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Statistical physics and representations in real and artificial neural networks

Author

Listed:
  • Cocco, S.
  • Monasson, R.
  • Posani, L.
  • Rosay, S.
  • Tubiana, J.

Abstract

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we consider the neural representations of space (maps) in the hippocampus. We introduce an extension of the Hopfield model, able to store multiple spatial maps as continuous, finite-dimensional attractors. The phase diagram and dynamical properties of the model are analyzed. We then show how spatial representations can be dynamically decoded using an effective Ising model capturing the correlation structure in the neural data, and compare applications to data obtained from hippocampal multi-electrode recordings and by (sub)sampling our attractor model. In a second part, we focus on the problem of learning data representations in machine learning, in particular with artificial neural networks. We start by introducing data representations through some illustrations. We then analyze two important algorithms, Principal Component Analysis and Restricted Boltzmann Machines, with tools from statistical physics.

Suggested Citation

  • Cocco, S. & Monasson, R. & Posani, L. & Rosay, S. & Tubiana, J., 2018. "Statistical physics and representations in real and artificial neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 45-76.
    • Handle: RePEc:eee:phsmap:v:504:y:2018:i:c:p:45-76
    DOI: 10.1016/j.physa.2017.11.153
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    References listed on IDEAS

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    1. Simona Cocco & Remi Monasson & Martin Weigt, 2013. "From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction," PLOS Computational Biology, Public Library of Science, vol. 9(8), pages 1-17, August.
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    Cited by:

    1. Oostwal, Elisa & Straat, Michiel & Biehl, Michael, 2021. "Hidden unit specialization in layered neural networks: ReLU vs. sigmoidal activation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).

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