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 $R_g=I(Z; T)$. 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.

Mixture-of-Experts under Finite-Rate Gating: Communication--Generalization Trade-offs

Mixture-of-Experts (MoE) architectures decompose prediction tasks into specialized expert sub-networks selected by a gating mechanism. This letter adopts a communication-theoretic view of MoE gating, modeling the gate as a stochastic channel operating under a finite information rate. Within an information-theoretic learning framework, we specialize a mutual-information generalization bound and develop a rate-distortion characterization $D(R_g)$ of finite-rate gating, where $R_g:=I(X; T)$, yielding (under a standard empirical rate-distortion optimality condition) $\mathbb{E}[R(W)] \le D(R_g)+δ_m+\sqrt{(2/m)\, I(S; W)}$. The analysis yields capacity-aware limits for communication-constrained MoE systems, and numerical simulations on synthetic multi-expert models empirically confirm the predicted trade-offs between gating rate, expressivity, and generalization.