Ising models for networks of real neurons

Abstract

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the retina, and show that pairwise interactions account for observed higher-order correlations. By first finding a representative ensemble for observed networks we can create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses.

4 pages, 3 figures

Cited by in corpus (11)

• Faster solutions of the inverse pairwise Ising problem
• A discrete time neural network model with spiking neurons II. Dynamics with noise
• Inductive Game Theory and the Dynamics of Animal Conflict
• Rediscovering the power of pairwise interactions
• When are correlations strong?
• Criticality & Deep Learning II: Momentum Renormalisation Group
• Statistics of spikes trains, synaptic plasticity and Gibbs distributions
• Go game formal revealing by Ising model
• Inverse problems in spin models
• The refractory period matters: unifying mechanisms of macroscopic brain waves
• Developing a Maximum-Entropy Restricted Boltzmann Machine with a Quantum Thermodynamics Formalism