Instantaneous shrinking of supports for stochastic PDEs

What the math gives to ML

The paper identifies a sparsification mechanism in which sublinear multiplicative noise that vanishes at zero can create compact support instantly, despite diffusion and initially noncompact positive data. The transferable asset is an absorbing-boundary dynamic: near zero, the ratio of noise amplitude to signal amplitude diverges, potentially producing exact zeros rather than merely small values. A practical neural analogue is a nonnegative spatial, graph, or token activation field evolved by short stochastic diffusion steps, then used as a sparse representation or routing mask. The key experiment should compare it against dropout, deterministic diffusion, hard-concrete gates, and L1 sparsity at matched accuracy.