Equivalence between algorithmic instability and transition to replica symmetry breaking in perceptron learning systems
This work provides insights into bridging non-convex learning dynamics with statistical mechanics for more complex neural networks, though it is incremental as it builds on existing fundamental models.
The study tackled the relationship between algorithmic instability and replica symmetry breaking in binary perceptron learning systems, showing that the instability condition at the algorithmic fixed point matches the instability for breaking the replica symmetric solution in free energy analysis.
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.