Figures of merit for the performance of Hebbian-type associative memories

Statistical parameters that can be used to estimate the convergence probability of arbitrary-order Hebbian-type neural network associative memories (HAMs) with
N
neurons and
M
stored patterns are developed. The principle involves using two figures of merit, ε/η and η
N
, to determine the convergence probability for indirect (iterative) convergence and direct (one-step) convergence HAMs. Given η, the probability that a neuron changes to an incorrect bit after one update, the parameter ε/η determines the capability of converging iteratively to at most ε
N
bits away from the stored vector after a stable state is reached, where 0<ε<0.5. It is shown that the indirect convergence probability
P
_ic
≈1.0 for all HAMs having ε/η>20. If precise convergence to the stored vector is required in one step, the parameter η
N
is used to determine the probability of direct convergence,
P
_dc