TY - JOUR

T1 - Statistical physics and representations in real and artificial neural networks

AU - Cocco, S.

AU - Monasson, R.

AU - Posani, L.

AU - Rosay, S.

AU - Tubiana, J.

N1 - Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2018/8/15

Y1 - 2018/8/15

N2 - 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.

AB - 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.

KW - Continuous attractors

KW - Machine learning

KW - Neural network

KW - Place cell

KW - Principal component analysis

KW - Restricted Boltzmann Machine

UR - http://www.scopus.com/inward/record.url?scp=85038839266&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2017.11.153

DO - 10.1016/j.physa.2017.11.153

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AN - SCOPUS:85038839266

SN - 0378-4371

VL - 504

SP - 45

EP - 76

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -