Towards the memory capacity of neurons with active dendrites

Active dendrites can be viewed as linear classi"ers augmented by a few second-order product terms representing multiplicative synaptic interactions [4]. To quantify the degree to which local synaptic interactions could augment the memory capacity of a neuron, we have studied the family of `subsampled quadratica (SQ) classi"ers. Each SQ classi"er is a linear classi"er augmented by a subset k of the K"O(d2) second-order product terms available in d dimensions. Using a randomized classi"cation task, we show that the error rate of an SQ classi"er depends only on: (1) the product term ratio p"k/K, which identi"es a family of isomorphic classi"ers, and (2) the number of bits contained in the SQ classi"er's speci"cation. Finally, we quantify the increase in memory capacity of any SQ classi"er relative to its linear counterpart. ( 1999 Elsevier Science B.V. All rights reserved.