Number of stable points for spin-glasses and neural networks of higher orders

Abstract

We study the number of stable points for spin-glasses and neural networks of higher orders, i.e., with Hamiltonians given by an algebraic form of degree d. For spin-glasses, we derive a rigorous exact expression, in the thermodynamic limit, assuming long-range independent exchange Gaussian interactions among sets of d spins. For neural networks we introduce several upper bounds on the number of programmable stable states, according to different storage schemes.