Equivalence between algorithmic instability and transition to replica symmetry breaking in perceptron learning systems

TL;DR

This paper demonstrates that the algorithmic instability in binary perceptron learning corresponds exactly to the transition point where replica symmetry breaks, linking learning dynamics with statistical mechanics insights.

Contribution

It establishes a precise equivalence between algorithmic instability and replica symmetry breaking in perceptron models, bridging learning dynamics and statistical physics.

Findings

Instability condition matches replica symmetry breaking point.

Provides a theoretical link between learning dynamics and statistical mechanics.

Insights applicable to complex neural network models.

Abstract

Binary perceptron is a fundamental model of supervised learning for the non-convex optimization, which is a root of the popular deep learning. Binary perceptron is able to achieve a classification of random high-dimensional data by computing the marginal probabilities of binary synapses. The relationship between the algorithmic instability and the equilibrium analysis of the model remains elusive. Here, we establish the relationship by showing that the instability condition around the algorithmic fixed point is identical to the instability for breaking the replica symmetric saddle point solution of the free energy function. Therefore, our analysis would hopefully provide insights towards other learning systems in bridging the gap between non-convex learning dynamics and statistical mechanics properties of more complex neural networks.