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ENS-Data Science colloquium – Michael Chertkov : Samples That Cooperate, Samples That Remember: Two Exactly Solvable Bridge Diffusions
ENS-Data Science colloquium – Michael Chertkov : Samples That Cooperate, Samples That Remember: Two Exactly Solvable Bridge Diffusions
Diffusion-based generative models treat samples as independent and memoryless. I will show that relaxing each assumption leads to rich, exactly solvable physics — with no neural networks anywhere.Giving samples a present — coupling them through their evolving mean field — produces a McKean–Vlasov optimal transport problem whose self-consistent guidance is provably the linear interpolant between endpoint means, for arbitrary distributions and any interaction schedule; applied to building-fleet demand response, this saves 20%+ in actuation energy.Giving samples a past produces a continual-learning agent whose memory is a Bridge Diffusion and whose […]