Effective Hardcore Exclusion Without Exclusion: Two-Species Pair Annihilation Revisited

What the math gives to ML

The paper provides a constructive reaction-diffusion mechanism in which two mutually annihilating species exhibit anomalous density decay controlled by microscopic transport rules rather than by hardcore exclusion. The transferable asset is the combination of pairwise cross-channel annihilation with density-dependent asymmetric transport, whose predicted decay exponent changes from approximately 1/4 for symmetric or three-particle transport to 1/3 when pair-induced asymmetric transport is present. A neural analogue is a two-channel feature-mixing layer in which positive and negative feature populations move along token or spatial coordinates with rates depending on local population density and annihilate when co-located. This gives a falsifiable architectural signature: power-law disappearance of competing feature mass and a transition near exponent 1/3 versus 1/4.