ATFA: Topology-aware aggregation with Laplacian-based heat diffusion for federated learning.

Federated Learning (FL) faces significant performance degradation in non-IID scenarios due to divergent optimization directions among local models. Conventional aggregation techniques, which are mostly based on Euclidean averaging, are susceptible to stochastic optimization and frequently fail to capture the intrinsic manifold structure of client updates. To address these limitations, we propose the Adaptive Topology-aware Federated Aggregation (ATFA), which reformulates global aggregation as a topology-aware knowledge fusion process over a dynamically evolving client graph topology. Specifically, ATFA introduces historical trend information to capture the cross-round evolution of inter-client relationships. Based on this, a density-calibrated soft adjacency employs robust dispersion statistics to construct a sparse and adaptive client graph topology. ATFA then performs structured knowledge fusion through a heat diffusion derived from the normalized Laplacian, enabling model information to fuse preferentially among strongly related clients. Extensive experiments on both standard benchmarks and three medical imaging benchmark datasets demonstrate that ATFA achieves competitive overall performance and notable improvements under various heterogeneity settings. Further experimental analyses confirm the contributions of the proposed mechanisms can improve aggregation stability and robustness.