רשתות עצביות אסוציאטיביות לדפוסים דלילים

תקציר מקורי באנגליתarXiv:2603.26217v2 Announce Type: replace-cross Abstract: Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, associative memories for sparse patterns, such as the Willshaw and Amari models, already exhibit enhanced storage capacities in the sparse regime. In this paper we combine these two mechanisms. We introduce higher-order versions of sparse associative memory models and study their storage capacities in the sense of fixed-pattern stability. For the Amari and Willshaw models with fixed interaction order $n$, we obtain storage scales of order $\frac{N^n}{(\log N)^n}$. When the interaction order grows logarithmically with the number of neurons, the