2024 FFT

From Generative AI to Statistical Physics Through Harmonic Analysis

Stephane Mallat (Collège de France)

Abstract: Score based diffusions generate impressive models of images, sounds and complex physical systems. Are they generalising or memorising ? How can deep network estimate high-dimensional scores without curse of dimensionality ? This talk shows that generalisation does occur for deep network estimation of scores, with enough training data. We prove that these deep networks perform a denoising by shrinking image coefficients in a best basis adapted to the image geometry. The ability to avoid the curse of dimensionality seems to rely on multiscale properties revealed by a renormalisation group decomposition coming from statistical physics. Applications to models of turbulences will be introduced and discussed.