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arXiv · 2506.10801

Dense Associative Memory with Epanechnikov Energy

Benjamin Hoover·Zhaoyang Shi·Krishnakumar Balasubramanian·Dmitry Krotov·Parikshit Ram
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Abstract

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.

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Benjamin Hoover, Zhaoyang Shi, Krishnakumar Balasubramanian, Dmitry Krotov, Parikshit Ram. 2025-06-12. Dense Associative Memory with Epanechnikov Energy. https://arxiv.org/abs/2506.10801

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