Deep Manifold
Through the lens of manifold covers, we open a mathematical window into neural networks. At its core lies something unexpectedly simple: inequality, integration, and differentiation.
| Platform |  | Pricing | Only free issues | Publishes | Daily |
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| Issues | 187 | Founded | 2 years ago | Last Issue | 6 days ago |
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不动点理论简史
English Edition: A Brief History of Fixed-Point Theory
本文简要回顾不动点理论的发展历史，从其早期数学基础，到不动点类理论与数值计算的发展，为更好地理解深度流形提出的 神经不动点场 提供历史背景与数学脉络。
不动点理论是现代数学的一项基础性发展，连接着微积分、拓扑学、非线性分析与数值计算。其历史从早期对解的存在性与收敛性的研究，逐步深入到不动点类的拓扑分类。本文简要回顾这一发展历程中的重要数学贡献，特别是 Nielse...
A Brief History of Fixed-Point Theory
English Edition: 不动点理论简史
This article provides a brief historical overview of fixed-point theory, from its early mathematical foundations to the development of fixed-point classes and numerical computation. It offers historical and mathema...
前沿大语言模型的两个数学盲区：我的亲身经历
English Edition: Two Mathematical Blind Spots of Frontier LLMs: My Personal Experience
英语不是我的母语，而且我有阅读障碍（Dyslexia）。无论是用英语，还是用我的母语中文，写作对我来说始终是一件颇具挑战性的事情。因此，我经常借助大语言模型（LLM）来帮助起草和润色文章。
在本文中，我想分享两段亲身经历，以说明当今前沿大语言模型在数学知识与理解方面存在的一些重要局限。这里所说的大语言...
Two Mathematical Blind Spots of Frontier LLMs: My Personal Experience
Chinese Edition: 前沿大语言模型的两个数学盲区：我的亲身经历
English is not my native language, and I have dyslexia. Writing has always been challenging for me, whether in English or Chinese, my native language. As a result, I often turn to large language model...
关于人工智能仿真与 RSI 的数学思考
English Edition: Mathematical Considerations for AI Simulation & RSI
人工智能仿真：2020年提出的一个设想
1989年至1999年，我长期从事非连续系统的数值分析与仿真研究，尤其是涉及复杂接触、分离、滑移和变形的岩体系统。我的大部分工作集中在地震分析领域，包括历史砌体结构在地震作用下的响应，例如建于1827年的意大利都灵莫斯卡桥，以及广泛分布于近东和地中海地区的历史细长砌体塔楼。通过非连续变形分...
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Through the lens of manifold covers, we open a mathematical window into neural networks. At its core lies something unexpectedly simple: inequality, integration, and differentiation.
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