Optimal storage capacity of neural networks at finite temperatures

Details Optimal storage capacity of neural networks at finite temperatures Optimal storage capacity of neural networks at finite temperatures

1993-06-15

arxiv.org/abs/cond-mat/9306032v1

Physics

Condensed Matter

22 pages in LaTex, 4 figures upon request, SNUTP-93-26

Scientific paper

Gardner's analysis of the optimal storage capacity of neural networks is extended to study finite-temperature effects. The typical volume of the space of interactions is calculated for strongly-diluted networks as a function of the storage ratio $\alpha$, temperature $T$, and the tolerance parameter $m$, from which the optimal storage capacity $\alpha_c$ is obtained as a function of $T$ and $m$. At zero temperature it is found that $\alpha_c = 2$ regardless of $m$ while $\alpha_c$ in general increases with the tolerance at finite temperatures. We show how the best performance for given $\alpha$ and $T$ is obtained, which reveals a first-order transition from high-quality performance to low-quality one at low temperatures. An approximate criterion for recalling, which is valid near $m=1$, is also discussed.

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