Sparse In-Network Learning via Shortest-Path Backpropagation and Finite-Rate Gating

In-network learning (INL) trains distributed neural modules by exchanging latent activations and backpropagated errors over a communication graph. This letter proposes Dijkstra-pruned INL (D-INL), which removes non-tree links by retaining a capacity-aware shortest-path tree rooted at the fusion node. To balance sparsity and predictive information, local routing (or aggregation) is modeled as a finite-rate stochastic gate with rate Rg=I(Z; T). We derive a rate-distortion-generalization bound and validate the method on a reproducible distributed-classification experiment, where D-INL reduces training exchange by 70.4% while preserving accuracy within the standard deviation of dense INL. Adding finite-rate regularization further reduces the estimated latent rate by 45.7% relative to unregularized Dijkstra INL.