Capacity of the Hebbian-Hopfield network associative memory

arXiv:2403.01907v1 Announce Type: cross
Abstract: In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small fraction of errors is tolerated in the stored patterns retrieval, the capacity of the network (maximal number of memorized patterns, $m$) scales linearly with each pattern's size, $n$. Moreover, he famously predicted $\alpha_c=\lim_{n\rightarrow\infty}\frac{m}{n}\approx 0.14$. We study this very same scenario with …

abstract arxiv binary capacity cond-mat.dis-nn cs.it cs.lg errors math.it math.pr memory network neural network patterns random retrieval small stat.ml studying type