Dense Associative Memory with Epanechnikov Energy

Krishnakumar Balasubramanian (University of California, Davis) · Benjamin Hoover (IBM Research; Georgia Tech) · Zhaoyang Shi (Harvard University) · Dmitry Krotov (IBM Research) · Parikshit Ram (IBM Research)
creativitydense associative memoryemergent local minimaenergy functionepanechnikov kernelexponential capacitygenerative tasksimage datasetslog-likelihoodlog-sum-relumemory retrievalnoveltyoptimal kernel density estimationpattern recoveryseparation functions

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. Uniquely, it introduces abundant additional emergent local minima while preserving perfect pattern recovery