AI RESEARCH
Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory
arXiv CS.LG
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ArXi:2604.07401v2 Announce Type: replace-cross We study the thermodynamic memory capacity of modern Hopfield networks (Dense Associative Memory models) with continuous states under geometric constraints, extending classical analyses of pairwise associative memory. We derive thermodynamic phase boundaries for Dense Associative Memory networks with exponential capacity $M = e^{\alpha N}$, comparing Gaussian (LSE) and Epanechniko (LSR) kernels. For continuous neurons on an $N$-sphere, the geometric entropy depends solely on the spherical geometry, not the kernel.