Daily Papers

Modern machine learning (ML) systems demand substantial training data, often resorting to external sources. Nevertheless, this practice renders them vulnerable to backdoor poisoning attacks. Prior backdoor defense strategies have primarily focused on the identification of backdoored models or poisoned data characteristics, typically operating under the assumption of access to clean data. In this work, we delve into a relatively underexplored challenge: the automatic identification of backdoor data within a poisoned dataset, all under realistic conditions, i.e., without the need for additional clean data or without manually defining a threshold for backdoor detection. We draw an inspiration from the scaled prediction consistency (SPC) technique, which exploits the prediction invariance of poisoned data to an input scaling factor. Based on this, we pose the backdoor data identification problem as a hierarchical data splitting optimization problem, leveraging a novel SPC-based loss function as the primary optimization objective. Our innovation unfolds in several key aspects. First, we revisit the vanilla SPC method, unveiling its limitations in addressing the proposed backdoor identification problem. Subsequently, we develop a bi-level optimization-based approach to precisely identify backdoor data by minimizing the advanced SPC loss. Finally, we demonstrate the efficacy of our proposal against a spectrum of backdoor attacks, encompassing basic label-corrupted attacks as well as more sophisticated clean-label attacks, evaluated across various benchmark datasets. Experiment results show that our approach often surpasses the performance of current baselines in identifying backdoor data points, resulting in about 4%-36% improvement in average AUROC. Codes are available at https://github.com/OPTML-Group/BackdoorMSPC.

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the sequential predictive conformal inference (SPCI). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of SPCI compared to other existing methods under the desired empirical coverage.

Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants, Adaptive self-consistency (ASC) and Early-stopping self-consistency (ESC), dynamically adjust the number of samples based on the posterior distribution of a set of pre-samples, reducing the cost of SC with minimal impact on performance. Both methods, however, do not exploit the prior information about question difficulty. It often results in unnecessary repeated sampling for easy questions that could be accurately answered with just one attempt, wasting resources. To tackle this problem, we propose Difficulty-Adaptive Self-Consistency (DSC), which leverages the difficulty information from both prior and posterior perspectives to adaptively allocate inference resources, further reducing the cost of SC. To demonstrate the effectiveness of DSC, we conduct extensive experiments on three popular categories of reasoning tasks: arithmetic, commonsense and symbolic reasoning on six benchmarks. The empirical results show that DSC consistently surpasses the strong baseline ASC and ESC in terms of costs by a significant margin, while attaining comparable performances.

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.

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.

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.

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.

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.

Machine learning models are widely used, but can also often be wrong. Users would benefit from a reliable indication of whether a given output from a given model should be trusted, so a rational decision can be made whether to use the output or not. For example, outputs can be associated with a confidence measure; if this confidence measure is strongly associated with likelihood of correctness, then the model is said to be well-calibrated. A well-calibrated confidence measure can serve as a basis for rational, graduated decision-making on how much review and care is needed when using generated code. Calibration has so far been studied in mostly non-generative (e.g. classification) settings, especially in software engineering. However, generated code can quite often be wrong: Given generated code, developers must decide whether to use directly, use after varying intensity of careful review, or discard model-generated code. Thus, calibration is vital in generative settings. We make several contributions. We develop a framework for evaluating the calibration of code-generating models. We consider several tasks, correctness criteria, datasets, and approaches, and find that, by and large, generative code models we test are not well-calibrated out of the box. We then show how calibration can be improved using standard methods, such as Platt scaling. Since Platt scaling relies on the prior availability of correctness data, we evaluate the applicability and generalizability of Platt scaling in software engineering, discuss settings where it has good potential for practical use, and settings where it does not. Our contributions will lead to better-calibrated decision-making in the current use of code generated by language models, and offers a framework for future research to further improve calibration methods for generative models in software engineering.

Accurate prediction of climate in the subseasonal-to-seasonal scale is crucial for disaster readiness, reduced economic risk, and improved policy-making amidst climate change. Yet, S2S prediction remains challenging due to the chaotic nature of the system. At present, existing benchmarks for weather and climate applications, tend to (1) have shorter forecasting range of up-to 14 days, (2) do not include a wide range of operational baseline forecasts, and (3) lack physics-based constraints for explainability. Thus, we propose ChaosBench, a large-scale, multi-channel, physics-based benchmark for S2S prediction. ChaosBench has over 460K frames of real-world observations and simulations, each with 60 variable-channels and spanning for up-to 45 years. We also propose several physics-based, in addition to vision-based metrics, that enables for a more physically-consistent model. Furthermore, we include a diverse set of physics-based forecasts from 4 national weather agencies as baselines to our data-driven counterpart. We establish two tasks that vary in complexity: full and sparse dynamics prediction. Our benchmark is one of the first to perform large-scale evaluation on existing models including PanguWeather, FourCastNetV2, GraphCast, and ClimaX, and finds methods originally developed for weather-scale applications fails on S2S task. We release our benchmark code and datasets at https://leap-stc.github.io/ChaosBench.

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore this problem in the context of solving real-world GitHub issues from the SWE-bench dataset. Our system, named CodeMonkeys, allows models to iteratively edit a codebase by jointly generating and running a testing script alongside their draft edit. We sample many of these multi-turn trajectories for every issue to generate a collection of candidate edits. This approach lets us scale "serial" test-time compute by increasing the number of iterations per trajectory and "parallel" test-time compute by increasing the number of trajectories per problem. With parallel scaling, we can amortize up-front costs across multiple downstream samples, allowing us to identify relevant codebase context using the simple method of letting an LLM read every file. In order to select between candidate edits, we combine voting using model-generated tests with a final multi-turn trajectory dedicated to selection. Overall, CodeMonkeys resolves 57.4% of issues from SWE-bench Verified using a budget of approximately 2300 USD. Our selection method can also be used to combine candidates from different sources. Selecting over an ensemble of edits from existing top SWE-bench Verified submissions obtains a score of 66.2% and outperforms the best member of the ensemble on its own. We fully release our code and data at https://scalingintelligence.stanford.edu/pubs/codemonkeys.

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.

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning engineers with their simplicity. However, one of the weaknesses of this type of methods is the necessity to tune learning rate (step-size) for every loss function and dataset combination to solve an optimization problem and get an efficient performance in a given time budget. Stochastic Gradient Descent with Polyak Step-size (SPS) is a method that offers an update rule that alleviates the need of fine-tuning the learning rate of an optimizer. In this paper, we propose an extension of SPS that employs preconditioning techniques, such as Hutchinson's method, Adam, and AdaGrad, to improve its performance on badly scaled and/or ill-conditioned datasets.

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.

Diffusion Models (DM) and Consistency Models (CM) are two types of popular generative models with good generation quality on various tasks. When training DM and CM, intermediate weight checkpoints are not fully utilized and only the last converged checkpoint is used. In this work, we find that high-quality model weights often lie in a basin which cannot be reached by SGD but can be obtained by proper checkpoint averaging. Based on these observations, we propose LCSC, a simple but effective and efficient method to enhance the performance of DM and CM, by combining checkpoints along the training trajectory with coefficients deduced from evolutionary search. We demonstrate the value of LCSC through two use cases: (a) Reducing training cost. With LCSC, we only need to train DM/CM with fewer number of iterations and/or lower batch sizes to obtain comparable sample quality with the fully trained model. For example, LCSC achieves considerable training speedups for CM (23times on CIFAR-10 and 15times on ImageNet-64). (b) Enhancing pre-trained models. Assuming full training is already done, LCSC can further improve the generation quality or speed of the final converged models. For example, LCSC achieves better performance using 1 number of function evaluation (NFE) than the base model with 2 NFE on consistency distillation, and decreases the NFE of DM from 15 to 9 while maintaining the generation quality on CIFAR-10. Our code is available at https://github.com/imagination-research/LCSC.

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.

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.

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

Diffusion models achieve superior generation quality but suffer from slow generation speed due to the iterative nature of denoising. In contrast, consistency models, a new generative family, achieve competitive performance with significantly faster sampling. These models are trained either through consistency distillation, which leverages pretrained diffusion models, or consistency training/tuning directly from raw data. In this work, we propose a novel framework for understanding consistency models by modeling the denoising process of the diffusion model as a Markov Decision Process (MDP) and framing consistency model training as the value estimation through Temporal Difference~(TD) Learning. More importantly, this framework allows us to analyze the limitations of current consistency training/tuning strategies. Built upon Easy Consistency Tuning (ECT), we propose Stable Consistency Tuning (SCT), which incorporates variance-reduced learning using the score identity. SCT leads to significant performance improvements on benchmarks such as CIFAR-10 and ImageNet-64. On ImageNet-64, SCT achieves 1-step FID 2.42 and 2-step FID 1.55, a new SoTA for consistency models.

Consistency models are a nascent family of generative models that can sample high quality data in one step without the need for adversarial training. Current consistency models achieve optimal sample quality by distilling from pre-trained diffusion models and employing learned metrics such as LPIPS. However, distillation limits the quality of consistency models to that of the pre-trained diffusion model, and LPIPS causes undesirable bias in evaluation. To tackle these challenges, we present improved techniques for consistency training, where consistency models learn directly from data without distillation. We delve into the theory behind consistency training and identify a previously overlooked flaw, which we address by eliminating Exponential Moving Average from the teacher consistency model. To replace learned metrics like LPIPS, we adopt Pseudo-Huber losses from robust statistics. Additionally, we introduce a lognormal noise schedule for the consistency training objective, and propose to double total discretization steps every set number of training iterations. Combined with better hyperparameter tuning, these modifications enable consistency models to achieve FID scores of 2.51 and 3.25 on CIFAR-10 and ImageNet 64times 64 respectively in a single sampling step. These scores mark a 3.5times and 4times improvement compared to prior consistency training approaches. Through two-step sampling, we further reduce FID scores to 2.24 and 2.77 on these two datasets, surpassing those obtained via distillation in both one-step and two-step settings, while narrowing the gap between consistency models and other state-of-the-art generative models.

Increasing test-time compute for LLMs shows promise across domains but remains underexplored in code generation, despite extensive study in math. In this paper, we propose S*, the first hybrid test-time scaling framework that substantially improves the coverage and selection accuracy of generated code. S* extends the existing parallel scaling paradigm with sequential scaling to push performance boundaries. It further leverages a novel selection mechanism that adaptively generates distinguishing inputs for pairwise comparison, combined with execution-grounded information to robustly identify correct solutions. We evaluate across 12 Large Language Models and Large Reasoning Model and show: (1) S* consistently improves performance across model families and sizes, enabling a 3B model to outperform GPT-4o-mini; (2) S* enables non-reasoning models to surpass reasoning models - GPT-4o-mini with S* outperforms o1-preview by 3.7% on LiveCodeBench; (3) S* further boosts state-of-the-art reasoning models - DeepSeek-R1-Distill-Qwen-32B with S* achieves 85.7% on LiveCodeBench, approaching o1 (high) at 88.5%. Code will be available under https://github.com/NovaSky-AI/SkyThought.

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.

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.

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

In many industries, predicting metric outcomes of large systems is a fundamental problem, driven largely by traditional tabular regression. However, such methods struggle on complex systems data in the wild such as configuration files or system logs, where feature engineering is often infeasible. We propose text-to-text regression as a general, scalable alternative. For predicting resource efficiency on Borg, Google's massive compute cluster scheduling system, a 60M parameter encoder-decoder, trained from random initialization, achieves up to a near perfect 0.99 (0.9 average) rank correlation across the entire fleet, and 100x lower MSE than tabular approaches. The model also easily adapts to new tasks in only 500 few-shot examples and captures the densities of complex outcome distributions. Ablation studies highlight the importance of using encoders, increasing sequence length, and the model's inherent uncertainty quantification. These findings pave the way for universal simulators of real-world outcomes.

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.

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.

Predictive Coding (PC) is a theoretical framework in cognitive science suggesting that the human brain processes cognition through spatiotemporal prediction of the visual world. Existing studies have developed spatiotemporal prediction neural networks based on the PC theory, emulating its two core mechanisms: Correcting predictions from residuals and hierarchical learning. However, these models do not show the enhancement of prediction skills on real-world forecasting tasks and ignore the Precision Weighting mechanism of PC theory. The precision weighting mechanism posits that the brain allocates more attention to signals with lower precision, contributing to the cognitive ability of human brains. This work introduces the Cognitive Diffusion Probabilistic Models (CogDPM), which demonstrate the connection between diffusion probabilistic models and PC theory. CogDPM features a precision estimation method based on the hierarchical sampling capabilities of diffusion models and weight the guidance with precision weights estimated by the inherent property of diffusion models. We experimentally show that the precision weights effectively estimate the data predictability. We apply CogDPM to real-world prediction tasks using the United Kindom precipitation and ERA surface wind datasets. Our results demonstrate that CogDPM outperforms both existing domain-specific operational models and general deep prediction models by providing more proficient forecasting.

We develop a variant of the stochastic prox-linear method for minimizing the Conditional Value-at-Risk (CVaR) objective. CVaR is a risk measure focused on minimizing worst-case performance, defined as the average of the top quantile of the losses. In machine learning, such a risk measure is useful to train more robust models. Although the stochastic subgradient method (SGM) is a natural choice for minimizing the CVaR objective, we show that our stochastic prox-linear (SPL+) algorithm can better exploit the structure of the objective, while still providing a convenient closed form update. Our SPL+ method also adapts to the scaling of the loss function, which allows for easier tuning. We then specialize a general convergence theorem for SPL+ to our setting, and show that it allows for a wider selection of step sizes compared to SGM. We support this theoretical finding experimentally.

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.

Software engineering (SWE) has recently emerged as a crucial testbed for next-generation LLM agents, demanding inherent capabilities in two critical dimensions: sustained iterative problem-solving (e.g., >50 interaction rounds) and long-context dependency resolution (e.g., >32k tokens). However, the data curation process in SWE remains notoriously time-consuming, as it heavily relies on manual annotation for code file filtering and the setup of dedicated runtime environments to execute and validate unit tests. Consequently, most existing datasets are limited to only a few thousand GitHub-sourced instances. To this end, we propose an incremental, automated data-curation pipeline that systematically scales both the volume and diversity of SWE datasets. Our dataset comprises 10,169 real-world Python task instances from 2,531 distinct GitHub repositories, each accompanied by a task specified in natural language and a dedicated runtime-environment image for automated unit-test validation. We have carefully curated over 8,000 successfully runtime-validated training trajectories from our proposed SWE dataset. When fine-tuning the Skywork-SWE model on these trajectories, we uncover a striking data scaling phenomenon: the trained model's performance for software engineering capabilities in LLMs continues to improve as the data size increases, showing no signs of saturation. Notably, our Skywork-SWE model achieves 38.0% pass@1 accuracy on the SWE-bench Verified benchmark without using verifiers or multiple rollouts, establishing a new state-of-the-art (SOTA) among the Qwen2.5-Coder-32B-based LLMs built on the OpenHands agent framework. Furthermore, with the incorporation of test-time scaling techniques, the performance further improves to 47.0% accuracy, surpassing the previous SOTA results for sub-32B parameter models. We release the Skywork-SWE-32B model checkpoint to accelerate future research.

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.

Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing definition for calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new definition that escapes this caveat and an evaluation method using a simple histogram-based approach. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple, scaling-based calibration method that preforms as well as much more complex ones. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Class-incremental learning (CIL) is a particularly challenging variant of continual learning, where the goal is to learn to discriminate between all classes presented in an incremental fashion. Existing approaches often suffer from excessive forgetting and imbalance of the scores assigned to classes that have not been seen together during training. In this study, we introduce a novel approach, Prediction Error-based Classification (PEC), which differs from traditional discriminative and generative classification paradigms. PEC computes a class score by measuring the prediction error of a model trained to replicate the outputs of a frozen random neural network on data from that class. The method can be interpreted as approximating a classification rule based on Gaussian Process posterior variance. PEC offers several practical advantages, including sample efficiency, ease of tuning, and effectiveness even when data are presented one class at a time. Our empirical results show that PEC performs strongly in single-pass-through-data CIL, outperforming other rehearsal-free baselines in all cases and rehearsal-based methods with moderate replay buffer size in most cases across multiple benchmarks.

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good discrimination in the non-asymptotic regime. In this paper, we provide the first systematic finite-sample study of proper scoring rules for time-series forecasting evaluation. Through a power analysis, we identify the "region of reliability" of a scoring rule, i.e., the set of practical conditions where it can be relied on to identify forecasting errors. We carry out our analysis on a comprehensive synthetic benchmark, specifically designed to test several key discrepancies between ground-truth and forecast distributions, and we gauge the generalizability of our findings to real-world tasks with an application to an electricity production problem. Our results reveal critical shortcomings in the evaluation of multivariate probabilistic forecasts as commonly performed in the literature.

This paper presents our approach to accelerate computer architecture simulation by leveraging machine learning techniques. Traditional computer architecture simulations are time-consuming, making it challenging to explore different design choices efficiently. Our proposed model utilizes a combination of application features and micro-architectural features to predict the performance of an application. These features are derived from simulations of a small portion of the application. We demonstrate the effectiveness of our approach by building and evaluating a machine learning model that offers significant speedup in architectural exploration. This model demonstrates the ability to predict IPC values for the testing data with a root mean square error of less than 0.1.

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.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

Building on developments in machine learning and prior work in the science of judicial prediction, we construct a model designed to predict the behavior of the Supreme Court of the United States in a generalized, out-of-sample context. To do so, we develop a time evolving random forest classifier which leverages some unique feature engineering to predict more than 240,000 justice votes and 28,000 cases outcomes over nearly two centuries (1816-2015). Using only data available prior to decision, our model outperforms null (baseline) models at both the justice and case level under both parametric and non-parametric tests. Over nearly two centuries, we achieve 70.2% accuracy at the case outcome level and 71.9% at the justice vote level. More recently, over the past century, we outperform an in-sample optimized null model by nearly 5%. Our performance is consistent with, and improves on the general level of prediction demonstrated by prior work; however, our model is distinctive because it can be applied out-of-sample to the entire past and future of the Court, not a single term. Our results represent an important advance for the science of quantitative legal prediction and portend a range of other potential applications.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

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.

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.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

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.

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.

While LLMs have demonstrated remarkable potential in time series forecasting, their practical deployment remains constrained by excessive computational demands and memory footprints. Existing LLM-based approaches typically suffer from three critical limitations: Inefficient parameter utilization in handling numerical time series patterns; Modality misalignment between continuous temporal signals and discrete text embeddings; and Inflexibility for real-time expert knowledge integration. We present SMETimes, the first systematic investigation of sub-3B parameter SLMs for efficient and accurate time series forecasting. Our approach centers on three key innovations: A statistically-enhanced prompting mechanism that bridges numerical time series with textual semantics through descriptive statistical features; A adaptive fusion embedding architecture that aligns temporal patterns with language model token spaces through learnable parameters; And a dynamic mixture-of-experts framework enabled by SLMs' computational efficiency, adaptively combining base predictions with domain-specific models. Extensive evaluations across seven benchmark datasets demonstrate that our 3B-parameter SLM achieves state-of-the-art performance on five primary datasets while maintaining 3.8x faster training and 5.2x lower memory consumption compared to 7B-parameter LLM baselines. Notably, the proposed model exhibits better learning capabilities, achieving 12.3% lower MSE than conventional LLM. Ablation studies validate that our statistical prompting and cross-modal fusion modules respectively contribute 15.7% and 18.2% error reduction in long-horizon forecasting tasks. By redefining the efficiency-accuracy trade-off landscape, this work establishes SLMs as viable alternatives to resource-intensive LLMs for practical time series forecasting. Code and models are available at https://github.com/xiyan1234567/SMETimes.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

Interpreting time series models is uniquely challenging because it requires identifying both the location of time series signals that drive model predictions and their matching to an interpretable temporal pattern. While explainers from other modalities can be applied to time series, their inductive biases do not transfer well to the inherently challenging interpretation of time series. We present TimeX, a time series consistency model for training explainers. TimeX trains an interpretable surrogate to mimic the behavior of a pretrained time series model. It addresses the issue of model faithfulness by introducing model behavior consistency, a novel formulation that preserves relations in the latent space induced by the pretrained model with relations in the latent space induced by TimeX. TimeX provides discrete attribution maps and, unlike existing interpretability methods, it learns a latent space of explanations that can be used in various ways, such as to provide landmarks to visually aggregate similar explanations and easily recognize temporal patterns. We evaluate TimeX on eight synthetic and real-world datasets and compare its performance against state-of-the-art interpretability methods. We also conduct case studies using physiological time series. Quantitative evaluations demonstrate that TimeX achieves the highest or second-highest performance in every metric compared to baselines across all datasets. Through case studies, we show that the novel components of TimeX show potential for training faithful, interpretable models that capture the behavior of pretrained time series models.

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty. Selective regression, also known as the "reject option," allows models to abstain from predictions in cases of considerable uncertainty. Initially proposed seven decades ago, approaches to selective regression have mostly focused on distribution-based proxies for measuring uncertainty, particularly conditional variance. However, this focus neglects the significant influence of model-specific biases on a model's performance. In this paper, we propose a novel approach to selective regression by leveraging conformal prediction, which provides grounded confidence measures for individual predictions based on model-specific biases. In addition, we propose a standardized evaluation framework to allow proper comparison of selective regression approaches. Via an extensive experimental approach, we demonstrate how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.

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.

Reliable usage of object detectors require them to be calibrated -- a crucial problem that requires careful attention. Recent approaches towards this involve (1) designing new loss functions to obtain calibrated detectors by training them from scratch, and (2) post-hoc Temperature Scaling (TS) that learns to scale the likelihood of a trained detector to output calibrated predictions. These approaches are then evaluated based on a combination of Detection Expected Calibration Error (D-ECE) and Average Precision. In this work, via extensive analysis and insights, we highlight that these recent evaluation frameworks, evaluation metrics, and the use of TS have notable drawbacks leading to incorrect conclusions. As a step towards fixing these issues, we propose a principled evaluation framework to jointly measure calibration and accuracy of object detectors. We also tailor efficient and easy-to-use post-hoc calibration approaches such as Platt Scaling and Isotonic Regression specifically for object detection task. Contrary to the common notion, our experiments show that once designed and evaluated properly, post-hoc calibrators, which are extremely cheap to build and use, are much more powerful and effective than the recent train-time calibration methods. To illustrate, D-DETR with our post-hoc Isotonic Regression calibrator outperforms the recent train-time state-of-the-art calibration method Cal-DETR by more than 7 D-ECE on the COCO dataset. Additionally, we propose improved versions of the recently proposed Localization-aware ECE and show the efficacy of our method on these metrics as well. Code is available at: https://github.com/fiveai/detection_calibration.

Language models (LMs) perform well on standardized coding benchmarks but struggle with real-world software engineering tasks such as resolving GitHub issues in SWE-Bench, especially when model parameters are less than 100B. While smaller models are preferable in practice due to their lower computational cost, improving their performance remains challenging. Existing approaches primarily rely on supervised fine-tuning (SFT) with high-quality data, which is expensive to curate at scale. An alternative is test-time scaling: generating multiple outputs, scoring them using a verifier, and selecting the best one. Although effective, this strategy often requires excessive sampling and costly scoring, limiting its practical application. We propose Evolutionary Test-Time Scaling (EvoScale), a sample-efficient method that treats generation as an evolutionary process. By iteratively refining outputs via selection and mutation, EvoScale shifts the output distribution toward higher-scoring regions, reducing the number of samples needed to find correct solutions. To reduce the overhead from repeatedly sampling and selection, we train the model to self-evolve using reinforcement learning (RL). Rather than relying on external verifiers at inference time, the model learns to self-improve the scores of its own generations across iterations. Evaluated on SWE-Bench-Verified, EvoScale enables our 32B model, Satori-SWE-32B, to match or exceed the performance of models with over 100B parameters while using a few samples. Code, data, and models will be fully open-sourced.

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.

Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing the actual ground truth. While the original formulation assumes data exchangeability, some extensions handle non-exchangeable data, which is often the case in many real-world scenarios. In parallel, some progress has been made in conformal methods that provide statistical guarantees for a broader range of objectives, such as bounding the best F_1-score or minimizing the false negative rate in expectation. In this paper, we leverage and extend these two lines of work by proposing non-exchangeable conformal risk control, which allows controlling the expected value of any monotone loss function when the data is not exchangeable. Our framework is flexible, makes very few assumptions, and allows weighting the data based on its relevance for a given test example; a careful choice of weights may result on tighter bounds, making our framework useful in the presence of change points, time series, or other forms of distribution drift. Experiments with both synthetic and real world data show the usefulness of our method.

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.

Vaccine supply chain optimization can benefit from hierarchical time series forecasting, when grouping the vaccines by type or location. However, forecasts of different hierarchy levels become incoherent when higher levels do not match the sum of the lower levels forecasts, which can be addressed by reconciliation methods. In this paper, we tackle the vaccine sale forecasting problem by modeling sales data from GSK between 2010 and 2021 as a hierarchical time series. After forecasting future values with several ARIMA models, we systematically compare the performance of various reconciliation methods, using statistical tests. We also compare the performance of the forecast before and after COVID. The results highlight Minimum Trace and Weighted Least Squares with Structural scaling as the best performing methods, which provided a coherent forecast while reducing the forecast error of the baseline ARIMA.

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8times reduction in average KV cache size during the search process, leading to 1.4times increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

We introduce our first reflective generative model MetaStone-S1, which obtains OpenAI o3's performance via the self-supervised process reward model (SPRM). Through sharing the backbone network and using task-specific heads for next token prediction and process scoring respectively, SPRM successfully integrates the policy model and process reward model(PRM) into a unified interface without extra process annotation, reducing over 99% PRM parameters for efficient reasoning. Equipped with SPRM, MetaStone-S1 is naturally suitable for test time scaling (TTS), and we provide three reasoning effort modes (low, medium, and high), based on the controllable thinking length. Moreover, we empirically establish a scaling law that reveals the relationship between total thinking computation and TTS performance. Experiments demonstrate that our MetaStone-S1 achieves comparable performance to OpenAI-o3-mini's series with only 32B parameter size. To support the research community, we have open-sourced MetaStone-S1 at https://github.com/MetaStone-AI/MetaStone-S1.

We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant. By analyzing the squared prediction risk of ridge ensembles as a function of the explicit penalty lambda and the limiting subsample aspect ratio phi_s (the ratio of the feature size to the subsample size), we characterize contours in the (lambda, phi_s)-plane at any achievable risk. As a consequence, we prove that the risk of the optimal full ridgeless ensemble (fitted on all possible subsamples) matches that of the optimal ridge predictor. In addition, we prove strong uniform consistency of generalized cross-validation (GCV) over the subsample sizes for estimating the prediction risk of ridge ensembles. This allows for GCV-based tuning of full ridgeless ensembles without sample splitting and yields a predictor whose risk matches optimal ridge risk.

Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel decoding, which increase answer diversity but scale poorly in efficiency. To address this efficiency-accuracy trade-off, we propose SSR (Speculative Parallel Scaling Reasoning), a training-free framework that leverages a key insight: by introducing speculative decoding at the step level, we can accelerate reasoning without sacrificing correctness. SSR integrates two components: a Selective Parallel Module (SPM) that identifies a small set of promising reasoning strategies via model-internal scoring, and Step-level Speculative Decoding (SSD), which enables efficient draft-target collaboration for fine-grained reasoning acceleration. Experiments on three mathematical benchmarks-AIME 2024, MATH-500, and LiveMathBench - demonstrate that SSR achieves strong gains over baselines. For instance, on LiveMathBench, SSR improves pass@1 accuracy by 13.84% while reducing computation to 80.5% of the baseline FLOPs. On MATH-500, SSR reduces compute to only 30% with no loss in accuracy.

This work describes a process for efficiently fine-tuning the GraphCast data-driven forecast model to simulate another analysis system, here the Global Deterministic Prediction System (GDPS) of Environment and Climate Change Canada (ECCC). Using two years of training data (July 2019 -- December 2021) and 37 GPU-days of computation to tune the 37-level, quarter-degree version of GraphCast, the resulting model significantly outperforms both the unmodified GraphCast and operational forecast, showing significant forecast skill in the troposphere over lead times from 1 to 10 days. This fine-tuning is accomplished through abbreviating DeepMind's original training curriculum for GraphCast, relying on a shorter single-step forecast stage to accomplish the bulk of the adaptation work and consolidating the autoregressive stages into separate 12hr, 1d, 2d, and 3d stages with larger learning rates. Additionally, training over 3d forecasts is split into two sub-steps to conserve host memory while maintaining a strong correlation with training over the full period.

We revisit the common practice of evaluating adaptation of Online Continual Learning (OCL) algorithms through the metric of online accuracy, which measures the accuracy of the model on the immediate next few samples. However, we show that this metric is unreliable, as even vacuous blind classifiers, which do not use input images for prediction, can achieve unrealistically high online accuracy by exploiting spurious label correlations in the data stream. Our study reveals that existing OCL algorithms can also achieve high online accuracy, but perform poorly in retaining useful information, suggesting that they unintentionally learn spurious label correlations. To address this issue, we propose a novel metric for measuring adaptation based on the accuracy on the near-future samples, where spurious correlations are removed. We benchmark existing OCL approaches using our proposed metric on large-scale datasets under various computational budgets and find that better generalization can be achieved by retaining and reusing past seen information. We believe that our proposed metric can aid in the development of truly adaptive OCL methods. We provide code to reproduce our results at https://github.com/drimpossible/EvalOCL.

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.

Reinforcement learning (RL) has been widely adopted in post-training for large language models (LLMs) at scale. Recently, the incentivization of reasoning capabilities in LLMs from RL indicates that proper learning methods could enable effective inference-time scalability. A key challenge of RL is to obtain accurate reward signals for LLMs in various domains beyond verifiable questions or artificial rules. In this work, we investigate how to improve reward modeling (RM) with more inference compute for general queries, i.e. the inference-time scalability of generalist RM, and further, how to improve the effectiveness of performance-compute scaling with proper learning methods. For the RM approach, we adopt pointwise generative reward modeling (GRM) to enable flexibility for different input types and potential for inference-time scaling. For the learning method, we propose Self-Principled Critique Tuning (SPCT) to foster scalable reward generation behaviors in GRMs through online RL, to generate principles adaptively and critiques accurately, resulting in DeepSeek-GRM models. Furthermore, for effective inference-time scaling, we use parallel sampling to expand compute usage, and introduce a meta RM to guide voting process for better scaling performance. Empirically, we show that SPCT significantly improves the quality and scalability of GRMs, outperforming existing methods and models in various RM benchmarks without severe biases, and could achieve better performance compared to training-time scaling. DeepSeek-GRM still meets challenges in some tasks, which we believe can be addressed by future efforts in generalist reward systems. The models will be released and open-sourced.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets and code repository are publicly available.

Evaluating anomaly detection algorithms in time series data is critical as inaccuracies can lead to flawed decision-making in various domains where real-time analytics and data-driven strategies are essential. Traditional performance metrics assume iid data and fail to capture the complex temporal dynamics and specific characteristics of time series anomalies, such as early and delayed detections. We introduce Proximity-Aware Time series anomaly Evaluation (PATE), a novel evaluation metric that incorporates the temporal relationship between prediction and anomaly intervals. PATE uses proximity-based weighting considering buffer zones around anomaly intervals, enabling a more detailed and informed assessment of a detection. Using these weights, PATE computes a weighted version of the area under the Precision and Recall curve. Our experiments with synthetic and real-world datasets show the superiority of PATE in providing more sensible and accurate evaluations than other evaluation metrics. We also tested several state-of-the-art anomaly detectors across various benchmark datasets using the PATE evaluation scheme. The results show that a common metric like Point-Adjusted F1 Score fails to characterize the detection performances well, and that PATE is able to provide a more fair model comparison. By introducing PATE, we redefine the understanding of model efficacy that steers future studies toward developing more effective and accurate detection models.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

Large reasoning models (LRMs) have exhibited the capacity of enhancing reasoning performance via internal test-time scaling. Building upon this, a promising direction is to further scale test-time compute to unlock even greater reasoning capabilities. However, as we push these scaling boundaries, systematically understanding the practical limits and achieving optimal resource allocation becomes a critical challenge. In this paper, we investigate the scaling Pareto of test-time scaling and introduce the Test-Time Scaling Performance Model (TTSPM). We theoretically analyze two fundamental paradigms for such extended scaling, parallel scaling and sequential scaling, from a probabilistic modeling perspective. Our primary contribution is the derivation of the saturation point on the scaling budget for both strategies, identifying thresholds beyond which additional computation yields diminishing returns. Remarkably, despite their distinct mechanisms, both paradigms converge to a unified mathematical structure in their upper bounds. We empirically validate our theoretical findings on challenging reasoning benchmarks, including AIME, MATH-500, and GPQA, demonstrating the practical utility of these bounds for test-time resource allocation. We hope that this work provides insights into the cost-benefit trade-offs of test-time scaling, guiding the development of more resource-efficient inference strategies for large reasoning models.

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection; (ii) grouping of rare categorical features; and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional data.

The pulp and paper manufacturing industry requires precise quality control to ensure pure, contaminant-free end products suitable for various applications. Fungal spore concentration is a crucial metric that affects paper usability, and current testing methods are labor-intensive with delayed results, hindering real-time control strategies. To address this, a machine learning algorithm utilizing time-series data and domain knowledge was proposed. The optimal model employed Ridge Regression achieving an MSE of 2.90 on training and validation data. This approach could lead to significant improvements in efficiency and sustainability by providing real-time predictions for fungal spore concentrations. This paper showcases a promising method for real-time fungal spore concentration prediction, enabling stringent quality control measures in the pulp-and-paper industry.

Data Drift is the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory that is similar in structure to the neocortex, and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is its independence from training and testing cycle; all the learning takes place online with streaming data and no separate training and testing cycle is required. In sequential learning paradigm, Sequential Probability Ratio Test (SPRT) offers some unique benefit for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each dimension of the data, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Large language models (LLMs) have attracted significant attention in recommendation systems. Current work primarily applies supervised fine-tuning (SFT) to adapt the model for recommendation tasks. However, SFT on positive examples only limits the model's ability to align with user preference. To address this, researchers recently introduced Direct Preference Optimization (DPO), which explicitly aligns LLMs with user preferences using offline preference ranking data. However, we found that DPO inherently biases the model towards a few items, exacerbating the filter bubble issue and ultimately degrading user experience. In this paper, we propose SPRec, a novel self-play framework designed to mitigate over-recommendation and improve fairness without requiring additional data or manual intervention. In each self-play iteration, the model undergoes an SFT step followed by a DPO step, treating offline interaction data as positive samples and the predicted outputs from the previous iteration as negative samples. This effectively re-weights the DPO loss function using the model's logits, adaptively suppressing biased items. Extensive experiments on multiple real-world datasets demonstrate SPRec's effectiveness in enhancing recommendation accuracy and fairness. The implementation is available via https://github.com/RegionCh/SPRec

In recent years, the introduction of self-supervised contrastive learning (SSCL) has demonstrated remarkable improvements in representation learning across various domains, including natural language processing and computer vision. By leveraging the inherent benefits of self-supervision, SSCL enables the pre-training of representation models using vast amounts of unlabeled data. Despite these advances, there remains a significant gap in understanding the impact of different SSCL strategies on time series forecasting performance, as well as the specific benefits that SSCL can bring. This paper aims to address these gaps by conducting a comprehensive analysis of the effectiveness of various training variables, including different SSCL algorithms, learning strategies, model architectures, and their interplay. Additionally, to gain deeper insights into the improvements brought about by SSCL in the context of time-series forecasting, a qualitative analysis of the empirical receptive field is performed. Through our experiments, we demonstrate that the end-to-end training of a Transformer model using the Mean Squared Error (MSE) loss and SSCL emerges as the most effective approach in time series forecasting. Notably, the incorporation of the contrastive objective enables the model to prioritize more pertinent information for forecasting, such as scale and periodic relationships. These findings contribute to a better understanding of the benefits of SSCL in time series forecasting and provide valuable insights for future research in this area. Our codes are available at https://github.com/chiyuzhang94/contrastive_learning_time-series_e2e.

In light of recent work on scheduling with predicted job sizes, we consider the effect of the cost of predictions in queueing systems, removing the assumption in prior research that predictions are external to the system's resources and/or cost-free. In particular, we introduce a novel approach to utilizing predictions, SkipPredict, designed to address their inherent cost. Rather than uniformly applying predictions to all jobs, we propose a tailored approach that categorizes jobs based on their prediction requirements. To achieve this, we employ one-bit "cheap predictions" to classify jobs as either short or long. SkipPredict prioritizes predicted short jobs over long jobs, and for the latter, SkipPredict applies a second round of more detailed "expensive predictions" to approximate Shortest Remaining Processing Time for these jobs. Our analysis takes into account the cost of prediction. We examine the effect of this cost for two distinct models. In the external cost model, predictions are generated by some external method without impacting job service times but incur a cost. In the server time cost model, predictions themselves require server processing time, and are scheduled on the same server as the jobs.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

Recently, channel-independent methods have achieved state-of-the-art performance in multivariate time series (MTS) forecasting. Despite reducing overfitting risks, these methods miss potential opportunities in utilizing channel dependence for accurate predictions. We argue that there exist locally stationary lead-lag relationships between variates, i.e., some lagged variates may follow the leading indicators within a short time period. Exploiting such channel dependence is beneficial since leading indicators offer advance information that can be used to reduce the forecasting difficulty of the lagged variates. In this paper, we propose a new method named LIFT that first efficiently estimates leading indicators and their leading steps at each time step and then judiciously allows the lagged variates to utilize the advance information from leading indicators. LIFT plays as a plugin that can be seamlessly collaborated with arbitrary time series forecasting methods. Extensive experiments on six real-world datasets demonstrate that LIFT improves the state-of-the-art methods by 5.5% in average forecasting performance. Our code is available at https://github.com/SJTU-Quant/LIFT.

In a legal system, judgment consistency is regarded as one of the most important manifestations of fairness. However, due to the complexity of factual elements that impact sentencing in real-world scenarios, few works have been done on quantitatively measuring judgment consistency towards real-world data. In this paper, we propose an evaluation metric for judgment inconsistency, Legal Inconsistency Coefficient (LInCo), which aims to evaluate inconsistency between data groups divided by specific features (e.g., gender, region, race). We propose to simulate judges from different groups with legal judgment prediction (LJP) models and measure the judicial inconsistency with the disagreement of the judgment results given by LJP models trained on different groups. Experimental results on the synthetic data verify the effectiveness of LInCo. We further employ LInCo to explore the inconsistency in real cases and come to the following observations: (1) Both regional and gender inconsistency exist in the legal system, but gender inconsistency is much less than regional inconsistency; (2) The level of regional inconsistency varies little across different time periods; (3) In general, judicial inconsistency is negatively correlated with the severity of the criminal charges. Besides, we use LInCo to evaluate the performance of several de-bias methods, such as adversarial learning, and find that these mechanisms can effectively help LJP models to avoid suffering from data bias.

Neural networks have shown remarkable performance in computer vision, but their deployment in numerous scientific and technical fields is challenging due to their black-box nature. Scientists and practitioners need to evaluate the reliability of a decision, i.e., to know simultaneously if a model relies on the relevant features and whether these features are robust to image corruptions. Existing attribution methods aim to provide human-understandable explanations by highlighting important regions in the image domain, but fail to fully characterize a decision process's reliability. To bridge this gap, we introduce the Wavelet sCale Attribution Method (WCAM), a generalization of attribution from the pixel domain to the space-scale domain using wavelet transforms. Attribution in the wavelet domain reveals where {\it and} on what scales the model focuses, thus enabling us to assess whether a decision is reliable.

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.

Sparse Autoencoders (SAEs) are a prominent tool in mechanistic interpretability (MI) for decomposing neural network activations into interpretable features. However, the aspiration to identify a canonical set of features is challenged by the observed inconsistency of learned SAE features across different training runs, undermining the reliability and efficiency of MI research. This position paper argues that mechanistic interpretability should prioritize feature consistency in SAEs -- the reliable convergence to equivalent feature sets across independent runs. We propose using the Pairwise Dictionary Mean Correlation Coefficient (PW-MCC) as a practical metric to operationalize consistency and demonstrate that high levels are achievable (0.80 for TopK SAEs on LLM activations) with appropriate architectural choices. Our contributions include detailing the benefits of prioritizing consistency; providing theoretical grounding and synthetic validation using a model organism, which verifies PW-MCC as a reliable proxy for ground-truth recovery; and extending these findings to real-world LLM data, where high feature consistency strongly correlates with the semantic similarity of learned feature explanations. We call for a community-wide shift towards systematically measuring feature consistency to foster robust cumulative progress in MI.

Foundation models rely on large-scale web-crawled datasets, which frequently contain noisy data, biases, and irrelevant content. Existing data selection techniques typically use human heuristics, downstream evaluation datasets, or specialized scoring models, and can overlook samples' utility in the training process. Instead, we propose a new approach, Mimic Score, a data quality metric that uses a pretrained reference model as a guide to assess the usefulness of data samples for training a new model. It relies on the alignment between the gradient of the new model parameters and the vector pointing toward the reference model in weight space. Samples that misalign with this direction are considered low-value and can be filtered out. Motivated by the Mimic score, we develop Grad-Mimic, a data selection framework that identifies and prioritizes useful samples, automating the selection process to create effective filters. Empirically, using Mimic scores to guide model training results in consistent performance gains across six image datasets and enhances the performance of CLIP models. Moreover, Mimic scores and their associated filters improve upon existing filtering methods and offer accurate estimation of dataset quality.

Foundation models have become increasingly popular for forecasting due to their ability to provide predictions without requiring a lot of training data. In this work, we demonstrate how TabPFN-v2, a general tabular foundation model, can be effectively applied to time series forecasting. We introduce TabPFN-TS, a simple method that combines TabPFN-v2 with lightweight feature engineering to enable both point and probabilistic forecasting. Despite its simplicity and compact size (11M parameters), TabPFN-TS achieves top rank on the public GIFT-Eval leaderboard in both forecasting tasks. Through ablation studies, we investigate factors contributing to this surprising effectiveness, especially considering TabPFN-v2 was pretrained solely on synthetic tabular data with no exposure to time series. Our results highlights the potential of tabular foundation models like TabPFN-v2 as a valuable new approach for time series forecasting. Our implementation is available at https://github.com/PriorLabs/tabpfn-time-series.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

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

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the largest empirical study to date to assess the probabilistic calibration of neural networks. We also analyze the performance of recalibration, conformal, and regularization methods to enhance probabilistic calibration. Additionally, we introduce novel differentiable recalibration and regularization methods, uncovering new insights into their effectiveness. Our findings reveal that regularization methods offer a favorable tradeoff between calibration and sharpness. Post-hoc methods exhibit superior probabilistic calibration, which we attribute to the finite-sample coverage guarantee of conformal prediction. Furthermore, we demonstrate that quantile recalibration can be considered as a specific case of conformal prediction. Our study is fully reproducible and implemented in a common code base for fair comparisons.

Knowledge of mixtures' phase equilibria is crucial in nature and technical chemistry. Phase equilibria calculations of mixtures require activity coefficients. However, experimental data on activity coefficients is often limited due to high cost of experiments. For an accurate and efficient prediction of activity coefficients, machine learning approaches have been recently developed. However, current machine learning approaches still extrapolate poorly for activity coefficients of unknown molecules. In this work, we introduce the SMILES-to-Properties-Transformer (SPT), a natural language processing network to predict binary limiting activity coefficients from SMILES codes. To overcome the limitations of available experimental data, we initially train our network on a large dataset of synthetic data sampled from COSMO-RS (10 Million data points) and then fine-tune the model on experimental data (20 870 data points). This training strategy enables SPT to accurately predict limiting activity coefficients even for unknown molecules, cutting the mean prediction error in half compared to state-of-the-art models for activity coefficient predictions such as COSMO-RS, UNIFAC, and improving on recent machine learning approaches.

We introduce TimeSeriesGym, a scalable benchmarking framework for evaluating Artificial Intelligence (AI) agents on time series machine learning engineering challenges. Existing benchmarks lack scalability, focus narrowly on model building in well-defined settings, and evaluate only a limited set of research artifacts (e.g., CSV submission files). To make AI agent benchmarking more relevant to the practice of machine learning engineering, our framework scales along two critical dimensions. First, recognizing that effective ML engineering requires a range of diverse skills, TimeSeriesGym incorporates challenges from diverse sources spanning multiple domains and tasks. We design challenges to evaluate both isolated capabilities (including data handling, understanding research repositories, and code translation) and their combinations, and rather than addressing each challenge independently, we develop tools that support designing multiple challenges at scale. Second, we implement evaluation mechanisms for multiple research artifacts, including submission files, code, and models, using both precise numeric measures and more flexible LLM-based evaluation approaches. This dual strategy balances objective assessment with contextual judgment. Although our initial focus is on time series applications, our framework can be readily extended to other data modalities, broadly enhancing the comprehensiveness and practical utility of agentic AI evaluation. We open-source our benchmarking framework to facilitate future research on the ML engineering capabilities of AI agents.

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in high-stakes contexts, such as medical diagnosis and finance. We show that this inconsistent behavior extends beyond predictions to feature attributions, which may likewise have negative implications for the intelligibility of a model, and one's ability to find recourse for subjects. We then introduce selective ensembles to mitigate such inconsistencies by applying hypothesis testing to the predictions of a set of models trained using randomly-selected starting conditions; importantly, selective ensembles can abstain in cases where a consistent outcome cannot be achieved up to a specified confidence level. We prove that that prediction disagreement between selective ensembles is bounded, and empirically demonstrate that selective ensembles achieve consistent predictions and feature attributions while maintaining low abstention rates. On several benchmark datasets, selective ensembles reach zero inconsistently predicted points, with abstention rates as low 1.5%.

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.

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.

Enhancing the reasoning capabilities of large language models effectively using reinforcement learning (RL) remains a crucial challenge. Existing approaches primarily adopt two contrasting advantage estimation granularities: Token-level methods (e.g., PPO) aim to provide the fine-grained advantage signals but suffer from inaccurate estimation due to difficulties in training an accurate critic model. On the other extreme, trajectory-level methods (e.g., GRPO) solely rely on a coarse-grained advantage signal from the final reward, leading to imprecise credit assignment. To address these limitations, we propose Segment Policy Optimization (SPO), a novel RL framework that leverages segment-level advantage estimation at an intermediate granularity, achieving a better balance by offering more precise credit assignment than trajectory-level methods and requiring fewer estimation points than token-level methods, enabling accurate advantage estimation based on Monte Carlo (MC) without a critic model. SPO features three components with novel strategies: (1) flexible segment partition; (2) accurate segment advantage estimation; and (3) policy optimization using segment advantages, including a novel probability-mask strategy. We further instantiate SPO for two specific scenarios: (1) SPO-chain for short chain-of-thought (CoT), featuring novel cutpoint-based partition and chain-based advantage estimation, achieving 6-12 percentage point improvements in accuracy over PPO and GRPO on GSM8K. (2) SPO-tree for long CoT, featuring novel tree-based advantage estimation, which significantly reduces the cost of MC estimation, achieving 7-11 percentage point improvements over GRPO on MATH500 under 2K and 4K context evaluation. We make our code publicly available at https://github.com/AIFrameResearch/SPO.

Background: Collaborative Software Package Registries (SPRs) are an integral part of the software supply chain. Much engineering work synthesizes SPR package into applications. Prior research has examined SPRs for traditional software, such as NPM (JavaScript) and PyPI (Python). Pre-Trained Model (PTM) Registries are an emerging class of SPR of increasing importance, because they support the deep learning supply chain. Aims: Recent empirical research has examined PTM registries in ways such as vulnerabilities, reuse processes, and evolution. However, no existing research synthesizes them to provide a systematic understanding of the current knowledge. Some of the existing research includes qualitative claims lacking quantitative analysis. Our research fills these gaps by providing a knowledge synthesis and quantitative analyses. Methods: We first conduct a systematic literature review (SLR). We then observe that some of the claims are qualitative. We identify quantifiable metrics associated with those claims, and measure in order to substantiate these claims. Results: From our SLR, we identify 12 claims about PTM reuse on the HuggingFace platform, 4 of which lack quantitative validation. We successfully test 3 of these claims through a quantitative analysis, and directly compare one with traditional software. Our findings corroborate qualitative claims with quantitative measurements. Our findings are: (1) PTMs have a much higher turnover rate than traditional software, indicating a dynamic and rapidly evolving reuse environment within the PTM ecosystem; and (2) There is a strong correlation between documentation quality and PTM popularity. Conclusions: We confirm qualitative research claims with concrete metrics, supporting prior qualitative and case study research. Our measures show further dynamics of PTM reuse, inspiring research infrastructure and new measures.

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?

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

Building trusted datasets is critical for transparent and responsible Medical AI (MAI) research, but creating even small, high-quality datasets can take years of effort from multidisciplinary teams. This process often delays AI benefits, as human-centric data creation and AI-centric model development are treated as separate, sequential steps. To overcome this, we propose ScaleMAI, an agent of AI-integrated data curation and annotation, allowing data quality and AI performance to improve in a self-reinforcing cycle and reducing development time from years to months. We adopt pancreatic tumor detection as an example. First, ScaleMAI progressively creates a dataset of 25,362 CT scans, including per-voxel annotations for benign/malignant tumors and 24 anatomical structures. Second, through progressive human-in-the-loop iterations, ScaleMAI provides Flagship AI Model that can approach the proficiency of expert annotators (30-year experience) in detecting pancreatic tumors. Flagship Model significantly outperforms models developed from smaller, fixed-quality datasets, with substantial gains in tumor detection (+14%), segmentation (+5%), and classification (72%) on three prestigious benchmarks. In summary, ScaleMAI transforms the speed, scale, and reliability of medical dataset creation, paving the way for a variety of impactful, data-driven applications.

As of September 2023, ChatGPT correctly answers "what is 7+8" with 15, but when asked "7+8=15, True or False" it responds with "False". This inconsistency between generating and validating an answer is prevalent in language models (LMs) and erodes trust. In this paper, we propose a framework for measuring the consistency between generation and validation (which we call generator-validator consistency, or GV-consistency), finding that even GPT-4, a state-of-the-art LM, is GV-consistent only 76% of the time. To improve the consistency of LMs, we propose to finetune on the filtered generator and validator responses that are GV-consistent, and call this approach consistency fine-tuning. We find that this approach improves GV-consistency of Alpaca-30B from 60% to 93%, and the improvement extrapolates to unseen tasks and domains (e.g., GV-consistency for positive style transfers extrapolates to unseen styles like humor). In addition to improving consistency, consistency fine-tuning improves both generator quality and validator accuracy without using any labeled data. Evaluated across 6 tasks, including math questions, knowledge-intensive QA, and instruction following, our method improves the generator quality by 16% and the validator accuracy by 6.3% across all tasks.

We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven highly effective in consistency models derived from the score matching. However, for the diffusion counterparts, the methodology and efficacy of adding extra metric functions remain unclear. One major challenge is the mismatch between the noise predicted by a DDPM at each step and the desired clean image that the metric function works well on. To address this problem, we propose Cas-DM, a network architecture that cascades two network modules to effectively apply metric functions to the diffusion model training. The first module, similar to a standard DDPM, learns to predict the added noise and is unaffected by the metric function. The second cascaded module learns to predict the clean image, thereby facilitating the metric function computation. Experiment results show that the proposed diffusion model backbone enables the effective use of the LPIPS loss, leading to state-of-the-art image quality (FID, sFID, IS) on various established benchmarks.

We introduce DS-1000, a code generation benchmark with a thousand data science problems spanning seven Python libraries, such as NumPy and Pandas. Compared to prior works, DS-1000 incorporates three core features. First, our problems reflect diverse, realistic, and practical use cases since we collected them from StackOverflow. Second, our automatic evaluation is highly specific (reliable) -- across all Codex-002-predicted solutions that our evaluation accept, only 1.8% of them are incorrect; we achieve this with multi-criteria metrics, checking both functional correctness by running test cases and surface-form constraints by restricting API usages or keywords. Finally, we proactively defend against memorization by slightly modifying our problems to be different from the original StackOverflow source; consequently, models cannot answer them correctly by memorizing the solutions from pre-training. The current best public system (Codex-002) achieves 43.3% accuracy, leaving ample room for improvement. We release our benchmark at https://ds1000-code-gen.github.io.

Comprehensively understanding and accurately predicting the performance of large language models across diverse downstream tasks has emerged as a pivotal challenge in NLP research. The pioneering scaling law on downstream works demonstrated intrinsic similarities within model families and utilized such similarities for performance prediction. However, they tend to overlook the similarities between model families and only consider design factors listed in the original scaling law. To overcome these limitations, we introduce a novel framework, Collaborative Performance Prediction (CPP), which significantly enhances prediction accuracy by leveraging the historical performance of various models on downstream tasks and other design factors for both model and task. We also collect a collaborative data sourced from online platforms containing both historical performance and additional design factors. With the support of the collaborative data, CPP not only surpasses traditional scaling laws in predicting the performance of scaled LLMs but also facilitates a detailed analysis of factor importance, an area previously overlooked.

The rapid advancement of Large Language Models (LLMs) necessitates robust evaluation methodologies. Current benchmarking approaches often rely on comparing model outputs against predefined prompts and reference outputs. Relying on predefined reference outputs hinders flexible adaptation of benchmarks to the rapidly evolving capabilities of LLMs. This limitation necessitates periodic efforts to prepare new benchmarks. To keep pace with rapidly evolving LLM capabilities, we propose a more flexible benchmarking approach. Our method, \textbf{Varco Arena}, provides reference-free benchmarking of LLMs in tournament style. \textbf{Varco Arena} directly compares LLM outputs across a diverse set of prompts, determining model rankings through a single-elimination tournament structure. This direct pairwise comparison offers two key advantages: (1) Direct comparison, unmediated by reference text, more effectively orders competing LLMs, resulting in more reliable rankings, and (2) reference-free approach to benchmarking adds flexibility in updating benchmark prompts by eliminating the need for quality references. Our empirical results, supported by simulation experiments, demonstrate that the \textbf{Varco Arena} tournament approach aligns better with the current Elo model for benchmarking LLMs. The alignment is measured in terms of Spearman correlation, showing improvement over current practice of benchmarking that use reference outputs as comparison anchors.

Time series forecasting has attracted significant attention in recent decades. Previous studies have demonstrated that the Channel-Independent (CI) strategy improves forecasting performance by treating different channels individually, while it leads to poor generalization on unseen instances and ignores potentially necessary interactions between channels. Conversely, the Channel-Dependent (CD) strategy mixes all channels with even irrelevant and indiscriminate information, which, however, results in oversmoothing issues and limits forecasting accuracy. There is a lack of channel strategy that effectively balances individual channel treatment for improved forecasting performance without overlooking essential interactions between channels. Motivated by our observation of a correlation between the time series model's performance boost against channel mixing and the intrinsic similarity on a pair of channels, we developed a novel and adaptable Channel Clustering Module (CCM). CCM dynamically groups channels characterized by intrinsic similarities and leverages cluster information instead of individual channel identities, combining the best of CD and CI worlds. Extensive experiments on real-world datasets demonstrate that CCM can (1) boost the performance of CI and CD models by an average margin of 2.4% and 7.2% on long-term and short-term forecasting, respectively; (2) enable zero-shot forecasting with mainstream time series forecasting models; (3) uncover intrinsic time series patterns among channels and improve interpretability of complex time series models.

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

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%.

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We first show that the marginal coverage guarantee of conformal prediction holds on imputed data for any missingness distribution and almost all imputation functions. However, we emphasize that the average coverage varies depending on the pattern of missing values: conformal methods tend to construct prediction intervals that under-cover the response conditionally to some missing patterns. This motivates our novel generalized conformalized quantile regression framework, missing data augmentation, which yields prediction intervals that are valid conditionally to the patterns of missing values, despite their exponential number. We then show that a universally consistent quantile regression algorithm trained on the imputed data is Bayes optimal for the pinball risk, thus achieving valid coverage conditionally to any given data point. Moreover, we examine the case of a linear model, which demonstrates the importance of our proposal in overcoming the heteroskedasticity induced by missing values. Using synthetic and data from critical care, we corroborate our theory and report improved performance of our methods.

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a square root scaling rule to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

Test-time scaling has emerged as a powerful technique for enhancing the reasoning capabilities of large language models. However, its effectiveness in medical reasoning remains uncertain, as the medical domain fundamentally differs from mathematical tasks in terms of knowledge representation and decision-making processes. In this paper, we provide the first comprehensive investigation of test-time scaling for medical reasoning and present m1, a simple yet effective approach that increases a model's medical reasoning capability at inference. Our evaluation across diverse medical tasks demonstrates that test-time scaling consistently enhances medical reasoning, enabling lightweight fine-tuned models under 10B parameters to establish new state-of-the-art performance, while our 32B model rivals previous 70B-scale medical LLMs. However, we identify an optimal reasoning token budget of approximately 4K, beyond which performance may degrade due to overthinking. Budget forcing, which extends test-time computation through iterative prompts, helps models double-check answers but does not necessarily improve the overall medical QA performance and, in some cases, even introduces errors into previously correct responses. Our case-by-case analysis identifies insufficient medical knowledge as a key bottleneck that prevents further performance gains through test-time scaling. We find that increasing data scale, improving data quality, and expanding model capacity consistently enhance medical knowledge grounding, enabling continued performance improvements, particularly on challenging medical benchmarks where smaller models reach saturation. These findings underscore fundamental differences between medical and mathematical reasoning in LLMs, highlighting that enriched medical knowledge, other than increased reasoning depth alone, is essential for realizing the benefits of test-time scaling.

Diffusion models have shown promising ability in generating high-quality time series (TS) data. Despite the initial success, existing works mostly focus on the authenticity of data at the individual level, but pay less attention to preserving the population-level properties on the entire dataset. Such population-level properties include value distributions for each dimension and distributions of certain functional dependencies (e.g., cross-correlation, CC) between different dimensions. For instance, when generating house energy consumption TS data, the value distributions of the outside temperature and the kitchen temperature should be preserved, as well as the distribution of CC between them. Preserving such TS population-level properties is critical in maintaining the statistical insights of the datasets, mitigating model bias, and augmenting downstream tasks like TS prediction. Yet, it is often overlooked by existing models. Hence, data generated by existing models often bear distribution shifts from the original data. We propose Population-aware Diffusion for Time Series (PaD-TS), a new TS generation model that better preserves the population-level properties. The key novelties of PaD-TS include 1) a new training method explicitly incorporating TS population-level property preservation, and 2) a new dual-channel encoder model architecture that better captures the TS data structure. Empirical results in major benchmark datasets show that PaD-TS can improve the average CC distribution shift score between real and synthetic data by 5.9x while maintaining a performance comparable to state-of-the-art models on individual-level authenticity.

As general purpose vision models get increasingly effective at a wide set of tasks, it is imperative that they be consistent across the tasks they support. Inconsistent AI models are considered brittle and untrustworthy by human users and are more challenging to incorporate into larger systems that take dependencies on their outputs. Measuring consistency between very heterogeneous tasks that might include outputs in different modalities is challenging since it is difficult to determine if the predictions are consistent with one another. As a solution, we introduce a benchmark dataset, COCOCON, where we use contrast sets created by modifying test instances for multiple tasks in small but semantically meaningful ways to change the gold label, and outline metrics for measuring if a model is consistent by ranking the original and perturbed instances across tasks. We find that state-of-the-art systems suffer from a surprisingly high degree of inconsistent behavior across tasks, especially for more heterogeneous tasks. Finally, we propose using a rank correlation-based auxiliary objective computed over large automatically created cross-task contrast sets to improve the multi-task consistency of large unified models, while retaining their original accuracy on downstream tasks. Project website available at https://adymaharana.github.io/cococon/

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

Continuous-time event sequences play a vital role in real-world domains such as healthcare, finance, online shopping, social networks, and so on. To model such data, temporal point processes (TPPs) have emerged as the most natural and competitive models, making a significant impact in both academic and application communities. Despite the emergence of many powerful models in recent years, there hasn't been a central benchmark for these models and future research endeavors. This lack of standardization impedes researchers and practitioners from comparing methods and reproducing results, potentially slowing down progress in this field. In this paper, we present EasyTPP, the first central repository of research assets (e.g., data, models, evaluation programs, documentations) in the area of event sequence modeling. Our EasyTPP makes several unique contributions to this area: a unified interface of using existing datasets and adding new datasets; a wide range of evaluation programs that are easy to use and extend as well as facilitate reproducible research; implementations of popular neural TPPs, together with a rich library of modules by composing which one could quickly build complex models. All the data and implementation can be found at https://github.com/ant-research/EasyTemporalPointProcess. We will actively maintain this benchmark and welcome contributions from other researchers and practitioners. Our benchmark will help promote reproducible research in this field, thus accelerating research progress as well as making more significant real-world impacts.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility.

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many replication efforts. We seek the simplest approach to achieve test-time scaling and strong reasoning performance. First, we curate a small dataset s1K of 1,000 questions paired with reasoning traces relying on three criteria we validate through ablations: difficulty, diversity, and quality. Second, we develop budget forcing to control test-time compute by forcefully terminating the model's thinking process or lengthening it by appending "Wait" multiple times to the model's generation when it tries to end. This can lead the model to double-check its answer, often fixing incorrect reasoning steps. After supervised finetuning the Qwen2.5-32B-Instruct language model on s1K and equipping it with budget forcing, our model s1 exceeds o1-preview on competition math questions by up to 27% (MATH and AIME24). Further, scaling s1 with budget forcing allows extrapolating beyond its performance without test-time intervention: from 50% to 57% on AIME24. Our model, data, and code are open-source at https://github.com/simplescaling/s1.

Large language models (LLMs) have demonstrated strong capabilities in translating natural language questions about relational databases into SQL queries. In particular, test-time scaling techniques such as Self-Consistency and Self-Correction can enhance SQL generation accuracy by increasing computational effort during inference. However, these methods have notable limitations: Self-Consistency may select suboptimal outputs despite majority votes, while Self-Correction typically addresses only syntactic errors. To leverage the strengths of both approaches, we propose CSC-SQL, a novel method that integrates Self-Consistency and Self-Correction. CSC-SQL selects the two most frequently occurring outputs from parallel sampling and feeds them into a merge revision model for correction. Additionally, we employ the Group Relative Policy Optimization (GRPO) algorithm to fine-tune both the SQL generation and revision models via reinforcement learning, significantly enhancing output quality. Experimental results confirm the effectiveness and generalizability of CSC-SQL. On the BIRD development set, our 3B model achieves 65.28% execution accuracy, while the 7B model achieves 69.19%. The code will be open sourced at https://github.com/CycloneBoy/csc_sql.

Machine learning models often experience performance degradation post-deployment due to shifts in data distribution. It is challenging to assess model's performance accurately when labels are missing or delayed. Existing proxy methods, such as drift detection, fail to measure the effects of these shifts adequately. To address this, we introduce a new method, Probabilistic Adaptive Performance Estimation (PAPE), for evaluating classification models on unlabeled data that accurately quantifies the impact of covariate shift on model performance. It is model and data-type agnostic and works for various performance metrics. Crucially, PAPE operates independently of the original model, relying only on its predictions and probability estimates, and does not need any assumptions about the nature of the covariate shift, learning directly from data instead. We tested PAPE on tabular data using over 900 dataset-model combinations created from US census data, assessing its performance against multiple benchmarks. Overall, PAPE provided more accurate performance estimates than other evaluated methodologies.

Prediction sets capture uncertainty by predicting sets of labels rather than individual labels, enabling downstream decisions to conservatively account for all plausible outcomes. Conformal inference algorithms construct prediction sets guaranteed to contain the true label with high probability. These guarantees fail to hold in the face of distribution shift, which is precisely when reliable uncertainty quantification can be most useful. We propose a novel algorithm for constructing prediction sets with PAC guarantees in the label shift setting. This method estimates the predicted probabilities of the classes in a target domain, as well as the confusion matrix, then propagates uncertainty in these estimates through a Gaussian elimination algorithm to compute confidence intervals for importance weights. Finally, it uses these intervals to construct prediction sets. We evaluate our approach on five datasets: the CIFAR-10, ChestX-Ray and Entity-13 image datasets, the tabular CDC Heart dataset, and the AGNews text dataset. Our algorithm satisfies the PAC guarantee while producing smaller, more informative, prediction sets compared to several baselines.

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

Contrastive representation learning is crucial in medical time series analysis as it alleviates dependency on labor-intensive, domain-specific, and scarce expert annotations. However, existing contrastive learning methods primarily focus on one single data level, which fails to fully exploit the intricate nature of medical time series. To address this issue, we present COMET, an innovative hierarchical framework that leverages data consistencies at all inherent levels in medical time series. Our meticulously designed model systematically captures data consistency from four potential levels: observation, sample, trial, and patient levels. By developing contrastive loss at multiple levels, we can learn effective representations that preserve comprehensive data consistency, maximizing information utilization in a self-supervised manner. We conduct experiments in the challenging patient-independent setting. We compare COMET against six baselines using three diverse datasets, which include ECG signals for myocardial infarction and EEG signals for Alzheimer's and Parkinson's diseases. The results demonstrate that COMET consistently outperforms all baselines, particularly in setup with 10% and 1% labeled data fractions across all datasets. These results underscore the significant impact of our framework in advancing contrastive representation learning techniques for medical time series. The source code is available at https://github.com/DL4mHealth/COMET.

The relationships between workload and fatigue or sleepiness are investigated through the analysis of rosters and responses to questionnaires from Brazilian aircrews, taken from Fadig\^ometro database. The approach includes temporal markers - coinciding with Samn-Perelli (SP) and Karolinska Sleepiness Scale (KSS) responses - where SAFTE-FAST model outcomes are calculated. The model results follow the increase of fatigue and sleepiness perceptions during the dawn (0h00 to 05h59), but underestimate the self-rated scores during the evening (18h00 to 23h59). On the other hand, the KSS scores fit the relative risk of pilot errors, representing a reasonable proxy for risk assessment. Linear relationships obtained between workload metrics, computed within 168-hours prior to the responses, and self-rated SP and KSS scores provide a consistent method to estimate accumulated fatigue and sleepiness. Considering 7149 rosters of 2023, the duty time (DT), the number of flight sectors (N_{CREW}) and the sum of flight sectors with sit periods longer than one hour (N_{CREW}+N_{SIT}) are associated with 70.1%/60.6% of the highest predicted scores of SP/KSS. Applying the mitigations DTleq44h, N_{CREW}leq15 and N_{CREW}+N_{SIT}leq19 for every 168-hour interval yields a significant decrease in the higher values of SP/KSS with minimal impact on aircrew productivity.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model debate approaches, our method leverages consistency in a sequence of self-reflection actions to improve verification accuracy. Empirical evaluations across diverse mathematical process error identification benchmarks (Mathcheck, ProcessBench, and PRM800K) show consistent performance improvements over baseline methods. When applied to the recent DeepSeek R1 distilled models, our method demonstrates strong performance, enabling 7B/8B distilled models to outperform all 70B/72B models and GPT-4o on ProcessBench. Notably, the distilled 14B model with our method achieves performance comparable to Deepseek-R1. Our codes are available at https://github.com/jcguo123/Temporal-Consistency

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.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a "closed-loop" variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length ell and state-space size d, we go from O(d ell) na\"ively to O(d + ell). In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR(p) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

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

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

Learning curve extrapolation aims to predict model performance in later epochs of training, based on the performance in earlier epochs. In this work, we argue that, while the inherent uncertainty in the extrapolation of learning curves warrants a Bayesian approach, existing methods are (i) overly restrictive, and/or (ii) computationally expensive. We describe the first application of prior-data fitted neural networks (PFNs) in this context. A PFN is a transformer, pre-trained on data generated from a prior, to perform approximate Bayesian inference in a single forward pass. We propose LC-PFN, a PFN trained to extrapolate 10 million artificial right-censored learning curves generated from a parametric prior proposed in prior art using MCMC. We demonstrate that LC-PFN can approximate the posterior predictive distribution more accurately than MCMC, while being over 10 000 times faster. We also show that the same LC-PFN achieves competitive performance extrapolating a total of 20 000 real learning curves from four learning curve benchmarks (LCBench, NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets with varying input modalities (tabular, image, text, and protein data). Finally, we investigate its potential in the context of model selection and find that a simple LC-PFN based predictive early stopping criterion obtains 2 - 6x speed-ups on 45 of these datasets, at virtually no overhead.

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.

Time series foundation models excel in zero-shot forecasting, handling diverse tasks without explicit training. However, the advancement of these models has been hindered by the lack of comprehensive benchmarks. To address this gap, we introduce the General Time Series Forecasting Model Evaluation, GIFT-Eval, a pioneering benchmark aimed at promoting evaluation across diverse datasets. GIFT-Eval encompasses 28 datasets over 144,000 time series and 177 million data points, spanning seven domains, 10 frequencies, multivariate inputs, and prediction lengths ranging from short to long-term forecasts. To facilitate the effective pretraining and evaluation of foundation models, we also provide a non-leaking pretraining dataset containing approximately 230 billion data points. Additionally, we provide a comprehensive analysis of 17 baselines, which includes statistical models, deep learning models, and foundation models. We discuss each model in the context of various benchmark characteristics and offer a qualitative analysis that spans both deep learning and foundation models. We believe the insights from this analysis, along with access to this new standard zero-shot time series forecasting benchmark, will guide future developments in time series foundation models. The codebase, datasets, and a leaderboard showing all the results in detail will be available soon.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

Score distillation sampling (SDS) and its variants have greatly boosted the development of text-to-3D generation, but are vulnerable to geometry collapse and poor textures yet. To solve this issue, we first deeply analyze the SDS and find that its distillation sampling process indeed corresponds to the trajectory sampling of a stochastic differential equation (SDE): SDS samples along an SDE trajectory to yield a less noisy sample which then serves as a guidance to optimize a 3D model. However, the randomness in SDE sampling often leads to a diverse and unpredictable sample which is not always less noisy, and thus is not a consistently correct guidance, explaining the vulnerability of SDS. Since for any SDE, there always exists an ordinary differential equation (ODE) whose trajectory sampling can deterministically and consistently converge to the desired target point as the SDE, we propose a novel and effective "Consistent3D" method that explores the ODE deterministic sampling prior for text-to-3D generation. Specifically, at each training iteration, given a rendered image by a 3D model, we first estimate its desired 3D score function by a pre-trained 2D diffusion model, and build an ODE for trajectory sampling. Next, we design a consistency distillation sampling loss which samples along the ODE trajectory to generate two adjacent samples and uses the less noisy sample to guide another more noisy one for distilling the deterministic prior into the 3D model. Experimental results show the efficacy of our Consistent3D in generating high-fidelity and diverse 3D objects and large-scale scenes, as shown in Fig. 1. The codes are available at https://github.com/sail-sg/Consistent3D.

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

The advent of test-time scaling in large language models (LLMs), exemplified by OpenAI's o1 series, has advanced reasoning capabilities by scaling computational resource allocation during inference. While successors like QwQ, Deepseek-R1 (R1) and LIMO replicate these advancements, whether these models truly possess test-time scaling capabilities remains underexplored. This study found that longer CoTs of these o1-like models do not consistently enhance accuracy; in fact, correct solutions are often shorter than incorrect ones for the same questions. Further investigation shows this phenomenon is closely related to models' self-revision capabilities - longer CoTs contain more self-revisions, which often lead to performance degradation. We then compare sequential and parallel scaling strategies on QwQ, R1 and LIMO, finding that parallel scaling achieves better coverage and scalability. Based on these insights, we propose Shortest Majority Vote, a method that combines parallel scaling strategies with CoT length characteristics, significantly improving models' test-time scalability compared to conventional majority voting approaches.

The Kov\'ats Retention index (RI) is a quantity measured using gas chromatography and commonly used in the identification of chemical structures. Creating libraries of observed RI values is a laborious task, so we explore the use of a deep neural network for predicting RI values from structure for standard semipolar columns. This network generated predictions with a mean absolute error of 15.1 and, in a quantification of the tail of the error distribution, a 95th percentile absolute error of 46.5. Because of the Artificial Intelligence Retention Indices (AIRI) network's accuracy, it was used to predict RI values for the NIST EI-MS spectral libraries. These RI values are used to improve chemical identification methods and the quality of the library. Estimating uncertainty is an important practical need when using prediction models. To quantify the uncertainty of our network for each individual prediction, we used the outputs of an ensemble of 8 networks to calculate a predicted standard deviation for each RI value prediction. This predicted standard deviation was corrected to follow the error between observed and predicted RI values. The Z scores using these predicted standard deviations had a standard deviation of 1.52 and a 95th percentile absolute Z score corresponding to a mean RI value of 42.6.

California is a global leader in agricultural production, contributing 12.5% of the United States total output and ranking as the fifth-largest food and cotton supplier in the world. Despite the availability of extensive historical yield data from the USDA National Agricultural Statistics Service, accurate and timely crop yield forecasting remains a challenge due to the complex interplay of environmental, climatic, and soil-related factors. In this study, we introduce a comprehensive crop yield benchmark dataset covering over 70 crops across all California counties from 2008 to 2022. The benchmark integrates diverse data sources, including Landsat satellite imagery, daily climate records, monthly evapotranspiration, and high-resolution soil properties. To effectively learn from these heterogeneous inputs, we develop a multi-modal deep learning model tailored for county-level, crop-specific yield forecasting. The model employs stratified feature extraction and a timeseries encoder to capture spatial and temporal dynamics during the growing season. Static inputs such as soil characteristics and crop identity inform long-term variability. Our approach achieves an overall R2 score of 0.76 across all crops of unseen test dataset, highlighting strong predictive performance across California diverse agricultural regions. This benchmark and modeling framework offer a valuable foundation for advancing agricultural forecasting, climate adaptation, and precision farming. The full dataset and codebase are publicly available at our GitHub repository.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

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.

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.

The release of ChatGPT in November 2022 sparked an explosion of interest in post-training and an avalanche of new preference optimization (PO) methods. These methods claim superior alignment by virtue of better correspondence with human pairwise preferences, often measured by LLM judges. In this work, we attempt to answer the following question -- do LLM-judge preferences translate to progress on other, more concrete metrics for alignment, and if not, why not? We define a concrete metric for alignment, and introduce SOS-Bench, the largest standardized, reproducible LLM meta-benchmark to date. We find that (1) LLM-judgments do not correlate with concrete measures of safety, world knowledge, and instruction following; (2) LLM judges have powerful implicit biases, prioritizing style over factuality and safety; and (3) the supervised fine-tuning (SFT) stage of post-training, and not the PO stage, has the greatest impact on alignment, with data scaling and prompt diversity as the driving factors. Our codebase and complete results can be found at https://github.com/penfever/sos-bench.

In this study, we aimed to determine if fine-tuned large language models (LLMs) can generate accurate, personalized impressions for whole-body PET reports. Twelve language models were trained on a corpus of PET reports using the teacher-forcing algorithm, with the report findings as input and the clinical impressions as reference. An extra input token encodes the reading physician's identity, allowing models to learn physician-specific reporting styles. Our corpus comprised 37,370 retrospective PET reports collected from our institution between 2010 and 2022. To identify the best LLM, 30 evaluation metrics were benchmarked against quality scores from two nuclear medicine (NM) physicians, with the most aligned metrics selecting the model for expert evaluation. In a subset of data, model-generated impressions and original clinical impressions were assessed by three NM physicians according to 6 quality dimensions (3-point scale) and an overall utility score (5-point scale). Each physician reviewed 12 of their own reports and 12 reports from other physicians. Bootstrap resampling was used for statistical analysis. Of all evaluation metrics, domain-adapted BARTScore and PEGASUSScore showed the highest Spearman's rank correlations (0.568 and 0.563) with physician preferences. Based on these metrics, the fine-tuned PEGASUS model was selected as the top LLM. When physicians reviewed PEGASUS-generated impressions in their own style, 89% were considered clinically acceptable, with a mean utility score of 4.08 out of 5. Physicians rated these personalized impressions as comparable in overall utility to the impressions dictated by other physicians (4.03, P=0.41). In conclusion, personalized impressions generated by PEGASUS were clinically useful, highlighting its potential to expedite PET reporting.

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of early warning indicators such as rising variance or increased return times. Despite widespread appreciation of the difficulties and uncertainty involved in such forecasts, proposed methods hardly ever characterize their expected error rates. Without the benefits of replicates, controls, or hindsight, applications of these approaches must quantify how reliable different indicators are in avoiding false alarms, and how sensitive they are to missing subtle warning signs. We propose a model based approach in order to quantify this trade-off between reliability and sensitivity and allow comparisons between different indicators. We show these error rates can be quite severe for common indicators even under favorable assumptions, and also illustrate how a model-based indicator can improve this performance. We demonstrate how the performance of an early warning indicator varies in different data sets, and suggest that uncertainty quantification become a more central part of early warning predictions.

In Machine Learning, a benchmark refers to an ensemble of datasets associated with one or multiple metrics together with a way to aggregate different systems performances. They are instrumental in (i) assessing the progress of new methods along different axes and (ii) selecting the best systems for practical use. This is particularly the case for NLP with the development of large pre-trained models (e.g. GPT, BERT) that are expected to generalize well on a variety of tasks. While the community mainly focused on developing new datasets and metrics, there has been little interest in the aggregation procedure, which is often reduced to a simple average over various performance measures. However, this procedure can be problematic when the metrics are on a different scale, which may lead to spurious conclusions. This paper proposes a new procedure to rank systems based on their performance across different tasks. Motivated by the social choice theory, the final system ordering is obtained through aggregating the rankings induced by each task and is theoretically grounded. We conduct extensive numerical experiments (on over 270k scores) to assess the soundness of our approach both on synthetic and real scores (e.g. GLUE, EXTREM, SEVAL, TAC, FLICKR). In particular, we show that our method yields different conclusions on state-of-the-art systems than the mean-aggregation procedure while being both more reliable and robust.

This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight updating. Our approach involves a stepwise process, starting with user-defined parameters. The linear regression model is trained using SGD, tracking weights and loss separately and zipping them finally. A Kalman filter is then trained based on weight and loss arrays to predict the next consolidated weights. Predictions result from multiplying input averages with weights, evaluated for loss to form a weight-versus-loss curve. The curve's equation is derived using the two-point formula, and area under the curve is calculated via integration. The linear regression equation with minimum area becomes the optimal curve for prediction. Benefits include avoiding constant weight updates via gradient descent and working with partial datasets, unlike methods needing the entire set. However, computational complexity should be considered. The Kalman filter's accuracy might diminish beyond a certain prediction range.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

The goal of predictive data attribution is to estimate how adding or removing a given set of training datapoints will affect model predictions. In convex settings, this goal is straightforward (i.e., via the infinitesimal jackknife). In large-scale (non-convex) settings, however, existing methods are far less successful -- current methods' estimates often only weakly correlate with ground truth. In this work, we present a new data attribution method (MAGIC) that combines classical methods and recent advances in metadifferentiation to (nearly) optimally estimate the effect of adding or removing training data on model predictions.

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.

Understanding why a model makes a certain prediction can be as crucial as the prediction's accuracy in many applications. However, the highest accuracy for large modern datasets is often achieved by complex models that even experts struggle to interpret, such as ensemble or deep learning models, creating a tension between accuracy and interpretability. In response, various methods have recently been proposed to help users interpret the predictions of complex models, but it is often unclear how these methods are related and when one method is preferable over another. To address this problem, we present a unified framework for interpreting predictions, SHAP (SHapley Additive exPlanations). SHAP assigns each feature an importance value for a particular prediction. Its novel components include: (1) the identification of a new class of additive feature importance measures, and (2) theoretical results showing there is a unique solution in this class with a set of desirable properties. The new class unifies six existing methods, notable because several recent methods in the class lack the proposed desirable properties. Based on insights from this unification, we present new methods that show improved computational performance and/or better consistency with human intuition than previous approaches.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Current large language models (LLMs) often struggle to produce accurate responses on the first attempt for complex reasoning tasks like code generation. Prior research tackles this challenge by generating multiple candidate solutions and validating them with LLM-generated unit tests. The execution results of unit tests serve as reward signals to identify correct solutions. As LLMs always confidently make mistakes, these unit tests are not reliable, thereby diminishing the quality of reward signals. Motivated by the observation that scaling the number of solutions improves LLM performance, we explore the impact of scaling unit tests to enhance reward signal quality. Our pioneer experiment reveals a positive correlation between the number of unit tests and reward signal quality, with greater benefits observed in more challenging problems. Based on these insights, we propose CodeRM-8B, a lightweight yet effective unit test generator that enables efficient and high-quality unit test scaling. Additionally, we implement a dynamic scaling mechanism that adapts the number of unit tests based on problem difficulty, further improving efficiency. Experimental results show that our approach significantly improves performance across various models on three benchmarks (e.g., with gains of 18.43% for Llama3-8B and 3.42% for GPT-4o-mini on HumanEval Plus).

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

We present an improvement in the ability to meaningfully track features in high speed videos of Caribbean steelpan drums illuminated by Electronic Speckle Pattern Interferometry (ESPI). This is achieved through the use of up-to-date computer vision libraries for object detection and image segmentation as well as a significant effort toward cleaning the dataset previously used to train systems for this application. Besides improvements on previous metric scores by 10% or more, noteworthy in this project are the introduction of a segmentation-regression map for the entire drum surface yielding interference fringe counts comparable to those obtained via object detection, as well as the accelerated workflow for coordinating the data-cleaning-and-model-training feedback loop for rapid iteration allowing this project to be conducted on a timescale of only 18 days.

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models, variational inference (VI) is often the preferable option. Unfortunately, VI makes strong assumptions on both the factorization and functional form of the posterior. In this work, we propose a new non-parametric variational approximation that makes no assumptions about the approximate posterior's functional form and allows practitioners to specify the exact dependencies the algorithm should respect or break. The approach relies on a new Langevin-type algorithm that operates on a modified energy function, where parts of the latent variables are averaged over samples from earlier iterations of the Markov chain. This way, statistical dependencies can be broken in a controlled way, allowing the chain to mix faster. This scheme can be further modified in a "dropout" manner, leading to even more scalability. We test our scheme for ResNet-20 on CIFAR-10, SVHN, and FMNIST. In all cases, we find improvements in convergence speed and/or final accuracy compared to SG-MCMC and VI.

Most existing forecasting systems are memory-based methods, which attempt to mimic human forecasting ability by employing various memory mechanisms and have progressed in temporal modeling for memory dependency. Nevertheless, an obvious weakness of this paradigm is that it can only model limited historical dependence and can not transcend the past. In this paper, we rethink the temporal dependence of event evolution and propose a novel memory-anticipation-based paradigm to model an entire temporal structure, including the past, present, and future. Based on this idea, we present Memory-and-Anticipation Transformer (MAT), a memory-anticipation-based approach, to address the online action detection and anticipation tasks. In addition, owing to the inherent superiority of MAT, it can process online action detection and anticipation tasks in a unified manner. The proposed MAT model is tested on four challenging benchmarks TVSeries, THUMOS'14, HDD, and EPIC-Kitchens-100, for online action detection and anticipation tasks, and it significantly outperforms all existing methods. Code is available at https://github.com/Echo0125/Memory-and-Anticipation-Transformer.

Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples are able to manipulate conformal methods to construct prediction sets with invalid coverage rates, as the i.i.d. assumption is violated. To address this issue, a recent work, Randomized Smoothed Conformal Prediction (RSCP), was first proposed to certify the robustness of conformal prediction methods to adversarial noise. However, RSCP has two major limitations: (i) its robustness guarantee is flawed when used in practice and (ii) it tends to produce large uncertainty sets. To address these limitations, we first propose a novel framework called RSCP+ to provide provable robustness guarantee in evaluation, which fixes the issues in the original RSCP method. Next, we propose two novel methods, Post-Training Transformation (PTT) and Robust Conformal Training (RCT), to effectively reduce prediction set size with little computation overhead. Experimental results in CIFAR10, CIFAR100, and ImageNet suggest the baseline method only yields trivial predictions including full label set, while our methods could boost the efficiency by up to 4.36times, 5.46times, and 16.9times respectively and provide practical robustness guarantee. Our codes are available at https://github.com/Trustworthy-ML-Lab/Provably-Robust-Conformal-Prediction.

Despite the remarkable progress in the development of predictive models for healthcare, applying these algorithms on a large scale has been challenging. Algorithms trained on a particular task, based on specific data formats available in a set of medical records, tend to not generalize well to other tasks or databases in which the data fields may differ. To address this challenge, we propose General Healthcare Predictive Framework (GenHPF), which is applicable to any EHR with minimal preprocessing for multiple prediction tasks. GenHPF resolves heterogeneity in medical codes and schemas by converting EHRs into a hierarchical textual representation while incorporating as many features as possible. To evaluate the efficacy of GenHPF, we conduct multi-task learning experiments with single-source and multi-source settings, on three publicly available EHR datasets with different schemas for 12 clinically meaningful prediction tasks. Our framework significantly outperforms baseline models that utilize domain knowledge in multi-source learning, improving average AUROC by 1.2%P in pooled learning and 2.6%P in transfer learning while also showing comparable results when trained on a single EHR dataset. Furthermore, we demonstrate that self-supervised pretraining using multi-source datasets is effective when combined with GenHPF, resulting in a 0.6%P AUROC improvement compared to models without pretraining. By eliminating the need for preprocessing and feature engineering, we believe that this work offers a solid framework for multi-task and multi-source learning that can be leveraged to speed up the scaling and usage of predictive algorithms in healthcare.

We introduce marginalization models (MaMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling with tractable likelihoods by explicitly modeling all induced marginal distributions. Marginalization models enable fast evaluation of arbitrary marginal probabilities with a single forward pass of the neural network, which overcomes a major limitation of methods with exact marginal inference, such as autoregressive models (ARMs). We propose scalable methods for learning the marginals, grounded in the concept of "marginalization self-consistency". Unlike previous methods, MaMs support scalable training of any-order generative models for high-dimensional problems under the setting of energy-based training, where the goal is to match the learned distribution to a given desired probability (specified by an unnormalized (log) probability function such as energy function or reward function). We demonstrate the effectiveness of the proposed model on a variety of discrete data distributions, including binary images, language, physical systems, and molecules, for maximum likelihood and energy-based training settings. MaMs achieve orders of magnitude speedup in evaluating the marginal probabilities on both settings. For energy-based training tasks, MaMs enable any-order generative modeling of high-dimensional problems beyond the capability of previous methods. Code is at https://github.com/PrincetonLIPS/MaM.

Current approaches to chemical map generation from hyperspectral images are based on models such as partial least squares (PLS) regression, generating pixel-wise predictions that do not consider spatial context and suffer from a high degree of noise. This study proposes an end-to-end deep learning approach using a modified version of U-Net and a custom loss function to directly obtain chemical maps from hyperspectral images, skipping all intermediate steps required for traditional pixel-wise analysis. We compare the U-Net with the traditional PLS regression on a real dataset of pork belly samples with associated mean fat reference values. The U-Net obtains a test set root mean squared error of between 9% and 13% lower than that of PLS regression on the task of mean fat prediction. At the same time, U-Net generates fine detail chemical maps where 99.91% of the variance is spatially correlated. Conversely, only 2.53% of the variance in the PLS-generated chemical maps is spatially correlated, indicating that each pixel-wise prediction is largely independent of neighboring pixels. Additionally, while the PLS-generated chemical maps contain predictions far beyond the physically possible range of 0-100%, U-Net learns to stay inside this range. Thus, the findings of this study indicate that U-Net is superior to PLS for chemical map generation.

Weight oscillation is an undesirable side effect of quantization-aware training, in which quantized weights frequently jump between two quantized levels, resulting in training instability and a sub-optimal final model. We discover that the learnable scaling factor, a widely-used de facto setting in quantization aggravates weight oscillation. In this study, we investigate the connection between the learnable scaling factor and quantized weight oscillation and use ViT as a case driver to illustrate the findings and remedies. In addition, we also found that the interdependence between quantized weights in query and key of a self-attention layer makes ViT vulnerable to oscillation. We, therefore, propose three techniques accordingly: statistical weight quantization (rm StatsQ) to improve quantization robustness compared to the prevalent learnable-scale-based method; confidence-guided annealing (rm CGA) that freezes the weights with high confidence and calms the oscillating weights; and query-key reparameterization (rm QKR) to resolve the query-key intertwined oscillation and mitigate the resulting gradient misestimation. Extensive experiments demonstrate that these proposed techniques successfully abate weight oscillation and consistently achieve substantial accuracy improvement on ImageNet. Specifically, our 2-bit DeiT-T/DeiT-S algorithms outperform the previous state-of-the-art by 9.8% and 7.7%, respectively. Code and models are available at: https://github.com/nbasyl/OFQ.

Postprandial hyperglycemia, marked by the blood glucose level exceeding the normal range after meals, is a critical indicator of progression toward type 2 diabetes in prediabetic and healthy individuals. A key metric for understanding blood glucose dynamics after eating is the postprandial area under the curve (PAUC). Predicting PAUC in advance based on a person's diet and activity level and explaining what affects postprandial blood glucose could allow an individual to adjust their lifestyle accordingly to maintain normal glucose levels. In this paper, we propose GlucoLens, an explainable machine learning approach to predict PAUC and hyperglycemia from diet, activity, and recent glucose patterns. We conducted a five-week user study with 10 full-time working individuals to develop and evaluate the computational model. Our machine learning model takes multimodal data including fasting glucose, recent glucose, recent activity, and macronutrient amounts, and provides an interpretable prediction of the postprandial glucose pattern. Our extensive analyses of the collected data revealed that the trained model achieves a normalized root mean squared error (NRMSE) of 0.123. On average, GlucoLense with a Random Forest backbone provides a 16% better result than the baseline models. Additionally, GlucoLens predicts hyperglycemia with an accuracy of 74% and recommends different options to help avoid hyperglycemia through diverse counterfactual explanations. Code available: https://github.com/ab9mamun/GlucoLens.

With the rapid growth in language processing applications, fairness has emerged as an important consideration in data-driven solutions. Although various fairness definitions have been explored in the recent literature, there is lack of consensus on which metrics most accurately reflect the fairness of a system. In this work, we propose a new formulation : ACCUMULATED PREDICTION SENSITIVITY, which measures fairness in machine learning models based on the model's prediction sensitivity to perturbations in input features. The metric attempts to quantify the extent to which a single prediction depends on a protected attribute, where the protected attribute encodes the membership status of an individual in a protected group. We show that the metric can be theoretically linked with a specific notion of group fairness (statistical parity) and individual fairness. It also correlates well with humans' perception of fairness. We conduct experiments on two text classification datasets : JIGSAW TOXICITY, and BIAS IN BIOS, and evaluate the correlations between metrics and manual annotations on whether the model produced a fair outcome. We observe that the proposed fairness metric based on prediction sensitivity is statistically significantly more correlated with human annotation than the existing counterfactual fairness metric.

Fairness in artificial intelligence models has gained significantly more attention in recent years, especially in the area of medicine, as fairness in medical models is critical to people's well-being and lives. High-quality medical fairness datasets are needed to promote fairness learning research. Existing medical fairness datasets are all for classification tasks, and no fairness datasets are available for medical segmentation, while medical segmentation is an equally important clinical task as classifications, which can provide detailed spatial information on organ abnormalities ready to be assessed by clinicians. In this paper, we propose the first fairness dataset for medical segmentation named Harvard-FairSeg with 10,000 subject samples. In addition, we propose a fair error-bound scaling approach to reweight the loss function with the upper error-bound in each identity group, using the segment anything model (SAM). We anticipate that the segmentation performance equity can be improved by explicitly tackling the hard cases with high training errors in each identity group. To facilitate fair comparisons, we utilize a novel equity-scaled segmentation performance metric to compare segmentation metrics in the context of fairness, such as the equity-scaled Dice coefficient. Through comprehensive experiments, we demonstrate that our fair error-bound scaling approach either has superior or comparable fairness performance to the state-of-the-art fairness learning models. The dataset and code are publicly accessible via https://ophai.hms.harvard.edu/datasets/harvard-fairseg10k.

In machine learning (ML), a widespread adage is that the area under the precision-recall curve (AUPRC) is a superior metric for model comparison to the area under the receiver operating characteristic (AUROC) for binary classification tasks with class imbalance. This paper challenges this notion through novel mathematical analysis, illustrating that AUROC and AUPRC can be concisely related in probabilistic terms. We demonstrate that AUPRC, contrary to popular belief, is not superior in cases of class imbalance and might even be a harmful metric, given its inclination to unduly favor model improvements in subpopulations with more frequent positive labels. This bias can inadvertently heighten algorithmic disparities. Prompted by these insights, a thorough review of existing ML literature was conducted, utilizing large language models to analyze over 1.5 million papers from arXiv. Our investigation focused on the prevalence and substantiation of the purported AUPRC superiority. The results expose a significant deficit in empirical backing and a trend of misattributions that have fuelled the widespread acceptance of AUPRC's supposed advantages. Our findings represent a dual contribution: a significant technical advancement in understanding metric behaviors and a stark warning about unchecked assumptions in the ML community. All experiments are accessible at https://github.com/mmcdermott/AUC_is_all_you_need.

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.

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.

Score-based generative models like the diffusion model have been testified to be effective in modeling multi-modal data from image generation to reinforcement learning (RL). However, the inference process of diffusion model can be slow, which hinders its usage in RL with iterative sampling. We propose to apply the consistency model as an efficient yet expressive policy representation, namely consistency policy, with an actor-critic style algorithm for three typical RL settings: offline, offline-to-online and online. For offline RL, we demonstrate the expressiveness of generative models as policies from multi-modal data. For offline-to-online RL, the consistency policy is shown to be more computational efficient than diffusion policy, with a comparable performance. For online RL, the consistency policy demonstrates significant speedup and even higher average performances than the diffusion policy.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Matbench Discovery simulates the deployment of machine learning (ML) energy models in a high-throughput search for stable inorganic crystals. We address the disconnect between (i) thermodynamic stability and formation energy and (ii) in-domain vs out-of-distribution performance. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with further insights into trade-offs between various performance metrics. To answer the question which ML methodology performs best at materials discovery, our initial release explores a variety of models including random forests, graph neural networks (GNN), one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials (UIP). Ranked best-to-worst by their test set F1 score on thermodynamic stability prediction, we find CHGNet > M3GNet > MACE > ALIGNN > MEGNet > CGCNN > CGCNN+P > Wrenformer > BOWSR > Voronoi tessellation fingerprints with random forest. The top 3 models are UIPs, the winning methodology for ML-guided materials discovery, achieving F1 scores of ~0.6 for crystal stability classification and discovery acceleration factors (DAF) of up to 5x on the first 10k most stable predictions compared to dummy selection from our test set. We also highlight a sharp disconnect between commonly used global regression metrics and more task-relevant classification metrics. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV/atom above the convex hull where most materials are. Our results highlight the need to focus on classification metrics that actually correlate with improved stability hit rate.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

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.