A PERCEPTRON WITH A SKELETAL WEIGHT-SPACE

A perceptron whose space of interactions can interpolate between spher ically constrained and binary-valued synapses is introduced and invest igated as an associative neural-network memory. For maximally stable s torage, and where the weight-space remains connected, the critical sto rage capacity, alpha(c), is found to be reduced by a factor determined solely by the geometry of the weight space, and is shown to interpola te, within the replica-symmetric approximation, between alpha(c) = 2 ( in the Gardner-model limit) and alpha(c) = 4/pi. Various comparisons o f the synaptic weights with those of the binary perceptron show that s uch differences as remain between this weight space and that of the tr ue binary perceptron are crucial to obtaining alpha(c) greater-than-or -equal-to 4/pi. Although these differences limit the use of such model s in realizing optimal binary networks, they may yet provide worthwhil e binary systems by simple weight clipping. Simulation results are pre sented in support of the theoretical analyses.