The success of deep learning models in classification and regression is widely attributed to the low-dimensional structure that real-world data tend to exhibit, despite their high-dimensional representation. This work attempts to provide a mathematical framework for binary classification on low-dimensional data, building on Cover's (1965) function-counting theory. With our framework, we aim to address the question of how the low-dimensional structure of the data affects the classification capabilities of learning models. Cover's theory relies on a general position assumption that blinds it to the underlying data structure. We refine this assumption to account for the low-dimensionality of the data and derive dichotomy counts that reflect the data structure. We further extend Cover's separation capacity and problem of generalization to the low-dimensional setting, enabling the impact of the underlying data structure on both to be analyzed.

Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To counteract the degradation in convergence associated with compressed communication, error feedback schemes--most notably EF and EF21--were introduced. In this work, we provide a tight analysis of both of these methods. Specifically, we find the Lyapunov function that yields the best possible convergence rate for each method--with matching lower bounds.

Developing high-performance software is a complex task that requires specialized expertise. We introduce GSO, a benchmark for evaluating language models' capabilities in developing high-performance software. We develop an automated pipeline that generates and executes performance tests to analyze repository commit histories to identify 102challenging optimization tasks across 10codebases, spanning diverse domains and programming languages. An agent is provided with a codebase and performance test as a precise specification, and tasked to improve the runtime efficiency, which is measured against the expert developer optimization. Our quantitative evaluation reveals that leading SWE-Agents struggle significantly, achieving less than 5% success rate, with limited improvements even with inference-time scaling. Our qualitative analysis identifies key failure modes, including difficulties with low-level languages, practicing lazy optimization strategies, and challenges in accurately localizing bottlenecks. We release the code and artifacts of our benchmark along with agent trajectories to enable future research.

Reinforcement learning with verifiable rewards (RLVR) has shown promise in enhancing the reasoning capabilities of large language models by learning directly from rule-based outcome rewards. Recent RLVR works that operate under the zero setting avoid supervision in labeling the reasoning process, but still depend on manually curated collections of questions and answers for training. The scarcity of high-quality, human-produced examples raises concerns about the long-term scalability of relying on human supervision, a challenge already evident in the domain of language model pretraining. Furthermore, in a hypothetical future where AI surpasses human intelligence, tasks provided by humans may offer limited learning potential for a superintelligent system. To address these concerns, we propose a new RLVR paradigm called Absolute Zero, in which a single model learns to propose tasks that maximize its own learning progress and improves reasoning by solving them, without relying on any external human or distillation data. Under this paradigm, we introduce the Absolute Zero Reasoner (AZR), a system that self-evolves its training curriculum and reasoning ability. AZR uses a code executor to both validate self-proposed code reasoning tasks and verify answers, serving as an unified source of verifiable feedback to guide open-ended yet grounded learning. Despite being trained entirely without external data, AZR achieves overall SOTA performance on coding and mathematical reasoning tasks, outperforming existing zero-setting models that rely on tens of thousands of in-domain human-curated examples. Furthermore, we demonstrate that AZR can be effectively applied across different model scales and is compatible with various model classes.

We introduce a new approach to agent programming, the development of LLMbased agents.

Spreadsheets are widely used for data analysis and reporting, yet their complex structure and formula logic pose significant challenges for AI systems. We introduce Sheetpedia, a large-scale corpus of over 290,000 diverse spreadsheets (from 324,000+ workbooks) compiled from enterprise email archives and online forums. We detail a rigorous collection and preprocessing pipeline (integrating the Enron email spreadsheet archive and the Fuse web corpus, plus a new crawl of Excel forums) to standardize formats, filter languages, and remove duplicates. Sheetpedia provides extensive coverage of real formulas and annotations - addressing a gap left by prior table datasets (e.g.

The rapid development of Multimodal Large Language Models (MLLMs) poses increasing demands on the diversity and complexity of multimodal datasets. Yet manual annotation pipelines can no longer keep pace. Existing augmentation methods often follow fixed rules and lack verifiable control over sample diversity and reasoning complexity. To address this, we introduce Scalable COunterfactual Program Evolution (SCOPE), a framework that uses symbolic Visual Programming to guide program evolution via counterfactual reasoning. SCOPE performs the three steps of counterfactual inference: (1) Abduction, by generating verifiable programs to model reasoning associations; (2) Action, by intervening on program structure along three axes--reasoning path, visual context, and cross-instance composition; and (3) Prediction, by categorizing evolved instances by difficulty, structure, and input multiplicity. Based on this process, we build SCOPE-Train and SCOPE-Test, evolving benchmarks with expert validation. To support training, we propose MAP, a curriculum learning strategy that aligns model capacity with sample difficulty. Experiments show that SCOPEimproves reasoning performance, exposes model blind spots, and enhances visual dialog capabilities.

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The task of issue resolving aims to modify a codebase to generate a patch that addresses a given issue. However, most existing benchmarks focus almost exclusively on Python, making them insufficient for evaluating Large Language Models (LLMs) across different programming languages. To bridge this gap, we introduce a multilingual issue-resolving benchmark, called Multi-SWE-bench, covering 8 widely used programming languages: Python, Java, TypeScript, JavaScript, Go, Rust, C, and C++. In particular, this benchmark includes a total of 2,132 highquality instances, carefully curated by 68 expert annotators, ensuring a reliable and accurate evaluation of LLMs on the issue-resolving task. Based on humanannotated results, the issues are further classified into three difficulty levels. We evaluate a series of state-of-the-art models on Multi-SWE-bench, utilizing both procedural and agent-based frameworks for issue resolving. Experimental results based on Multi-SWE-bench reveal three key findings: (1) Limited generalization across languages: While existing LLMs perform well on Python issues, their ability to generalize across other languages remains limited; (2) Performance aligned with human-annotated difficulty: LLM-based agents' performance closely aligns with human-assigned difficulty, with resolved rates notably decreasing as issue complexity rises; and (3) Performance drop on cross-file issues: The performance of current methods significantly deteriorates when handling cross-file issues. These findings highlight the limitations of current LLMs and underscore the need for more robust models capable of handling a broader range of programming languages and complex issue scenarios.

State-space models (SSMs) are the standard formalism for Bayesian treatment of dynamical systems, with natural applications in statistics, signal processing, and machine learning. Despite their importance in both theory and application, dynamical systems have proven difficult to incorporate in modern probabilistic programming languages (PPLs), making state-of-the-art methods less accessible to practitioners and introducing friction in following the "Bayesian workflow." We introduce dynestyx, a probabilistic programming library with first-class support for SSMs, including state-of-the-art methods in the estimation of both states and parameters. Through a single, unified interface, users may specify arbitrary priors for discrete-time or continuous-time dynamical systems, perform inference over mixed-effect data, and make state and parameter estimates with principled uncertainty quantification.