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Minimal perceptrons for memorizing complex patterns

Author

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  • Pastor, Marissa
  • Song, Juyong
  • Hoang, Danh-Tai
  • Jo, Junghyo

Abstract

Feedforward neural networks have been investigated to understand learning and memory, as well as applied to numerous practical problems in pattern classification. It is a rule of thumb that more complex tasks require larger networks. However, the design of optimal network architectures for specific tasks is still an unsolved fundamental problem. In this study, we consider three-layered neural networks for memorizing binary patterns. We developed a new complexity measure of binary patterns, and estimated the minimal network size for memorizing them as a function of their complexity. We formulated the minimal network size for regular, random, and complex patterns. In particular, the minimal size for complex patterns, which are neither ordered nor disordered, was predicted by measuring their Hamming distances from known ordered patterns. Our predictions agree with simulations based on the back-propagation algorithm.

Suggested Citation

  • Pastor, Marissa & Song, Juyong & Hoang, Danh-Tai & Jo, Junghyo, 2016. "Minimal perceptrons for memorizing complex patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 31-37.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:31-37
    DOI: 10.1016/j.physa.2016.06.025
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    References listed on IDEAS

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    1. Silva, Luiz Eduardo Virgilio & Cabella, Brenno Caetano Troca & Neves, Ubiraci Pereira da Costa & Murta Junior, Luiz Otavio, 2015. "Multiscale entropy-based methods for heart rate variability complexity analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 143-152.
    2. Larrondo, H.A. & González, C.M. & Martín, M.T. & Plastino, A. & Rosso, O.A., 2005. "Intensive statistical complexity measure of pseudorandom number generators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 133-138.
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