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Sparse coding for layered neural networks

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  • Katayama, Katsuki
  • Sakata, Yasuo
  • Horiguchi, Tsuyoshi

Abstract

We investigate storage capacity of two types of fully connected layered neural networks with sparse coding when binary patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network, in which a transfer function of even layers is different from that of odd layers. The other is a layered network with intra-layer connections, in which the transfer function of inter-layer is different from that of intra-layer, and inter-layered neurons and intra-layered neurons are updated alternately. We derive recursion relations for order parameters by means of the signal-to-noise ratio method, and then apply the self-control threshold method proposed by Dominguez and Bollé to both layered networks with monotonic transfer functions. We find that a critical value αC of storage capacity is about 0.11|alna|−1 (a⪡1) for both layered networks, where a is a neuronal activity. It turns out that the basin of attraction is larger for both layered networks when the self-control threshold method is applied.

Suggested Citation

  • Katayama, Katsuki & Sakata, Yasuo & Horiguchi, Tsuyoshi, 2002. "Sparse coding for layered neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 532-546.
    • Handle: RePEc:eee:phsmap:v:310:y:2002:i:3:p:532-546
    DOI: 10.1016/S0378-4371(02)00785-9
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    Cited by:

    1. Rufiner, Hugo L. & Goddard, John & Rocha, Luis F. & Torres, María E., 2006. "Statistical method for sparse coding of speech including a linear predictive model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 231-251.

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