Topic: computational threshold

The talk studies sampling from mean-field spin-glass Gibbs distributions above a stochastic-localization temperature threshold. It establishes total-variation guarantees for denoising diffusion and proves success of simulated annealing through a local-to-global principle. The results extend beyond worst-case uniqueness guarantees and approach the conjectured computational threshold for pure p-spin models up to a constant factor.

Learning to generate new samples from an unknown Ising distribution exhibits a computational threshold determined by the interaction matrix's spectral width. Below the threshold, empirically initialized Glauber dynamics gives an efficient learner; just above it, a constructed family is cryptographically hard even with parameter access. The talk distinguishes sample generation from parameter estimation and studies a resulting memorization–hallucination trade-off.