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 | Twice weekly |
|---|---|---|---|---|---|
| Issues | 53 | Founded | 2 years ago | Last Issue | 2 days ago |
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deepmanifold.substack.comLatest Issues
An Expert, They Say
Expert data and expert environments are becoming central topics in AI today. It feels like the right time to share the story of my own “expert” years. About thirty years ago, in the mid-1990s, I was considered a well-known expert in numeric...
What Is Deep Manifold?
Chinses Edition: 什么是深度流形？
Deep Manifold is not a new branch of mathematics. It is a framework that reveals the mathematics of neural networks, including their geometry, equations, training dynamics, and inference computation.
Neural Netwo...
什么是深度流形？
English Edition: What is Deep Manifold ?
深度流形不是一个新的数学分支，而是一个揭示神经网络数学的框架，包括神经网络的几何结构、方程、训练动力学和推理计算。
神经网络几何： 分片堆叠流形将神经网络视为一个由相互连接、逐层堆叠的分片流形构成的可学习数值系统。数学覆盖位于单个权重的位置，激活则形成由数据生成的物理覆盖。
神经网络方程： 在全局层面，学习由不动点残差描述，而拉格朗日形式使得在损失与约束条件下寻找解成为可计算的过程。不动点...
III-Posed and Jagged Intelligence
The more power an AI model gains, the more visible its ill-posed behavior may become. The reason can be traced back to the definition of a “well-posed problem” given by the French mathematician Jacques Hadamard in 1902. A well-posed problem...
Deep Manifold Interpretation
Like many others, I read AI papers on a very frequent basis. In early May, I started the 'Deep Manifold Interpretation' series as a way to examine the breadth and depth of the framework. People often ask me how to start learning about Deep...
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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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