STABILITY OF THE REPLICA-SYMMETRICAL SOLUTION FOR A PERCEPTRON LEARNING FROM EXAMPLES

Abstract

We study the stability of the replica-symmetric solution for a perceptron learning from examples. By examining the replicon mode, we find the Almeida-Thouless (AT) line signaling a spin-glass phase transition. We find an interesting phase diagram where the AT line crosses the line of zero entropy. Entropy is still negative in a low-temperature region above the AT line. The possibility of a discontinuous phase transition to the replica-symmetry-breaking phase is also discussed.