[4L4-GS-1a] Fundamental AI, theory algorithm

2:00 PM - 2:15 PM JST(5:00 AM - 5:15 AM UTC)

[4L4-GS-1a-03] Particle Transport Models on Networks via Generalized Entropy Regularization

〇Shintaro Yoshizawa¹, Shin Suyama¹, Kota Shinjo¹ (1. Toyota Motor Corporation)

Keywords:

Transport model,Generalized entropy,Information geometry

We propose a generalized entropy regularization framework for optimal transport grounded in information geometry. Unlike traditional Tsallis entropy methods, our approach introduces a correction term that geometrically deforms the Riemannian metric on the transport polytope, allowing precise control over sparsity and diffusion in transport plans. We prove existence and uniqueness of solutions and derive explicit optimal plans characterized by asymmetric behaviors depending on the parameter q . Numerical experiments on various network topologies, including lattices and random graphs, show that our model captures phase-transition-like phenomena and bottleneck effects that conventional methods miss. The parameter q acts as a curvature controller of the transport space, providing a novel geometric interpretation distinct from Tsallis non-additivity. This work offers a flexible and geometrically consistent regularization approach for optimal transport on complex networks.