Algorithmic Analysis of Dense Associative Memory: Finite-Size Guarantees and Adversarial Robustness

ArXi:2604.12811v1 Announce Type: cross Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily study the thermodynamic limit $N\to\infty$ with randomly sampled patterns and. therefore. do not provide finite-size guarantees or explicit convergence rates. We develop an algorithmic analysis of DAM retrieval dynamics that yields finite-$N$ guarantees under explicit, verifiable pattern conditions.