# Population Scaling or Data Dilution? Dynamics of Local Topology Evolution in Decentralized Learning

arXiv: https://arxiv.org/abs/2610.05476 · HTML: https://mlsanity.com/paper/2610.05476/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 4 Oct 2026.

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

- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization](https://mlsanity.com/paper/1709.08765/) (2017)
- [Decentralized federated learning of deep neural networks on non-iid data](https://mlsanity.com/paper/2107.08517/) (2021)
- [Dynamic Topology Optimization for Non-IID Data in Decentralized Learning](https://mlsanity.com/paper/2602.03383/) (2026)

## Abstract (arXiv)

Scaling decentralized learning changes not only the number of clients N, but also the dynamics of information propagation and consensus. We argue that the effect of increasing N cannot be understood in isolation, because data allocation, topology-dependent mixing, and communication capacity may change simultaneously. We study these coupled effects on CIFAR-10 with N∈10,50,100,200, comparing a degree-two Ring, a Static Random graph, and Local-First Heuristic Evolution (LFHE), a locally adaptive topology process based on friend-of-friend discovery. The Ring provides an analytically transparent failure mode: its Metropolis spectral gap decays as Theta(N-2), implying progressively slower contraction of model disagreement as the population grows. Experiments show that holding the nominal local dataset size fixed substantially reduces the apparent population penalty observed when a fixed total dataset is divided among more clients. The remaining degradation depends strongly on communication structure: Ring enters a high-disagreement regime, whereas Static Random and LFHE remain close to consensus. Increasing LFHE's degree threshold further improves accuracy and consensus, but at a substantially higher model-transmission cost. These results show that decentralized scaling is governed by coupled learning and communication dynamics, rather than by the number of clients alone.