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大语言模型离“数学证明高手”还有多远？斯坦福、伯克利、MIT 团队提出 IneqMath 评测标准
AI前线· 2025-07-17 04:47
Core Viewpoint - The article discusses the limitations of large language models (LLMs) in mathematical reasoning, particularly in proving inequalities, and introduces a new framework called IneqMath to evaluate their reasoning capabilities [1][4][28]. Group 1: Challenges in Mathematical Reasoning - Current LLMs often provide seemingly correct answers but lack rigorous reasoning processes, raising questions about their true understanding of logical proofs [1][18]. - Formal systems like Lean and Coq can verify proofs but are complex and not easily scalable for intricate problems [1][4]. Group 2: IneqMath Framework - Researchers from Stanford, Berkeley, and MIT propose breaking down inequality proofs into two informal tasks: Bound Estimation and Relation Prediction, creating a bridge between natural language and formal logic [4][8]. - The IneqMath dataset consists of 1,252 training problems with detailed solutions and 200 test problems annotated by International Mathematical Olympiad gold medalists [8]. Group 3: Evaluation of Reasoning - An AI mathematical judging system was developed to assess the logical soundness of each reasoning step, achieving a high F1 score of 0.93, indicating strong agreement with human evaluations [15][17]. - The judging system includes various evaluators to check for logical gaps, numerical approximations, and computation accuracy [16]. Group 4: Model Performance Insights - Despite high answer accuracy, many models fail to provide logically sound reasoning, with Grok 3 mini showing only 6% of answers having a rigorous process [18][20]. - Larger models do not necessarily improve reasoning rigor, and simply increasing the number of tokens does not lead to significant enhancements in logical clarity [20][23]. Group 5: Effective Strategies for Improvement - Two effective methods identified are self-critique, which improves accuracy by about 5%, and theorem hints, which can enhance accuracy by up to 10% for complex problems [25]. - These findings suggest that improving reasoning in models requires more than just computational power; it involves teaching models to self-reflect and utilize tools effectively [25][28].
成功挽救8岁小男孩生命，华人学者一作Nature论文：利用辅酶Q10前体，缓解致命线粒体脑病
生物世界· 2025-07-15 03:31
撰文丨王聪 编辑丨王多鱼 排版丨水成文 一名 8 岁小男孩在短短几个月内病情迅速恶化。2023 年 8 月，他还在跑步、踢足球，而到 9 月，他的双踝就出现了不自主的肌肉收缩，10 月，他已无法跑步 和进行体育运动，而到了 11 月底，他开始频繁摔倒，医生建议他靠轮椅行动。 基因检测确认了这个小男孩的病因：他遗传了来自父母的 HPDL 基因纯合突变，HPDL 蛋白有助于生成一种名为 辅酶 Q10 （CoQ10） 的抗氧化剂，这种抗氧化 剂对于线粒体发挥正常功能至关重要。实际上，他的两个哥哥姐姐因为该疾病在婴儿时期就已离世，而他的严重程度略低，在 8 岁时才突然病情恶化。 该疾病没有可用的治疗药物或方法，幸运的是， 纽约大学的 Michael Pacold 教授 团队此前发现了 一种 辅酶 Q10 前体 分子—— 4-HB ，有望治疗辅酶 Q10 合成缺陷相关线粒体脑病，但这尚未在人体上验证过。在美国 FDA 的特别许可下，研究团队对这名小男孩进行了 实验性治疗。 经过不到一个月的治疗，这个小男孩就可以走上 1 公里的路，现如今，他已经可以徒步 6 公里，还能跑步，甚至还能骑自行车了 ，他的力气正在恢复，精力和 ...
当AI遇上数学：大语言模型如何掀起一场形式化数学的革命？ | Deep Talk
锦秋集· 2025-05-12 09:13
Core Viewpoint - The article discusses the transformative impact of large language models (LLMs) on the field of mathematics, particularly through the integration of formalized mathematics methods, which enhance the accuracy and reliability of theorem proofs [1][4]. Group 1: Challenges and Opportunities - The increasing complexity of modern mathematical theories has surpassed the capacity of traditional peer review and manual verification methods, necessitating a shift towards formalized mathematics [4][6]. - The "hallucination" problem in LLMs, where models generate plausible but incorrect content, poses significant challenges in the highly logical domain of mathematics, highlighting the need for rigorous verification methods [6][7]. Group 2: Formalized Theorem Proving - Formalized theorem proving utilizes a system of axioms and logical reasoning rules to express mathematical statements in a verifiable format, allowing for high certainty in validation results [8][9]. - Successful applications of formalized methods in mathematics and software engineering demonstrate their potential to ensure consistency between implementation and specifications, overcoming the limitations of traditional methods [9]. Group 3: Recent Advances Driven by LLMs - Advanced LLMs like AlphaProof and DeepSeek-Prover V2 have shown remarkable performance in solving competitive-level mathematical problems, indicating significant progress in the field of formalized theorem proving [10]. - Research is evolving from mere proof generation to the accumulation of knowledge and the construction of theoretical frameworks, as seen in projects like LEGO-Prover [10]. Group 4: Transition to Proof Engineering Agents - The transition from static "Theorem Provers" to dynamic "Proof Engineering Agents" is essential for addressing high labor costs and low collaboration efficiency in formalized mathematics [11]. - APE-Bench has been developed to evaluate and promote the performance of language models in long-term dynamic maintenance scenarios, filling a gap in current assessment tools [12][16]. Group 5: Impact and Future Outlook - The integration of LLMs with formalized methods is expected to enhance verification efficiency in mathematics and industrial applications, leading to rapid advancements in mathematical knowledge [17]. - The long-term vision includes the emergence of "Certified AI," which combines formal verification with dynamic learning mechanisms, promising a new paradigm in knowledge production and decision-making [17].
