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

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 in10,50,100,200, 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 Θ(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.