# Diffusion of Information on Networked Lattices by Gossip

arXiv: https://arxiv.org/abs/2204.00167 · HTML: https://mlsanity.com/paper/2204.00167/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2022.

## Built on by (most cited first, 4 of 4)

- [Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back](https://mlsanity.com/paper/2303.11323/) (2023)
- [Prospects for inconsistency detection using large language models and sheaves](https://mlsanity.com/paper/2401.16713/) (2024)
- [Tackling Feature and Sample Heterogeneity in Decentralized Multi-Task Learning: A Sheaf-Theoretic Approach](https://mlsanity.com/paper/2502.01145/) (2025)
- [Gaussian Sheaf Neural Networks](https://mlsanity.com/paper/2605.21435/) (2026)

## Abstract (arXiv)

We study time-dependent dynamics on a network of order lattices, where structure-preserving lattice maps are used to fuse lattice-valued data over vertices and edges. The principal contribution is a novel asynchronous Laplacian, generalizing the usual graph Laplacian, adapted to a network of heterogeneous lattices. The resulting gossip algorithm is shown to converge asymptotically to stable "harmonic" distributions of lattice data. This general theorem is applicable to several general problems, including lattice-valued consensus, Kripke semantics, and threat detection, all using asynchronous local update rules.