Long-term attraction in higher order neural networks
David Burshtein · IEEE Transactions on Neural Networks · 1998
Recent results on the memory storage capacity of higher order neural networks indicate a significant improvement compared to the limited capacity of the Hopfield model. However, such results have so far been obtained under the restriction that only a single iteration is allowed to converge. This paper presents a indirect convergence (long-term attraction) analysis of higher order neural networks. Our main result is that for any kappa(d)<d!2(d-1)/(2d)!, and 0< or =rho<1/2, a Hebbian higher order neural network of order d with n neurons can store a random set of kappa(d)n(d)/log n fundamental memories such that almost all memories have an attraction radius of size rhon. If kappa(d)