# On graphs with finite-time consensus and their use in gradient tracking

arXiv: https://arxiv.org/abs/2311.01317 · HTML: https://mlsanity.com/paper/2311.01317/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2023.

## Built on by (most cited first, 2 of 2)

- [Exact and Linear Convergence for Federated Learning under Arbitrary Client Participation is Attainable](https://mlsanity.com/paper/2503.20117/) (2025)
- [Beyond Scaffold: A Unified Spatio-Temporal Gradient Tracking Method](https://mlsanity.com/paper/2512.01732/) (2025)

## Abstract (arXiv)

This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in Gradient Tracking. We provide an explicit weight matrix representation of the studied sequences and prove their finite-time consensus property. Moreover, we incorporate the studied finite-time consensus topologies into Gradient Tracking and present a new algorithmic scheme called Gradient Tracking for Finite-Time Consensus Topologies (GT-FT). We analyze the new scheme for nonconvex problems with stochastic gradient estimates. Our analysis shows that the convergence rate of GT-FT does not depend on the heterogeneity of the agents' functions or the connectivity of any individual graph in the topology sequence. Furthermore, owing to the sparsity of the graphs, GT-FT requires lower communication costs than Gradient Tracking using the static counterpart of the topology sequence.