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.
(51) In the thermodynamic limit, the integral is dominated by the saddle point satisfying: β ∂u ∂φ + φ 1 − q = 0 , 1 1 − q − 1 − φ 2 (1 − q)2 = 0
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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.