Geometric entropy on the N-sphere sets retrieval phase boundaries in continuous thermal dense associative memories, achieving maximum capacity α=0.5 at zero temperature with kernel-dependent critical lines separating retrieval from failure.
Derivation of the Free Energy Density The disorder-averaged replicated partition function is: ⟨Z n⟩ = ∫ n∏ a=1 dxa δ(|xa|2 − N ) ⟨ exp ( − β n∑ a=1 H(xa, ξµ ) )⟩
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Geometric Entropy and Retrieval Phase Transitions in Continuous Thermal Dense Associative Memory
Geometric entropy on the N-sphere sets retrieval phase boundaries in continuous thermal dense associative memories, achieving maximum capacity α=0.5 at zero temperature with kernel-dependent critical lines separating retrieval from failure.