Winkel, J. Ó. and Schottky, B. and Krey, Uwe and Gerl, F. (1996) Storing semantically correlated and spatially segmented patterns in the perceptron. ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 101 (2). pp. 305-312. ISSN 0722-3277
Full text not available from this repository.Abstract
Within the framework of statistical physics, using a replica theory and an equivalent heuristic approach, we calculate the storage capacity alpha of the perceptron for patterns, which are semantically and spatially structured. The problem is abstracted from the task to recognize pairs of hand-written versions of a large number of two-letter words: Each pattern is divided into two segments, labeled 1 and 2, of lengths lambda(1) . N and lambda(2) . N, respectively. The patterns are grouped together in pairs, and the 1st and 2nd segments of the different patterns in a pair have overlaps c(1) and c(2), respectively, representing the similarity of the hand-writings. Patterns belonging to different pairs, as well as different segments of the same pattern, are assumed to be uncorrelated. We find that if the patterns in a pair have a vanishing global overlap R = lambda(1),c(1) + lambda(2)c(2), one always gets alpha = 2, independent on the local overlaps of the individual segments, whereas for R > 0 and R < 0, respectively, the storage capacity is > 2 (< 2): In these cases, the segmentation of the patterns leads to an enhancement (for R > 0) or reduction (for R < 0) of the storage capacity. Due to the segmentation, the couplings become structured in a certain non-trivial way, which reflects itself in the norms of the coupling vectors corresponding to the different segments.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NEURAL NETWORKS; STORAGE |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Jun 2023 10:33 |
| Last Modified: | 22 Jun 2023 10:33 |
| URI: | https://pred.uni-regensburg.de/id/eprint/51467 |
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