Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory
Analysis shows biased patterns cut dense associative memory capacity from N^(n-1)/ln N to O(N^(n/2)), with a bias-induced crossover.
The paper analyzes dense associative memory capacity for biased centered binary patterns under the Krotov-Hopfield single-site criterion. Unbiased patterns (q=1/2) with order-n polynomial interactions yield capacity of order N^(n-1)/ln N, while fixed bias q<1/2 reduces capacity to O(N^(n/2)) for even n>=4 and O(N^((n+1)/2)) for odd n>=5. A bias-dependent crosstalk mean destabilizes sites carrying the frequent value, and an activity-dependent control potential restores the higher capacity within the conditioned-Gaussian approximation.
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