Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory
The absolute capacity of dense associative memory has mainly been analyzed for unbiased patterns. Here we examine the effect of bias in centered binary patterns under the Krotov-Hopfield single-site criterion $P_{\mathrm{error}}=1/N$, where $P_{\mathrm{error}}$ is the probability that a single-site flip lowers the energy of a stored pattern and $N$ is the number of neurons. Each pattern component takes $1-q$ with probability $q$ and $-q$ otherwise, where $0<q\le1/2$. For polynomial interactions of order $n$, a signal-to-noise analysis gives an absolute capacity of order $N^{n-1}/\ln N$ at $q=1/2$. For fixed $q<1/2$, however, the capacity is $O(N^{n/2})$ for even $n\ge4$ and $O(N^{(n+1)/2}...
| Authors | Yuto Sakurai, Takeaki Shimokawa, Kazunori Iwata et al. |
|---|---|
| Primary category | cond-mat.dis-nn |
| Published | 15 September 2026 |
| Last updated at source | 4 October 2026 |
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