Technology Category
Machine Learning: Learning with ManifoldsGame Theory and Economic Paradigms: Imperfect InformationConstraint Satisfaction and Optimization: Distributed CSP/Optimization
The Fisher Paradox: Dissipation Interference in Information-Regularized Gradient Flows
🤖 AI Summary
This work investigates Wasserstein gradient flows regularized by Fisher information, uncovering a cross-dissipation term within the dissipation structure whose sign flips when the state width falls below a critical scale, thereby impeding the decay of the free energy functional—an effect termed the “Fisher paradox.” By reducing the dynamics to a Gaussian manifold, the authors derive a variance potential incorporating a logarithmic centrifugal potential, which analytically delineates three dynamical regimes separated by two critical scales. The theoretical predictions exhibit excellent agreement with numerical simulations on a 512-point grid (mean relative error < 5.21×10⁻⁴) and demonstrate universality across bimodal and Laplacian initial conditions, establishing a quantitative link between dissipation delay and the initial information distance.
Technology Category
Application Category
📝 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 manifold yields an exact Riccati-type variance equation with a closed-form trajectory, exposing three dynamical regimes separated by two critical scales: sigma = 1 (cross-dissipation sign flip) and sigma = sqrt(epsilon) (Fisher takeover). The variance potential V(u) = u^2 - 2u - epsilon ln(u) contains a logarithmic centrifugal barrier that shifts the equilibrium attractor by Delta sigma approx epsilon/4. The interference persists for a duration t_cross ~ D_KL, linking the dissipation delay directly to the initial information distance. Finite-difference simulations on a 512-point grid confirm all analytical predictions to within 5.21 x 10^-4 mean relative error. Numerical experiments with bimodal and Laplace initial conditions confirm the effect persists beyond Gaussian closure, with direct implications for information-geometric dissipative dynamics.
Problem
Research questions and friction points this paper is trying to address.
Fisher regularization
Wasserstein gradient flow
dissipation interference
Fisher Paradox
information geometry
Innovation
Methods, ideas, or system contributions that make the work stand out.
Fisher regularization
Wasserstein gradient flow
dissipation interference
Riccati variance dynamics
information geometry
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