Towards Trustworthy AI: Reflections on Learning and Smale's Legacy
summary
Two decades of work trace a throughline from the Smale 18 problem to concrete limits and fixes for modern ML: learnability requires condition number and stability of the data manifold (Partha Niyogi et al.’s topology bounds), adversarial examples and diffusion artifacts expose lack of physical invariances, and empirical results (Frankle & Carbin 2019) show pruning to find subnetworks that match dense nets. Tools used include the BSS real-machine model, stochastic and mirror-descent analyses, ADMM/BCD alternatives, and Hodge/persistent homology for topological learning.
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chapters (10)
- 0:00Introduction
- 4:57Smale’s 18 problems and AI limits
- 9:03Real computation model and condition
- 12:22Stability in modern AI
- 15:42Hallucinations and adversarial examples
- 18:39Online learning and Smale’s math
- 21:18Optimal algorithms and early stopping
- 23:29Non-gradient neural networks
- 25:13Topological learning and Hodge theory
- 26:59Summary and open questions
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