Decentralized learning is highly sensitive to communication topology when data are non‑IID. Adaptive peer‑selection methods can exploit local model information, yet broader peer discovery typically requires a rapidly growing control state, while direct spectral optimization relies on graph‑wide data. We focus on the intermediate setting of bounded local topology search and introduce Local‑First Heuristic Evolution (LFHE), a representation‑driven rewiring framework. LFHE discovers and scores candidates using only ego‑neighborhood and friend‑of‑a‑friend (FoF) information.
The structural score admits an exact interpretation as graph Dirichlet energy: the sum of scores across clients equals twice the representation Dirichlet energy. Under standard linear consensus dynamics this energy governs the instantaneous dissipation of representation disagreement. LFHE combines this state‑dependent structural signal with early exploration and degree control, while algebraic connectivity serves only as an offline graph diagnostic. Because degree is bounded, the FoF candidate set remains local rather than expanding to population‑wide peer tracking.
Experiments on four image, speech, and text benchmarks show that LFHE achieves competitive decentralized learning performance. Matched‑protocol controls identify the structural term as the principal empirical topology‑selection signal; comparison with broader peer discovery reveals a trade‑off between predictive performance and discovery‑state locality. Overall, the results motivate state‑aware bounded local topology search as a viable middle ground between pairwise peer selection and globally informed topology optimization.
Review: LFHE efficiently adapts topology using only two‑hop local information, balancing performance and communication overhead, and offers a fresh direction for decentralized learning under non‑IID conditions.