A dynamical learning process for the recognition of correlated patterns in symmetric spin glass models
In the framework of spin-glass models with symmetric ( multi-spin ) interactions of even order a local dynamical learning process is studied, by which the energy landscape is modified systematically in such a way that even strongly correlated noisy patterns can be recognized. Additionally the basins of attraction of the patterns can be systematically enlarged by performing the learning process with noisy patterns. After completion of the learning process the system typically recognizes for two-spin interactions as many patterns as there are neurons ( p ≃ Nm−1 for m-spin interactions ), and for small systems even more ( p > N for m = 2 ).
The dependence of the learning time on the parameters of the system ( e.g. the average correlation, the noise level, and the number p of patterns ) is studied and it is found that in the case of random patterns for p < N the learning time increases with p as px, with x ≃ 3.5, whereas for p > N the increase is much more drastic. Finally we give a proof for the convergence of the process and also discuss the possibility of a drastic improvement of the learning capacity for patterns with particular correlations ( “patched systems” ).
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