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均为 10 年以上未解难题：OpenAI 公布在数学与理论计算机科学领域的十项进展，Token 成本约 2000 美元
OpenAI下一代模型Astra攻克十余个十年难题，数学推理能力迎来质变，Token成本仅2000美元
IT之家 8 月 1 日消息，OpenAI 官方今日公布了在数学与理论计算机科学领域的十项进展，这些问题此前一直悬而未决，其核心研究在至少十年（多数情况下甚至更久）的时间里未曾取得任何实质性进展。 据悉，这些成果由 OpenAI 的下一代核心模型 Astra 的内部版本计算得出。若按 Sol API…
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Algebraic anti-unification
深度探讨代数反统一理论，助你理解程序综合与推理中的核心数学结构
arXiv:2407.15510v2 Announce Type: replace Abstract: Abstraction is key to human and artificial intelligence as it allows one to identify common struct…
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Towards Optimal Robustness in Learning-Augmented Paging
探索学习增强分页算法如何实现最优鲁棒性，理论突破值得关注
arXiv:2606.01342v1 Announce Type: cross Abstract: Learning-augmented paging has been extensively studied in recent years. A key advantage over naive M…
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Improved Distribution Estimation in $\ell_\infty$
无穷范数下分布估计新突破，理论保证更优，信息论与统计学习交汇。
arXiv:2605.30509v1 Announce Type: cross Abstract: We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$…
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Envy-Free Allocation of Indivisible Goods via Noisy Queries
噪声查询下公平分配不可分割物品的算法上下界，为真实场景中的公平性保障提供理论支撑。
arXiv:2602.06361v2 Announce Type: replace-cross Abstract: We introduce a problem of fairly allocating indivisible goods (items) in which the agents' v…
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Domain size asymptotics for Markov logic networks
概率图模型在无限域上的渐近行为，严格的数学分析揭示分布演化规律。
arXiv:2509.04192v2 Announce Type: replace Abstract: A Markov logic network (MLN) $\mathbb{M}$ determines a probability distribution $\mathbb{P}_n^\mat…
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LLMs versus the Halting Problem: Characterizing Program Termination Reasoning
用停机问题检验LLM的极限：这篇论文通过理论分析和实验对比，揭示了大语言模型在程序终止性推理上的能力与局限
arXiv:2601.18987v5 Announce Type: replace-cross Abstract: Determining whether a program terminates is a central problem in computer science. Turing's …
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Entropy Equivalence Testing
访问arXiv论文页面，快速获取熵等价检验最新研究成果，免费开放获取
arXiv:2605.23225v1 Announce Type: cross Abstract: We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a rela…
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Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs
结合Lean与理论计算机科学，可规模生成形式-非形式配对的定理证明挑战，助力AI数学推理研究。
arXiv:2508.15878v2 Announce Type: replace-cross Abstract: Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoni…
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An Approximation Algorithm for Graph Label Selection
被ICML 2026收录的图标签选择近似算法，9页7图含理论分析与证明。
arXiv:2605.18623v1 Announce Type: cross Abstract: In the graph label selection problem, one is given an $n$-vertex graph and a budget $k$, and seeks t…
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Learning How to Cube
arXiv最新预印本，系统探讨如何通过机器学习方法实现立方操作，理论严谨，适合算法研究者深读。
arXiv:2605.16632v1 Announce Type: new Abstract: Despite the effectiveness of Cube-and-Conquer (C&C) for solving challenging Boolean Satisfiability…
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Prediction-Intervention Games and Invariant Sets
探讨预测与干预博弈中不变集的数学结构，为理解智能体交互提供理论框架。
arXiv:2605.16828v1 Announce Type: cross Abstract: We consider the following two-player game: using observational data, the leader chooses a prediction…