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

arXiv: https://arxiv.org/abs/2605.23424 · HTML: https://mlsanity.com/paper/2605.23424/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 7 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 5 of 5)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [In-Network Learning: Distributed Training and Inference in Networks](https://mlsanity.com/paper/2107.03433/) (2021)
- [Mixture-of-Experts under Finite-Rate Gating: Communication--Generalization Trade-offs](https://mlsanity.com/paper/2602.15091/) (2026)
- [Expert Routing for Communication-Efficient MoE via Finite Expert Banks](https://mlsanity.com/paper/2605.05278/) (2026)

## Abstract (arXiv)

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.