PARISI PHASE IN A NEURON

Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses, we obtain a variational free energy funct ional for the neuron. The solution is demonstrated at high temperature and large relative number of examples, where several phases are ident ified by thermodynamical stability analysis, two of them exhibiting sp ontaneous full replica symmetry breaking. We give analytically the cur ved segments of the order parameter function and, in representative ca ses, compute the free energy, the storage error, and the entropy.