The Role of Odd Diffusivity in Multipoint Statistics of State-Dependent Observables

What the math gives to ML

The paper identifies a sharp gauge-like redundancy: the antisymmetric part of a diffusion tensor generates a transverse probability-current representation but contributes zero to arbitrary multipoint statistics of state-dependent observables. The transferable asset is a principled separation between antisymmetric mobility, which changes the drift and can accelerate nonreversible relaxation, and antisymmetric diffusivity, which can be omitted without changing scalar state-observable statistics. In neural-network optimization, this suggests retaining a deliberately nonreversible antisymmetric drift component while using only symmetric positive-semidefinite noise or preconditioning, avoiding computation spent on an observationally null diffusion component.