, then refine accordingly. This raises a natural question: what happens when we make this optimization explicit? To explore this, we propose benchmark-targeted ranking (BETR), a simple method that selects pretraining documents based on similarity to benchmark training examples. BETR embeds benchmark examples and a sample of pretraining documents in a shared space, scores this sample by similarity to benchmarks, then trains a lightweight classifier to predict these scores for the full corpus. We compare data selection methods by training over 500 models spanning 10^{19} to 10^{22} FLOPs and fitting scaling laws to them. From this, we find that simply aligning pretraining data to evaluation benchmarks using BETR achieves a 2.1x compute multiplier over DCLM-Baseline (4.7x over unfiltered data) and improves performance on 9 out of 10 tasks across all scales. BETR also generalizes well: when targeting a diverse set of benchmarks disjoint from our evaluation suite, it still matches or outperforms baselines. Our scaling analysis further reveals a clear trend: larger models require less aggressive filtering. Overall, our findings show that directly matching pretraining data to target tasks precisely shapes model capabilities and highlight that optimal selection strategies must adapt to model scale.

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.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

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.

The performance of transformers for time-series forecasting has improved significantly. Recent architectures learn complex temporal patterns by segmenting a time-series into patches and using the patches as tokens. The patch size controls the ability of transformers to learn the temporal patterns at different frequencies: shorter patches are effective for learning localized, high-frequency patterns, whereas mining long-term seasonalities and trends requires longer patches. Inspired by this observation, we propose a novel framework, Multi-resolution Time-Series Transformer (MTST), which consists of a multi-branch architecture for simultaneous modeling of diverse temporal patterns at different resolutions. In contrast to many existing time-series transformers, we employ relative positional encoding, which is better suited for extracting periodic components at different scales. Extensive experiments on several real-world datasets demonstrate the effectiveness of MTST in comparison to state-of-the-art forecasting techniques.

Network Architecture Search and specifically Regularized Evolution is a common way to refine the structure of a deep learning model.However, little is known about how models empirically evolve over time which has design implications for designing caching policies, refining the search algorithm for particular applications, and other important use cases.In this work, we algorithmically analyze and quantitatively characterize the patterns of model evolution for a set of models from the Candle project and the Nasbench-201 search space.We show how the evolution of the model structure is influenced by the regularized evolution algorithm. We describe how evolutionary patterns appear in distributed settings and opportunities for caching and improved scheduling. Lastly, we describe the conditions that affect when particular model architectures rise and fall in popularity based on their frequency of acting as a donor in a sliding window.

Training state-of-the-art neural networks requires a high cost in terms of compute and time. Model scale is recognized to be a critical factor to achieve and improve the state-of-the-art. Increasing the scale of a neural network normally requires restarting from scratch by randomly initializing all the parameters of the model, as this implies a change of architecture's parameters that does not allow for a straightforward transfer of knowledge from smaller size models. In this work, we propose six composable transformations to incrementally increase the size of transformer-based neural networks while preserving functionality, allowing to expand the capacity of the model as needed. We provide proof of exact function preservation under minimal initialization constraints for each transformation. The proposed methods may enable efficient training pipelines for larger and more powerful models by progressively expanding the architecture throughout training.

Continual Pre-Training (CPT) has become a popular and effective method to apply strong foundation models to specific downstream tasks. In this work, we explore the learning dynamics throughout the CPT process for large language models. We specifically focus on how general and downstream domain performance evolves at each training step, with domain performance measured via validation losses. We have observed that the CPT loss curve fundamentally characterizes the transition from one curve to another hidden curve, and could be described by decoupling the effects of distribution shift and learning rate annealing. We derive a CPT scaling law that combines the two factors, enabling the prediction of loss at any (continual) training steps and across learning rate schedules (LRS) in CPT. Our formulation presents a comprehensive understanding of several critical factors in CPT, including loss potential, peak learning rate, training steps, replay ratio, etc. Moreover, our approach can be adapted to customize training hyper-parameters to different CPT goals such as balancing general and domain-specific performance. Extensive experiments demonstrate that our scaling law holds across various CPT datasets and training hyper-parameters.

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 .

Time series foundation models have demonstrated impressive performance as zero-shot forecasters. However, achieving effectively unified training on time series remains an open challenge. Existing approaches introduce some level of model specialization to account for the highly heterogeneous nature of time series data. For instance, Moirai pursues unified training by employing multiple input/output projection layers, each tailored to handle time series at a specific frequency. Similarly, TimesFM maintains a frequency embedding dictionary for this purpose. We identify two major drawbacks to this human-imposed frequency-level model specialization: (1) Frequency is not a reliable indicator of the underlying patterns in time series. For example, time series with different frequencies can display similar patterns, while those with the same frequency may exhibit varied patterns. (2) Non-stationarity is an inherent property of real-world time series, leading to varied distributions even within a short context window of a single time series. Frequency-level specialization is too coarse-grained to capture this level of diversity. To address these limitations, this paper introduces Moirai-MoE, using a single input/output projection layer while delegating the modeling of diverse time series patterns to the sparse mixture of experts (MoE) within Transformers. With these designs, Moirai-MoE reduces reliance on human-defined heuristics and enables automatic token-level specialization. Extensive experiments on 39 datasets demonstrate the superiority of Moirai-MoE over existing foundation models in both in-distribution and zero-shot scenarios. Furthermore, this study conducts comprehensive model analyses to explore the inner workings of time series MoE foundation models and provides valuable insights for future research.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Recent neural network-based language models have benefited greatly from scaling up the size of training datasets and the number of parameters in the models themselves. Scaling can be complicated due to various factors including the need to distribute computation on supercomputer clusters (e.g., TPUs), prevent bottlenecks when infeeding data, and ensure reproducible results. In this work, we present two software libraries that ease these issues: t5x simplifies the process of building and training large language models at scale while maintaining ease of use, and seqio provides a task-based API for simple creation of fast and reproducible training data and evaluation pipelines. These open-source libraries have been used to train models with hundreds of billions of parameters on datasets with multiple terabytes of training data. Along with the libraries, we release configurations and instructions for T5-like encoder-decoder models as well as GPT-like decoder-only architectures. t5x and seqio are open source and available at https://github.com/google-research/t5x and https://github.com/google/seqio, respectively.

Food safety and quality are paramount concerns worldwide, especially concerning nutritional quality and its impact on human health. Ensuring the accuracy and efficiency of milk quality assessment is vital for maintaining the quality of dairy farm produce. Milk spectral data, Mid-infrared spectra (MIRS) of milk samples, are frequently employed for milk quality evaluations, encompassing various milk quality parameters. However, conventional milk quality analyses have overlooked the scaling nature, known as stochastic similarity in different scales, inherent in milk spectral data. Wavelet transforms are among the tools used in these analyses, although they are primarily used as data pre-processing techniques without fully realizing their potential in extracting valuable insights. The primary purpose of this study is to demonstrate the importance of accounting for scaling properties in assessing milk quality. A set of 12 descriptors is computed to characterize scaling properties in milk spectral data within the wavelet domain. These descriptors are then assessed for their effectiveness in milk quality assessments utilizing 18 different milk quality parameters. They notably demonstrated comparable performance to existing methods while utilizing fewer features when applied to an MIRS dataset. This innovative approach holds substantial promise for advancing the field of milk quality assessment, offering a means to achieve more accurate and efficient evaluations while shedding light on previously unexplored aspects of milk spectral data.

Hall-effect thrusters (HETs) are widely used for modern near-earth spacecraft propulsion and are vital for future deep-space missions. Methods of modeling HETs are developing rapidly. However, such methods are not yet precise enough and cannot reliably predict the parameters of a newly designed thruster, mostly due to the enormous computational cost of a HET plasma simulation. Another approach is to use scaling techniques based on available experimental data. This paper proposes an approach for scaling HETs using neural networks and other modern machine learning methods. The new scaling model was built with information from an extensive database of HET parameters collected from published papers. Predictions of the new scaling model are valid for the operating parameters domain covered by the database. During the design, this model can help HET developers estimate the performance of a newly-designed thruster. At the stage of experimental research, the model can be used to compare the achieved characteristics of the studied thruster with the level obtained by other developers. A comparison with the state-of-the-art HET scaling model is also presented.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

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 surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 (ge 175B) to T5 variants (le 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

As enthusiasm for scaling computation (data and parameters) in the pretraining era gradually diminished, test-time scaling (TTS), also referred to as ``test-time computing'' has emerged as a prominent research focus. Recent studies demonstrate that TTS can further elicit the problem-solving capabilities of large language models (LLMs), enabling significant breakthroughs not only in specialized reasoning tasks, such as mathematics and coding, but also in general tasks like open-ended Q&A. However, despite the explosion of recent efforts in this area, there remains an urgent need for a comprehensive survey offering a systemic understanding. To fill this gap, we propose a unified, multidimensional framework structured along four core dimensions of TTS research: what to scale, how to scale, where to scale, and how well to scale. Building upon this taxonomy, we conduct an extensive review of methods, application scenarios, and assessment aspects, and present an organized decomposition that highlights the unique functional roles of individual techniques within the broader TTS landscape. From this analysis, we distill the major developmental trajectories of TTS to date and offer hands-on guidelines for practical deployment. Furthermore, we identify several open challenges and offer insights into promising future directions, including further scaling, clarifying the functional essence of techniques, generalizing to more tasks, and more attributions.

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.

A key puzzle in search, ads, and recommendation is that the ranking model can only utilize a small portion of the vastly available user interaction data. As a result, increasing data volume, model size, or computation FLOPs will quickly suffer from diminishing returns. We examined this problem and found that one of the root causes may lie in the so-called ``item-centric'' formulation, which has an unbounded vocabulary and thus uncontrolled model complexity. To mitigate quality saturation, we introduce an alternative formulation named ``user-centric ranking'', which is based on a transposed view of the dyadic user-item interaction data. We show that this formulation has a promising scaling property, enabling us to train better-converged models on substantially larger data sets.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

Recently, Visual Autoregressive (VAR) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine "next-scale prediction" paradigm. However, the state-of-the-art algorithm of VAR models in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes O(n^4) time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of VAR Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which VAR computations can achieve sub-quadratic time complexity. Specifically, we establish a critical threshold for the norm of input matrices used in VAR attention mechanisms. Above this threshold, assuming the Strong Exponential Time Hypothesis (SETH) from fine-grained complexity theory, a sub-quartic time algorithm for VAR models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the VAR model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in VAR frameworks.

Foundation Models (FMs) serve as a general class for the development of artificial intelligence systems, offering broad potential for generalization across a spectrum of downstream tasks. Despite extensive research into self-supervised learning as the cornerstone of FMs, several outstanding issues persist in Graph Foundation Models that rely on graph self-supervised learning, namely: 1) Homogenization. The extent of generalization capability on downstream tasks remains unclear. 2) Scalability. It is unknown how effectively these models can scale to large datasets. 3) Efficiency. The training time and memory usage of these models require evaluation. 4) Training Stop Criteria. Determining the optimal stopping strategy for pre-training across multiple tasks to maximize performance on downstream tasks. To address these questions, we have constructed a rigorous benchmark that thoroughly analyzes and studies the generalization and scalability of self-supervised Graph Neural Network (GNN) models. Regarding generalization, we have implemented and compared the performance of various self-supervised GNN models, trained to generate node representations, across tasks such as node classification, link prediction, and node clustering. For scalability, we have compared the performance of various models after training using full-batch and mini-batch strategies. Additionally, we have assessed the training efficiency of these models by conducting experiments to test their GPU memory usage and throughput. Through these experiments, we aim to provide insights to motivate future research. The code for this benchmark is publicly available at https://github.com/NYUSHCS/GraphFM.

Inference-time scaling can enhance the reasoning capabilities of large language models (LLMs) on complex problems that benefit from step-by-step problem solving. Although lengthening generated scratchpads has proven effective for mathematical tasks, the broader impact of this approach on other tasks remains less clear. In this work, we investigate the benefits and limitations of scaling methods across nine state-of-the-art models and eight challenging tasks, including math and STEM reasoning, calendar planning, NP-hard problems, navigation, and spatial reasoning. We compare conventional models (e.g., GPT-4o) with models fine-tuned for inference-time scaling (e.g., o1) through evaluation protocols that involve repeated model calls, either independently or sequentially with feedback. These evaluations approximate lower and upper performance bounds and potential for future performance improvements for each model, whether through enhanced training or multi-model inference systems. Our extensive empirical analysis reveals that the advantages of inference-time scaling vary across tasks and diminish as problem complexity increases. In addition, simply using more tokens does not necessarily translate to higher accuracy in these challenging regimes. Results from multiple independent runs with conventional models using perfect verifiers show that, for some tasks, these models can achieve performance close to the average performance of today's most advanced reasoning models. However, for other tasks, a significant performance gap remains, even in very high scaling regimes. Encouragingly, all models demonstrate significant gains when inference is further scaled with perfect verifiers or strong feedback, suggesting ample potential for future improvements.

Low precision training and inference affect both the quality and cost of language models, but current scaling laws do not account for this. In this work, we devise "precision-aware" scaling laws for both training and inference. We propose that training in lower precision reduces the model's "effective parameter count," allowing us to predict the additional loss incurred from training in low precision and post-train quantization. For inference, we find that the degradation introduced by post-training quantization increases as models are trained on more data, eventually making additional pretraining data actively harmful. For training, our scaling laws allow us to predict the loss of a model with different parts in different precisions, and suggest that training larger models in lower precision may be compute optimal. We unify the scaling laws for post and pretraining quantization to arrive at a single functional form that predicts degradation from training and inference in varied precisions. We fit on over 465 pretraining runs and validate our predictions on model sizes up to 1.7B parameters trained on up to 26B tokens.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of Obigl(NKD^3bigr) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this paper, we manage to reduce this complexity to Obigl(NKD^2bigr) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Nowadays, data is represented by vectors. Retrieving those vectors, among millions and billions, that are similar to a given query is a ubiquitous problem, known as similarity search, of relevance for a wide range of applications. Graph-based indices are currently the best performing techniques for billion-scale similarity search. However, their random-access memory pattern presents challenges to realize their full potential. In this work, we present new techniques and systems for creating faster and smaller graph-based indices. To this end, we introduce a novel vector compression method, Locally-adaptive Vector Quantization (LVQ), that uses per-vector scaling and scalar quantization to improve search performance with fast similarity computations and a reduced effective bandwidth, while decreasing memory footprint and barely impacting accuracy. LVQ, when combined with a new high-performance computing system for graph-based similarity search, establishes the new state of the art in terms of performance and memory footprint. For billions of vectors, LVQ outcompetes the second-best alternatives: (1) in the low-memory regime, by up to 20.7x in throughput with up to a 3x memory footprint reduction, and (2) in the high-throughput regime by 5.8x with 1.4x less memory.