This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative inexactness occurs, for example, when compressing the gradient using fewer bits of information, which happens when dealing with large-scale problems on GPUs. Three major families of methods are analyzed: constant step gradient descent, long-step methods, and accelerated methods. The latter two are first shown to be theoretically not robust to inexactness. Then, a semi-heuristic shortening factor is introduced to improve their theoretical guarantees. All methods are subsequently tested on a concrete inexact problem, with two different types of relative inexactness, and it is observed that both accelerated methods are much more robust than expected, and that the shortening factor significantly helps the long-step methods. In the end, all shortened methods appear to be promising, even in this inexact setting.
Large language models (LLMs) excel at capturing global token dependencies via self-attention but face prohibitive compute and memory costs on lengthy inputs. While sub-quadratic methods (e.g., linear attention) can reduce these costs, they often degrade accuracy due to overemphasizing recent tokens. In this work, we first propose dual-state linear attention (DSLA), a novel design that maintains two specialized hidden states-one for preserving historical context and one for tracking recency-thereby mitigating the short-range bias typical of linear-attention architectures. To further balance efficiency and accuracy under dynamic workload conditions, we introduce DSLA-Serve, an online adaptive distillation framework that progressively replaces Transformer layers with DSLA layers at inference time, guided by a sensitivity-based layer ordering. DSLA-Serve uses a chained fine-tuning strategy to ensure that each newly converted DSLA layer remains consistent with previously replaced layers, preserving the overall quality. Extensive evaluations on commonsense reasoning, long-context QA, and text summarization demonstrate that DSLA-Serve yields 2.3x faster inference than Llama2-7B and 3.0x faster than the hybrid Zamba-7B, while retaining comparable performance across downstream tasks. Our ablation studies show that DSLA's dual states capture both global and local dependencies, addressing the historical-token underrepresentation seen in prior linear attentions. Codes are available at https://github.com/utnslab/DSLA-Serve.
Determining accurate numerical solutions of partial differential equations (PDEs) is an important task in many scientific disciplines. However, solvers can be computationally expensive, leading to the development of reduced-order models (ROMs). Recently, Latent Space Dynamics Identification (LaSDI) was proposed as a data-driven, non-intrusive ROM framework. LaSDI compresses the training data using an autoencoder and learns a system of user-chosen ordinary differential equations (ODEs), which govern the latent space dynamics. This allows for rapid predictions by interpolating and evolving the low-dimensional ODEs in the latent space. While LaSDI has produced effective ROMs for numerous problems, the autoencoder can have difficulty accurately reconstructing training data while also satisfying the imposed dynamics in the latent space, particularly in complex or high-frequency regimes. To address this, we propose multi-stage Latent Space Dynamics Identification (mLaSDI). With mLaSDI, several autoencoders are trained sequentially in stages, where each autoencoder learns to correct the error of the previous stages. We find that applying mLaSDI with small autoencoders results in lower prediction and reconstruction errors, while also reducing training time compared to LaSDI.
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs
Training Large Language Models (LLMs) is prohibitively expensive, creating a critical scaling gap where insights from small-scale experiments often fail to transfer to resource-intensive production systems, thereby hindering efficient innovation. To bridge this, we introduce Farseer, a novel and refined scaling law offering enhanced predictive accuracy across scales. By systematically constructing a model loss surface $L(N,D)$, Farseer achieves a significantly better fit to empirical data than prior laws (e.g., Chinchilla's law). Our methodology yields accurate, robust, and highly generalizable predictions, demonstrating excellent extrapolation capabilities, improving upon Chinchilla's law by reducing extrapolation error by 433\%. This allows for the reliable evaluation of competing training strategies across all $(N,D)$ settings, enabling conclusions from small-scale ablation studies to be confidently extrapolated to predict large-scale performance. Furthermore, Farseer provides new insights into optimal compute allocation, better reflecting the nuanced demands of modern LLM training. To validate our approach, we trained an extensive suite of approximately 1,000 LLMs across diverse scales and configurations, consuming roughly 3 million NVIDIA H100 GPU hours. We are comprehensively open-sourcing all models, data, results, and logs at https://github.com/Farseer-Scaling-Law/Farseer to foster further research.
We present a novel approach to neural code generation that incorporates real-time execution signals into the language model generation process. While large language models (LLMs) have demonstrated impressive code generation capabilities, they typically do not utilize execution feedback during inference, a critical signal that human programmers regularly leverage. Our method, Execution-Guided Classifier-Free Guidance (EG-CFG), dynamically incorporates execution signals as the model generates code, providing line-by-line feedback that guides the generation process toward executable solutions. EG-CFG employs a multi-stage process: first, we conduct beam search to sample candidate program completions for each line; second, we extract execution signals by executing these candidates against test cases; and finally, we incorporate these signals into the prompt during generation. By maintaining consistent signals across tokens within the same line and refreshing signals at line boundaries, our approach provides coherent guidance while preserving syntactic structure. Moreover, the method naturally supports native parallelism at the task level in which multiple agents operate in parallel, exploring diverse reasoning paths and collectively generating a broad set of candidate solutions. Our experiments across diverse coding tasks demonstrate that EG-CFG significantly improves code generation performance compared to standard approaches, achieving state-of-the-art results across various levels of complexity, from foundational problems to challenging competitive programming tasks. Our code is available at: https://github.com/boazlavon/eg_cfg
We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500 performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward), 13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting) -- nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning -- thinking in code without actual code execution -- to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.
Training large language models is generally done via optimization methods on clusters containing tens of thousands of accelerators, communicating over a high-bandwidth interconnect. Scaling up these clusters is expensive and can become impractical, imposing limits on the size of models that can be trained. Several recent studies have proposed training methods that are less communication intensive, avoiding the need for a highly connected compute cluster. These state-of-the-art low communication training methods still employ a synchronization step for model parameters, which, when performed over all model replicas, can become costly on a low-bandwidth network. In this work, we propose a novel optimization method, NoLoCo, that does not explicitly synchronize all model parameters during training and, as a result, does not require any collective communication. NoLoCo implicitly synchronizes model weights via a novel variant of the Nesterov momentum optimizer by partially averaging model weights with a randomly selected other one. We provide both a theoretical convergence analysis for our proposed optimizer as well as empirical results from language model training. We benchmark NoLoCo on a wide range of accelerator counts and model sizes, between 125M to 6.8B parameters. Our method requires significantly less communication overhead than fully sharded data parallel training or even widely used low communication training method, DiLoCo. The synchronization step itself is estimated to be one magnitude faster than the all-reduce used in DiLoCo for few hundred accelerators training over the internet. We also do not have any global blocking communication that reduces accelerator idling time. Compared to DiLoCo, we also observe up to $4\%$ faster convergence rate with wide range of model sizes and accelerator counts.
Finite mixtures of classifiers (a.k.a. randomized ensembles) have been proposed as a way to improve robustness against adversarial attacks. However, existing attacks have been shown to not suit this kind of classifier. In this paper, we discuss the problem of attacking a mixture in a principled way and introduce two desirable properties of attacks based on a geometrical analysis of the problem (effectiveness and maximality). We then show that existing attacks do not meet both of these properties. Finally, we introduce a new attack called {\em lattice climber attack} with theoretical guarantees in the binary linear setting, and demonstrate its performance by conducting experiments on synthetic and real datasets.
Despite the many recent advances in reinforcement learning (RL), the question of learning policies that robustly satisfy state constraints under unknown disturbances remains open. In this paper, we offer a new perspective on achieving robust safety by analyzing the interplay between two well-established techniques in model-free RL: entropy regularization, and constraints penalization. We reveal empirically that entropy regularization in constrained RL inherently biases learning toward maximizing the number of future viable actions, thereby promoting constraints satisfaction robust to action noise. Furthermore, we show that by relaxing strict safety constraints through penalties, the constrained RL problem can be approximated arbitrarily closely by an unconstrained one and thus solved using standard model-free RL. This reformulation preserves both safety and optimality while empirically improving resilience to disturbances. Our results indicate that the connection between entropy regularization and robustness is a promising avenue for further empirical and theoretical investigation, as it enables robust safety in RL through simple reward shaping.
Deep Learning Systems (DLSs) are increasingly deployed in real-time applications, including those in resourceconstrained environments such as mobile and IoT devices. To address efficiency challenges, Dynamic Deep Learning Systems (DDLSs) adapt inference computation based on input complexity, reducing overhead. While this dynamic behavior improves efficiency, such behavior introduces new attack surfaces. In particular, efficiency adversarial attacks exploit these dynamic mechanisms to degrade system performance. This paper systematically explores efficiency robustness of DDLSs, presenting the first comprehensive taxonomy of efficiency attacks. We categorize these attacks based on three dynamic behaviors: (i) attacks on dynamic computations per inference, (ii) attacks on dynamic inference iterations, and (iii) attacks on dynamic output production for downstream tasks. Through an in-depth evaluation, we analyze adversarial strategies that target DDLSs efficiency and identify key challenges in securing these systems. In addition, we investigate existing defense mechanisms, demonstrating their limitations against increasingly popular efficiency attacks and the necessity for novel mitigation strategies to secure future adaptive DDLSs.
Understanding and reasoning about dynamics governed by physical laws through visual observation, akin to human capabilities in the real world, poses significant challenges. Currently, object-centric dynamic simulation methods, which emulate human behavior, have achieved notable progress but overlook two critical aspects: 1) the integration of physical knowledge into models. Humans gain physical insights by observing the world and apply this knowledge to accurately reason about various dynamic scenarios; 2) the validation of model adaptability across diverse scenarios. Real-world dynamics, especially those involving fluids and objects, demand models that not only capture object interactions but also simulate fluid flow characteristics. To address these gaps, we introduce SlotPi, a slot-based physics-informed object-centric reasoning model. SlotPi integrates a physical module based on Hamiltonian principles with a spatio-temporal prediction module for dynamic forecasting. Our experiments highlight the model's strengths in tasks such as prediction and Visual Question Answering (VQA) on benchmark and fluid datasets. Furthermore, we have created a real-world dataset encompassing object interactions, fluid dynamics, and fluid-object interactions, on which we validated our model's capabilities. The model's robust performance across all datasets underscores its strong adaptability, laying a foundation for developing more advanced world models.
Large Language Models (LLMs) have shown remarkable capabilities in solving diverse tasks. However, their proficiency in iteratively optimizing complex solutions through learning from previous feedback remains insufficiently explored. To bridge this gap, we present OPT-BENCH, a comprehensive benchmark designed to evaluate LLM agents on large-scale search space optimization problems. OPT-BENCH includes 20 real-world machine learning tasks sourced from Kaggle and 10 classical NP problems, offering a diverse and challenging environment for assessing LLM agents on iterative reasoning and solution refinement. To enable rigorous evaluation, we introduce OPT-Agent, an end-to-end optimization framework that emulates human reasoning when tackling complex problems by generating, validating, and iteratively improving solutions through leveraging historical feedback. Through extensive experiments on 9 state-of-the-art LLMs from 6 model families, we analyze the effects of optimization iterations, temperature settings, and model architectures on solution quality and convergence. Our results demonstrate that incorporating historical context significantly enhances optimization performance across both ML and NP tasks. All datasets, code, and evaluation tools are open-sourced to promote further research in advancing LLM-driven optimization and iterative reasoning. Project page: \href{https://github.com/OliverLeeXZ/OPT-BENCH}{https://github.com/OliverLeeXZ/OPT-BENCH}.
Tabular in-context learning (ICL) has recently achieved state-of-the-art (SOTA) performance on several tabular prediction tasks. Previously restricted to classification problems on small tables, recent advances such as TabPFN and TabICL have extended its use to larger datasets. While being architecturally efficient and well-adapted to tabular data structures, current table-native ICL architectures, being trained exclusively on synthetic data, do not fully leverage the rich semantics and world knowledge contained in real-world tabular data. On another end of this spectrum, tabular ICL models based on pretrained large language models such as TabuLa-8B integrate deep semantic understanding and world knowledge but are only able to make use of a small amount of context due to inherent architectural limitations. With the aim to combine the best of both these worlds, we introduce ConTextTab, integrating semantic understanding and alignment into a table-native ICL framework. By employing specialized embeddings for different data modalities and by training on large-scale real-world tabular data, our model is competitive with SOTA across a broad set of benchmarks while setting a new standard on the semantically rich CARTE benchmark.
Continual learning poses a fundamental challenge for neural systems, which often suffer from catastrophic forgetting when exposed to sequential tasks. Self-Organizing Maps (SOMs), despite their interpretability and efficiency, are not immune to this issue. In this paper, we introduce Saturation Self-Organizing Maps (SatSOM)-an extension of SOMs designed to improve knowledge retention in continual learning scenarios. SatSOM incorporates a novel saturation mechanism that gradually reduces the learning rate and neighborhood radius of neurons as they accumulate information. This effectively freezes well-trained neurons and redirects learning to underutilized areas of the map.
Understanding the plausible upper bounds of extreme weather events is essential for risk assessment in a warming climate. Existing methods, based on large ensembles of physics-based models, are often computationally expensive or lack the fidelity needed to simulate rare, high-impact extremes. Here, we present a novel framework that leverages a differentiable hybrid climate model, NeuralGCM, to optimize initial conditions and generate physically consistent worst-case heatwave trajectories. Applied to the 2021 Pacific Northwest heatwave, our method produces temperature anomalies up to 3.7 $^\circ$C above the most extreme member of a 75-member ensemble. These trajectories feature intensified atmospheric blocking and amplified Rossby wave patterns--hallmarks of severe heat events. Our results demonstrate that differentiable climate models can efficiently explore the upper tails of event likelihoods, providing a powerful new approach for constructing targeted storylines of extreme weather under climate change.
This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the posterior distribution of latent variables given generated samples and uses this to learn the log-partition function, which defines the Fisher metric for exponential families. Theoretical convergence guarantees are provided, and the method is validated on the Ising and TASEP models, outperforming existing baselines in reconstructing thermodynamic quantities. Applied to diffusion models, the method reveals a fractal structure of phase transitions in the latent space, characterized by abrupt changes in the Fisher metric. We demonstrate that while geodesic interpolations are approximately linear within individual phases, this linearity breaks down at phase boundaries, where the diffusion model exhibits a divergent Lipschitz constant with respect to the latent space. These findings provide new insights into the complex structure of diffusion model latent spaces and their connection to phenomena like phase transitions. Our source code is available at https://github.com/alobashev/hessian-geometry-of-diffusion-models.
To advance time series forecasting (TSF), various methods have been proposed to improve prediction accuracy, evolving from statistical techniques to data-driven deep learning architectures. Despite their effectiveness, most existing methods still adhere to a fast thinking paradigm-relying on extracting historical patterns and mapping them to future values as their core modeling philosophy, lacking an explicit thinking process that incorporates intermediate time series reasoning. Meanwhile, emerging slow-thinking LLMs (e.g., OpenAI-o1) have shown remarkable multi-step reasoning capabilities, offering an alternative way to overcome these issues. However, prompt engineering alone presents several limitations - including high computational cost, privacy risks, and limited capacity for in-depth domain-specific time series reasoning. To address these limitations, a more promising approach is to train LLMs to develop slow thinking capabilities and acquire strong time series reasoning skills. For this purpose, we propose Time-R1, a two-stage reinforcement fine-tuning framework designed to enhance multi-step reasoning ability of LLMs for time series forecasting. Specifically, the first stage conducts supervised fine-tuning for warmup adaptation, while the second stage employs reinforcement learning to improve the model's generalization ability. Particularly, we design a fine-grained multi-objective reward specifically for time series forecasting, and then introduce GRIP (group-based relative importance for policy optimization), which leverages non-uniform sampling to further encourage and optimize the model's exploration of effective reasoning paths. Experiments demonstrate that Time-R1 significantly improves forecast performance across diverse datasets.
The design and optimization of Printed Circuit Board (PCB) schematics is crucial for the development of high-quality electronic devices. Thereby, an important task is to optimize drafts by adding components that improve the robustness and reliability of the circuit, e.g., pull-up resistors or decoupling capacitors. Since there is a shortage of skilled engineers and manual optimizations are very time-consuming, these best practices are often neglected. However, this typically leads to higher costs for troubleshooting in later development stages as well as shortened product life cycles, resulting in an increased amount of electronic waste that is difficult to recycle. Here, we present an approach for automating the addition of new components into PCB schematics by representing them as bipartite graphs and utilizing a node pair prediction model based on Graph Neural Networks (GNNs). We apply our approach to three highly relevant PCB design optimization tasks and compare the performance of several popular GNN architectures on real-world datasets labeled by human experts. We show that GNNs can solve these problems with high accuracy and demonstrate that our approach offers the potential to automate PCB design optimizations in a time- and cost-efficient manner.
We introduce Equivariant Neural Diffusion (END), a novel diffusion model for molecule generation in 3D that is equivariant to Euclidean transformations. Compared to current state-of-the-art equivariant diffusion models, the key innovation in END lies in its learnable forward process for enhanced generative modelling. Rather than pre-specified, the forward process is parameterized through a time- and data-dependent transformation that is equivariant to rigid transformations. Through a series of experiments on standard molecule generation benchmarks, we demonstrate the competitive performance of END compared to several strong baselines for both unconditional and conditional generation.