Corrective memory by a symmetric sparsely encoded network

A neural network that retrieves stored binary vectors, when probed by possibly corrupted versions of them, is presented. It employs sparse ternary internal coding and autocorrelation (Hebbian) storage. It is symmetrically structured and, consequently, can be folded into a feedback configuration. Bounds on the network parameters are derived from probabilistic considerations. It is shown that when the input dimension is n, the proportional activation radius is ρ and the network size is 2^νn with ν>1-h₂(ρ), the equilibrium capacity is at least 2^αn/8nρ(1-ρ) for any α<1-h₂(ρ), where h₂(·) is the binary entropy. A similar capacity bound is derived for the correction of errors of proportional size ρ or less, when ρ⩽0.3. The performance of a finite-size symmetric network is examined by simulation and found to exceed, at the cost of higher connectivity, that of the Kanerva (1988) model, operating as a content addressable memory