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.
- Fixed pattern bias cuts capacity from N^(n-1)/ln N to O(N^(n/2))
- Crossover region near 1-2q = O(ln N / N^(floor(n/2)-1))
- Bias-dependent crosstalk mean destabilizes sites holding the frequent value
- Activity-dependent control potential restores full capacity for fixed bias
From the original article
1 min read at arxiv.orgThe 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.
By Yuto Sakurai · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.