Statistical physics and representations in real and artificial neural networks

S. Cocco, R. Monasson*, L. Posani, S. Rosay, J. Tubiana

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)45-76
Number of pages32
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 15 Aug 2018
Externally publishedYes


  • Continuous attractors
  • Machine learning
  • Neural network
  • Place cell
  • Principal component analysis
  • Restricted Boltzmann Machine


Dive into the research topics of 'Statistical physics and representations in real and artificial neural networks'. Together they form a unique fingerprint.

Cite this