Abstract
We study the optimal learning capacity for neural networks withQ-state clock neurons, i.e. the states arecomplex numbers with magnitude 1 and azimuthal anglesn·2π/Q, withn=0, 1, ...,Q−1. Performing a phase space analysis, the learning capacity α c for given stability κ can be expressed by means of a double-integral with a simple geometrical interpretation, which for vanishing κ reduces to α c (Q) = 4Q/(3Q−4), forQ≧3. Then we define a training algorithm, which generalizes the well-known AdaTron algorithm fromQ=2 toQ≧3 and converges very fast to the network with optimal stability, if the numberp of random patterns to be learned is smaller than α c (Q). Finally, in the conclusions, we also give hints on applications for image recognition and in a „note added in proof” we generalize some results to Potts model networks.
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Gerl, F., Bauer, K. & Krey, U. Learning withQ-state clock neurons. Z. Physik B - Condensed Matter 88, 339–347 (1992). https://doi.org/10.1007/BF01470923
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DOI: https://doi.org/10.1007/BF01470923