The Fisher Paradox: Dissipation Interference in Information-Regularized Gradient Flows (opens in new tab)

arXiv:2603.12285v1 Announce Type: new Abstract: We show that Fisher-regularized Wasserstein gradient flows exhibit a previously unrecognized interference mechanism in their dissipation identity: a cross-dissipation term whose sign becomes positive when the state width falls below a critical scale. In this regime the geometric Fisher channel transiently opposes descent of the baseline free-energy functional, producing what we term the Fisher Paradox. Restricting the flow to the Gaussian manif...