Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 45: Focus Session: Physics of AI – Part I (joint session SOE/DY)
DY 45.3: Vortrag
Donnerstag, 12. März 2026, 10:15–10:30, GÖR/0226
Fundamental operating regimes, hyper-parameter fine-tuning and glassiness: towards an interpretable replica-theory for trained restricted Boltzmann machines — •Alberto Fachechi1, Elena Agliari1, Miriam Aquaro1, Anthony Coolen2, and Menno Mulder2 — 1Department of Mathematics, Sapienza University of Roma, P. le A. Moro 5, 00185 Roma, Italy — 2Theoretical Biophysics, DCN Donders Institute, Faculty of Science, Radboud University, 6525 AJ Nijmegen, The Netherlands
Since the seminal work by Amit, Gutfreund and Sompolinsky, statistical mechanics of spin-glasses with structural disorder has acquired a crucial role in theoretical investigations of artificial neural networks, as it enables the representation of their generalization and information processing capabilities as phases within the space of parameters. We study the relaxation towards equilibrium of the training procedure of restricted Boltzmann machines with a binary visible layer and a Gaussian hidden layer with an unlabelled dataset consisting of noisy realizations of a single ground pattern. We develop a statistical mechanics framework to describe the network generative capabilities by exploiting replica theory. We outline the effective control parameters (e.g., the relative number of weights to be trained, the regularization parameter), whose tuning can yield qualitatively different operative regimes. We also provide analytical and numerical evidence for the existence of a sub-region in the space of the hyperparameters where replica-symmetry breaking occurs.
Keywords: Neural networks; Spin glasses; Generative models