Jun 11, 2026 · cond-mat.dis-nnJ/K move · Enter open · S save
Giovanni Catania, Aurélien Decelle, Gianluca Manzan, Beatriz Seoane+1
Institute for Cross-disciplinary Physics and Complex Systems IFISC (CSIC-UIB), Campus Universitat Illes Balears, 07122 Palma de Mallorca, Spain. · Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, Calle de José Gutiérrez Abascal 2, Madrid 28006, Spain. · GISC - Grupo Interdisciplinar de Sistemas Complejos 28040 Madrid, Spain. · Inria Saclay - Tau team, Bât 660 Université Paris-Saclay, Orsay Cedex 91405 · LISN, Tau team, Bât 660 Université Paris-Saclay, Orsay Cedex 91405
We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larger overlap with the ground-truth signal. We derive the optimal Bayesian conditions for teacher recovery as functions of the sample complexity, noise level, and interaction strength, and validate these predictions through numerical simulations. The resulting dynamics can be mapped onto equilibrium sampling in a Restricted Boltzmann Machine with a structured hidden layer, providing a principled theoretical understanding of how interactions improve distributed generative modeling.