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Formal Verification: Why Has the “Code Checking” Technique from Half a Century Ago Been Revived by AI?

Earlier this year, Google CEO Sundar Pichai revealed at the Google Cloud Annual Conference that approximately 75% of the company’s new code is generated by AI and then reviewed and approved by engineers. Internal data from Anthropic shows that over 80% of its committed code has already been written by Claude. And it’s not just code that’s being produced in bulk. On October 26, the AI mathematics company Axiom Math announced that its team coordinated dozens of AI agents to completely rewrite, in just 24 days, the longest proof in the history of mathematics into formalized code that can be progressively verified by the theorem-proving assistant Lean—amounting to a staggering 43.1 million lines. With output increasing, quality issues have naturally followed. The code review company CodeRabbit analyzed pull requests from 470 open-source projects (pull ...

形式化验证:半个世纪前的“代码验算”技术,为何被AI捧红?
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AI Completes the Largest Mathematical Proof in Human History, Leaving Mathematicians in Tears on the Spot

Reported by New智元: The largest mathematical proof in human history has now been formally verified by computer. The Classification of Finite Simple Groups (CFSG) has just been completely formalized by AI! Over a century and a half, more than a hundred of the world’s top mathematicians painstakingly penned a 15,000-page “mathematical bible,” which was fully checked and validated within just 24 days by a multi-agent system developed by the startup Axiom. Even more astonishing is that the AI constructed...

AI补全人类史上最大数学证明,数学家当场泪崩
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Convex Potential Learning for Optimal Transport Between Medical Images

arXiv:2610.37844v1 Announce Type: new Abstract: Computing optimal transport maps between medical images plays a fundamental role in morphological analysis. However, existing methods are either difficult to scale to large 3D medical images or rely on regularized formulations that provide only approximate transport maps. To improve the accuracy of downstream medical image analysis, we propose a novel approach for estimating optimal transport maps by parameterizing the convex potential function. By construction, the resulting transport map is guaranteed to be curl-free, consistent with Brenier's theorem. We evaluate the proposed method on both 2D and 3D medical imaging datasets. Experimental results demonstrate that our approach achieves lower transport estimation errors and produces higher-q

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A Mathematical Theory of the Jacobian Lens

arXiv:2610.31955v1 Announce Type: new Abstract: Recent work from Anthropic introduced a new interpretability tool, called the Jacobian lens (J-lens, Gurnee et al., 2026). This method identified linear directions in the hidden states of frontier language models that had properties reminiscent of working memory-like representations. However, it is unclear what mechanistic properties of such features make them detectable to the J-lens. To this end, we introduce a mathematical theory of the J-lens, and show that it preferentially identifies coherent features -- directions that act like leading, spatially coherent Lyapunov modes. Small perturbations along these directions amplify across layers, remain roughly constant across token positions, and are consistent across different contexts. While w

新闻源配图 · arXiv cs.LG
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PRISM: Promoting Sampling Diversity of Large Language Models with Implicit Stochastic Modulation

arXiv:2610.32101v1 Announce Type: new Abstract: Large language models (LLMs) exhibit mode collapse, where their output distribution concentrates on familiar semantic modes. When diversity disappears, repeated sampling becomes semantic repetition rather than discovery, making rare but stronger solutions unlikely to surface and leaving self-evolution and continual learning difficult to sustain. Most remedies intervene only at inference time, shaping sam- ples without making diversity a model capability. We propose PRISM, a training-time framework that internalizes diversity within the model. PRISM combines (i) submodular curation that pairs each prompt with diverse-yet-correct multi-teacher solutions, and (ii) stochastic embedding modulation, which turns special-token perturbations into impl

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Putting Transformer Theories to the Test

arXiv:2610.32104v1 Announce Type: new Abstract: Several formal theories have been developed to characterize the capabilities and limitations of the transformer architecture, each employing different abstractions that capture different features of the architecture. Due to the differences in their underlying assumptions and conceptual frameworks, these theories can disagree in their predictions about what tasks transformers find easy or hard. We map out seven theories of transformer capability (Star-free, $\mathsf{AC}^0$, $\mathsf{TC}^0$, C-RASP, MPC, BAPO, and Sensitivity) and translate their results into a common matrix of predictions across a suite of tasks covering different computational structures. We provide new theoretical results to complete this matrix. We then evaluate theoretical

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