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

Researcher Madhava Gaikwad has published a significant paper titled 'Algorithmic Analysis of Dense Associative Memory: Finite-Size Guarantees and Adversarial Robustness' on arXiv. The work tackles a major limitation in the study of Dense Associative Memory (DAM) models, which are advanced neural networks that generalize classic Hopfield networks using higher-order interactions. While DAMs are known for their impressive storage capacity scaling as O(N^{n-1}), previous analyses only worked in the theoretical thermodynamic limit (N→∞) with random patterns. Gaikwad's research breaks new ground by providing the first algorithmic analysis that yields concrete, finite-size guarantees and explicit convergence rates under verifiable conditions.

Under specific pattern separation and bounded-interference assumptions, the paper proves that DAM retrieval dynamics converge geometrically. This translates to a practical O(log N) convergence time once the system enters its basin of attraction. Crucially, the research establishes explicit adversarial robustness bounds, quantifying exactly how many corrupted bits a DAM can tolerate per update sweep before failing. The analysis also confirms capacity scaling of Θ(N^{n-1}) in worst-case scenarios, recovering the classical scaling for random patterns. Furthermore, the paper shows DAM dynamics can be interpreted as a potential game, ensuring convergence to pure Nash equilibria under asynchronous updates.

The findings, accepted at the New Frontiers in Associative Memory workshop at ICLR 2026, move DAMs from purely theoretical constructs toward practically analyzable systems. By providing finite-N guarantees and explicit margins for adversarial corruption, this work lays a mathematical foundation for building more robust and predictable AI memory systems that could be deployed in real-world applications requiring reliable information retrieval and storage.