Relevance Propagation as Entropic Optimal Transport on Filippov Neural Networks: Sinkhorn Propagation and Region Relevance in Image Classifiers

arXiv:2611.05594v1 Announce Type: new Abstract: Relevance propagation, which redistributes a network's prediction backward through the layers, is usually treated as a heuristic. We show that it is the solution of a single variational problem: Layer-wise Relevance Propagation (LRP) is the divergence-free flow on the active computational graph of zero relative entropy to the backward transition law of the forward activation flow; for a non-negative reference, this is a relative entropy between Markov measures on backward paths. The rules LRP$_0$, LRP$_{z^+}$ and LRP$_{\alpha,\beta}$ follow from