Capacity of the Hopfield-Hebbian dynamics with correlated patterns

arXiv:2610.38437v1 Announce Type: new Abstract: Allowing for small fraction of errors in retrieved stored binary patterns, Hopfield-Hebbian neural network (NN) associative memory dynamics [14] achieves linearly scaled capacity. The famous proportionality constant $\alpha_c\approx 0.14$ is obtained in a large dimensional scenario as the ratio of the number of reliably stored patterns $m$ and the patterns' length $n$ under the assumption that uniformly randomly chosen binary patterns are \emph{independent} among themselves. While such an idealized scenario is now well understood, more practical