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

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