Consider the discrete cube {−1,1}N and a random collection of half spaces which includes each space H(x):={y∈{−1,1}N:x·y≥κ N} for x∈{−1,1}N independently with probability p. Is intersection these empty? This is called Ising perceptron model under Bernoulli disorder. We prove that this event has sharp threshold, is, empty increases quickly from ϵ to 1−ϵ when p only by factor 1+o(1) as N→∞.

This paper presents an extension of the Self Organizing Map model called Associative SOM that is able to process different types of input data in separated data-paths. The ASOM model can easily deal with situations of incomplete data-patterns and incorporate class labels for supervisory purposes. The ASOM is successfully compared with Multilayer Perceptrons in the incremental classification of ...

The Langevin updating rule, in which noise is added to the weights during learning, is presented and shown to improve learning on problems with initially ill-conditioned Hessians. This is particularly important for multilayer perceptrons with many hidden layers, that often have ill-conditioned Hessians. In addition, Manhattan updating is shown to have a similar eeect.