Dense associative memories (DAM), are widespread models in artificial intelligence used for pattern recognition tasks; computationally, they have been proven to be robust against adversarial input and theoretically, leveraging their analogy with spin-glass systems, they are usually treated by means of statistical-mechanics tools. Here we develop analytical methods, based on nonlinear PDEs, to investigate their functioning. In particular, we prove differential identities involving DAM partition function and macroscopic observables useful for a qualitative and quantitative analysis of the system. These results allow for a deeper comprehension of the mechanisms underlying DAMs and provide interdisciplinary tools for their study.
@article{arxiv.2203.14273,
title = {Non-linear PDEs approach to statistical mechanics of Dense Associative Memories},
author = {Elena Agliari and Alberto Fachechi and Chiara Marullo},
journal= {arXiv preprint arXiv:2203.14273},
year = {2022}
}