https://preview.redd.it/2hpvc5utczmh1.png?width=1507&format=png&auto=webp&s=6643bc2e95a74550fd15d2da6d1496abc8e22f19 At the same time, call for Reviewers: Mathematics for AI and Machine Learning It includes MathIcon project and Math4AIStudio project. We aim to bring math and arts together. The project site is: https://math4ai.org/ Please contact me if you want to review one of the 4 parts of the book. I will include the reviewer name in the acknowledgement. The 3rd edition has 600 pages (including covers). Change Log: chapter10.md : Added forward reference linking the discrete matrix view of attention to the mean-field interacting particle PDE in Chapter 21. chapter20.md : Added a remark explaining the duality between the optimization time limit (k→∞ k →∞) and the network depth limit (L→∞ L →∞, Neural ODE / optimal control). chapter2 1 ( Beyond Diffusion: Where This PDE Reappears in AI ): Mean-Field Training Dynamics : Modeled two-layer neural network training as a Wasserstein gradient flow over parameter space ρt ρt ; connected to Barron’s approximation theorem (O(1/n) O (1/ n ) dimension-free rate). Attention as Transport : Framed continuous-depth self-attention as a non-gradient transport conservation law ∂sμs+∇⋅(μsA(μs))=0∂ s μs +∇⋅( μs A( μs ))=0, explaining token clustering / anti-diffusion. Depth as Optimal Control : Formulated Neural ODEs / deep ResNet training as steering states x0→x1≈y x 0→ x 1≈ y via parameter controls (Us,Vs,bs)( Us , Vs , bs ). Next-Token Prediction as ERM : Framed autoregressive LLM training as standard self-supervised Empirical Risk Minimization under the matrix calculus / optimization umbrella. The Common Thread : Synthesized the microscopic-particle ↔↔ macroscopic-density duality unifying generative diffusion, network optimization, and Transformer depth representations. submitted by /u/wufuheng
Originally posted by u/wufuheng on r/ArtificialInteligence
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