Abstract
The binary perceptron is a fundamental model of supervised learning for nonconvex optimization, which is a root of the popular deep learning. The binary perceptron is able to achieve a classification of random high-dimensional data based on the marginal probabilities of binary synapses. The relationship between the belief propagation instability and the equilibrium analysis of the model remains elusive. Here, we establish the relationship by showing that the instability condition around the belief propagation fixed point is identical to the instability for breaking the replica symmetric saddle-point solution of the free-energy function. Therefore our analysis will hopefully provide insight towards other learning systems in bridging the gap between nonconvex learning dynamics and statistical mechanics properties of more complex neural networks.
- Received 15 December 2021
- Accepted 22 March 2022
DOI:https://doi.org/10.1103/PhysRevResearch.4.023023
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society