ASYMPTOTIC PROPERTIES OF A THIRD ORDER NEURAL NETWORK
Mats Bengtsson · International Journal of Neural Systems · 1991
We have investigated the storage capacity in the limit of large N (the network size) for a third order recurrent artificial neural network with Hebbian learning. Numerical results for the relation between the overlap to stored patterns, and the fraction of the number of stored patterns and N2 (the m—α relation), agree well with replica symmetric predictions. A comparative study is made of the m—α relation for a third and a second order network. Large differences exist between these two models, usually to the favour of the third order network. This result stands in some contrast to previous investigations. The phase transition temperature is investigated numerically and compared with mean field theory predictions.