We propose a novel energy function for Dense Associative Memory (DenseAM) networks, the log-sum-ReLU (LSR), inspired by optimal kernel density estimation. Unlike the common log-sum-exponential (LSE) function, LSR is based on the Epanechnikov kernel and enables exact memory retrieval with exponential capacity without requiring exponential separation functions. Moreover, it introduces abundant additional \emph{emergent} local minima while preserving perfect pattern recovery -- a characteristic previously unseen in DenseAM literature. Empirical results show that LSR energy has significantly more local minima (memories) that have comparable log-likelihood to LSE-based models. Analysis of LSR's emergent memories on image datasets reveals a degree of creativity and novelty, hinting at this method's potential for both large-scale memory storage and generative tasks.
Cite
@article{arxiv.2506.10801,
title = {Dense Associative Memory with Epanechnikov Energy},
author = {Benjamin Hoover and Zhaoyang Shi and Krishnakumar Balasubramanian and Dmitry Krotov and Parikshit Ram},
journal= {arXiv preprint arXiv:2506.10801},
year = {2026}
}
Comments
Accepted as Spotlight Poster to NeurIPS 2025 main conference