It has been recently observed in much of the literature that neural networks exhibit a bottleneck rank property: for larger depths, the activation and weights of neural networks trained with gradient-based methods tend to be of approximately low rank. In fact, the rank of the activations of each layer converges to a fixed value referred to as the "bottleneck rank", which is the minimum rank required to represent the training data. This perspective is in line with the observation that regularizing linear networks (without activations) with weight decay is equivalent to minimizing the Schatten p quasi norm of the neural network. In this paper we investigate the implications of this phenomenon for generalization. More specifically, we prove generalization bounds for neural networks which exploit the approximate low rank structure of the weight matrices if present. The final results rely on the Schatten p quasi norms of the weight matrices: for small p, the bounds exhibit a sample complexity rOpWrL2q where W and L are the width and depth of the neural network respectively and where r is the rank of the weight matrices. As p increases, the bound behaves more like a norm-based bound instead.

We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data distribution) to justify causal claims. A recent line of work on counterfactual inference shows promising results but lacks identification, undermining the causal validity of its estimates. To address this, we establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings under standard criteria. We characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map with tools from dynamic optimal transport, ensuring consistent inference. Building on this, we validate the theory in controlled scenarios with counterfactual ground-truth and demonstrate improvements in axiomatic counterfactual soundness on real images.

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-CFGemploys 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 and data science tasks.

A full understanding of the behavior of a large language model (LLM) requires our grasp of its input token space. If this space differs from our assumptions, our comprehension of and conclusions about the LLM will likely be flawed.

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an error. Here, we address this limitation by introducing the remasking diffusion model (ReMDM) sampler, a method that can be applied to pretrained masked diffusion models in a principled way and that is derived from a discrete diffusion model with a custom remasking backward process. Most interestingly, ReMDM endows discrete diffusion with a form of inferencetime compute scaling. By increasing the number of sampling steps, ReMDM generates natural language outputs that approach the quality of autoregressive models, whereas when the computation budget is limited, ReMDM better maintains quality. ReMDM also improves sample quality of masked diffusion models for discretized images, and in scientific domains such as molecule design, ReMDM facilitates diffusion guidance and pushes the Pareto frontier of controllability relative to classical masking and uniform noise diffusion. We provide the code along with a blog post on the project page: https://remdm.github.io

This paper proves a new fingerprinting method to embed the ownership information into a deep neural network (DNN) with theoretically guaranteed robustness to finetuning. Specifically, we prove that when the input feature of a convolutional layer only contains low-frequency components, specific frequency components of the convolutional filter will not be changed by gradient descent during the fine-tuning process, where we propose a revised Fourier transform to extract frequency components from the convolutional filter. Additionally, we also prove that these frequency components are equivariant to weight scaling and weight permutations.

The issue-resolving task, where a model generates patches to fix real-world bugs, has emerged as a key benchmark for evaluating the capabilities of large language models (LLMs). While SWE-bench has become the dominant benchmark in this domain, it suffers from several limitations: it has not been updated since its release, is restricted to only 12 repositories, and relies heavily on manual effort for constructing test instances and setting up executable environments, significantly limiting its scalability. We present SWE-bench-Live3, a live-updatable benchmark designed to address these limitations. SWE-bench-Live currently includes 1,890 tasks derived from real GitHub issues created since 2024, spanning 223 repositories. Each task is accompanied by a dedicated Docker image to ensure reproducible execution. Additionally, we introduce an automated curation pipeline that streamlines the entire process from instance creation to environment setup, removing manual bottlenecks and enabling scalability and continuous updates. We evaluate a range of state-of-the-art models and agent frameworks on SWE-bench-Live, offering detailed empirical insights into their real-world bug-fixing capabilities. By providing a fresh, diverse, and executable benchmark grounded in live repository activity, SWE-bench-Live supports reliable, large-scale assessment of code LLMs and code agents in realistic development settings.

Computing partial differential equation (PDE) operators via nested backpropagation is expensive, yet popular, and severely restricts their utility for scientific machine learning. Recent advances, like the forward Laplacian and randomizing Taylor mode automatic differentiation (AD), propose forward schemes to address this. We introduce an optimization technique for Taylor mode that "collapses" derivatives by rewriting the computational graph, and demonstrate how to apply it to general linear PDE operators, and randomized Taylor mode. The modifications simply require propagating a sum up the computational graph, which could--or should-- be done by a machine learning compiler, without exposing complexity to users. We implement our collapsing procedure and evaluate it on popular PDE operators, confirming it accelerates Taylor mode and outperforms nested backpropagation.

The scaling law for large language models (LLMs) depicts that the path towards machine intelligence necessitates training at large scale. Thus, companies continuously build large-scale GPU clusters, and launch training jobs that span over thousands of computing nodes. However, LLM pre-training presents unique challenges due to its complex communication patterns, where GPUs exchange data in sparse yet high-volume bursts within specific groups. Inefficient resource scheduling exacerbates bandwidth contention, leading to suboptimal training performance. This paper presents Arnold, a scheduling system summarizing our experience to effectively align LLM communication patterns with data center topology at scale. An in-depth characteristic study is performed to identify the impact of physical network topology to LLM pre-training jobs. Based on the insights, we develop a scheduling algorithm to effectively align communication patterns with the physical network topology in modern data centers. Through simulation experiments, we show the effectiveness of our algorithm in reducing the maximum spread of communication groups by up to 1.67x. In production training, our scheduling system improves the end-to-end performance by 10.6% when training with more than 9600 GPUs, a significant improvement for our training pipeline.

Despite their superior performance on a wide range of domains, large language models (LLMs) remain vulnerable to misuse for generating harmful content, a risk that has been further amplified by various jailbreak attacks. Existing jailbreak attacks mainly follow sequential logic, where LLMs understand and answer each given task one by one. However, concurrency, a natural extension of the sequential scenario, has been largely overlooked. In this work, we first propose a wordlevel method to enable task concurrency in LLMs, where adjacent words encode divergent intents. Although LLMs maintain strong utility in answering concurrent tasks, which is demonstrated by our evaluations on mathematical and general question-answering benchmarks, we notably observe that combining a harmful task with a benign one significantly reduces the probability of it being filtered by the guardrail, showing the potential risks associated with concurrency in LLMs. Based on these findings, we introduce JAIL-CON, an iterative attack framework that JAILbreaks LLMs via task CONcurrency. Experiments on widely-used LLMs demonstrate the strong jailbreak capabilities of JAIL-CON compared to existing attacks. Furthermore, when the guardrail is applied as a defense, compared to the sequential answers generated by previous attacks, the concurrent answers in our JAIL-CONexhibit greater stealthiness and are less detectable by the guardrail, highlighting the unique feature of task concurrency in jailbreaking LLMs.1 Disclaimer: This paper contains unsafe information.