NOTE THE NONSTANDARD DAY AND TIME

Nike Sun, MIT

Abstract: The perceptron is a toy model of a single-layer neural network that "stores" a collection of given patterns. We consider the model on the N-dimensional discrete cube with M=N*alpha patterns, with a general activation function U that is bounded above. For U bounded away from zero, or U a one-sided threshold function, it was shown by Talagrand (2000, 2011) that for small alpha, the free energy of the model converges in the large-N limit to the replica symmetric formula conjectured in the physics literature (Krauth and Mezard, 1989). We give a new proof of this result, which covers the more general class of all functions U that are bounded above and satisfy a certain variance bound.
Based on joint works with Jian Ding, Erwin Bolthausen, Shuta Nakajima, and Changji Xu.

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