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This paper presents a case study where a mathematician directed an AI to formalize the mean-field derivation of the Vlasov equation in the Lean proof assistant, framing the process as a strategy game. The formalization was completed in about a month, with the AI executing proofs under human guidance.
This paper develops a mean-field theory of dropout as a perturbation at the edge of chaos in neural networks, deriving scaling laws for correlation decay and establishing distinct universality classes for smooth and ReLU-like activations. It also yields optimal dropout scheduling that reduces test loss with no extra computational cost.
The paper introduces MEMOA, a decentralized strategy for massive online agents that achieves optimality via mean-field Nash equilibria, outperforming greedy baselines while scaling better than centralized approaches.