Parameter-Space Heat Flow, Gaussian Density Ratios, and Sharp Hermite Truncation Rates

What the math gives to ML

The paper identifies Gaussian density ratios with Hermite generating functions and turns variation of the Gaussian mean into an explicit heat flow in parameter space. Its transferable asset is a principled spectral representation of near-Gaussian objects: covariance mismatch controls the geometric decay of total-degree Hermite coefficients, with rate governed by the largest absolute covariance defect. This suggests replacing generic latent-feature truncation or uncertainty compression with an adaptive Hermite bottleneck whose degree is selected from the estimated covariance spectrum. The same construction can also provide a heat-flow consistency regularizer for models whose latent distributions are intended to remain close to Gaussian.