arXiv cs.AI· Yoshua Bengio, Esmeralda S. Whitammer·· 9 天前AI 评分26
面向 AI 数学家的机器学习与信息论概念
Machine learning and information theory concepts towards an AI Mathematician
AI 导读
一篇发表于 Bulletin of the AMS 的论文从信息论视角探讨如何构建 AI 数学家，认为当前深度学习擅长系统 1 能力（直觉与习惯行为），但在系统 2 能力（推理与稳健的不确定性估计）上仍有欠缺。其核心假设是：理想定理集合应能以较短描述长度概括所有可证命题，同时与大量可证命题的推导步数距离较近。研究重点不在证明给定定理，而在发现新的有趣猜想。
正文 · 原文
Abstract:The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities -- which correspond to our intuition and habitual behaviors -- but still lacks something important regarding system 2 abilities -- which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.
| Comments: | Bulletin of the AMS, 2024 |
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2403.04571 [cs.AI] |
| (or arXiv:2403.04571v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2403.04571 arXiv-issued DOI via DataCite |
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| Related DOI: | https://doi.org/10.1090/bull/1839
DOI(s) linking to related resources |
Submission history
From: Esmeralda Whitammer [view email]
[v1]
Thu, 7 Mar 2024 15:12:06 UTC (33 KB)
[v2]
Thu, 8 Oct 2026 13:58:38 UTC (29 KB)
来源：arXiv cs.AI · arxiv.org