# Vector-Valued Gossip over w-Holonomic Networks

arXiv: https://arxiv.org/abs/2311.04455 · HTML: https://mlsanity.com/paper/2311.04455/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Privacy Preserving Gossip Learning](https://mlsanity.com/paper/2609.14778/) (2026)

## Abstract (arXiv)

We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key contribution is providing conditions for the convergence of this non-homogeneous Markov process as well as the characterization of its limit set. To this end, we introduce the notion of "w-holonomy" of a set of stochastic matrices, which enables the characterization of sequences of gossiping pairs resulting in reaching a desired consensus in a decentralized manner. Stated otherwise, our result characterizes the limiting behavior of infinite products of (non-commuting, possibly with absorbing states) stochastic matrices.