[3H2-OS-9b] OS-9

11:15 AM - 11:30 AM JST(2:15 AM - 2:30 AM UTC)

[3H2-OS-9b-02] Boundary-Identified WFR Gradient Flows for Spiking Neural Inference

〇Akito Okamoto¹, Mahito Sugiyama² (1. Doshisha University, 2. National institute of Informatics)

Keywords:

Computational Neuroscience,Unbalanced Optimal Transport,Information Geometry,Spiking Neural Network,Differential Equation

We propose a unified framework in which spike-and-reset transitions are captured as continuous gradient flows on a measure space. The membrane-potential distribution is represented as a nonnegative measure, and inference is formulated as a Wasserstein–Fisher–Rao (unbalanced optimal transport) gradient flow. By identifying the endpoints of the voltage interval, a ring topology internalizes spike/reset discontinuities. Input currents deform the chemical potential induced by an energy functional; the distribution is transported while a reaction term reweights its mass. Learning is posed as action minimization subject to these inference dynamics. Numerical experiments confirm (i) equivalence between the ring formulation and an interval model with coupled boundaries, (ii) that both transport and reaction are required for spiking dynamics and mass regulation, and (iii) that the density shape ρ(θ) retains task-relevant information beyond total mass. The discrete adjoint gradient exhibits a pre×post×modulator structure, and eligibility traces can be interpreted as Green’s functions of synaptic filters.