数学为理解与优化神经网络提供关键工具，推动AI与数学双向发展。
The Mathematics of Artificial Intelligence
- 用分析与概率工具建模神经网络架构与优化过程
- 揭示特定任务架构背后的数学原理，助力技术突破
- 适合对AI底层机制感兴趣的数学与交叉领域研究者
本文综述了数学在人工智能（AI）中的核心作用，指出数学不仅为理解与改进AI系统提供了有力工具，也因AI的发展催生了新数学问题。文章聚焦于解析与概率方法在神经网络架构建模及优化理解中的应用，有意略过统计层面的泛化能力问题（尽管其极为重要）。同时，文章探讨了促使AI取得显著进展的若干思想演进，这些进展源于针对特定任务设计的架构，各自映射出不同的数学技术。目标是激励更多数学家关注并参与这一充满活力的领域。
原文摘要 · Abstract (English)
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the development of new mathematics at the intersection of various fields. This article focuses on the application of analytical and probabilistic tools to model neural network architectures and better understand their optimization. Statistical questions (particularly the generalization capacity of these networks) are intentionally set aside, though they are of crucial importance. We also shed light on the evolution of ideas that have enabled significant advances in AI through architectures tailored to specific tasks, each echoing distinct mathematical techniques. The goal is to encourage more mathematicians to take an interest in and contribute to this exciting field.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。