Abstract
Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such “K-pairwise” models—being systematic extensions of the previously used pairwise Ising models—provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.
Highlights
Physicists have long hoped that the functional behavior of large, highly interconnected neural networks could be described by statistical mechanics [1,2,3]
Because the computational substrate of neural states in these models are binary ‘‘spins,’’ and the memories are realized as locally stable states of the network dynamics, methods of statistical physics could be brought to bear on theoretically challenging issues such as the storage capacity of the network or its reliability in the presence of noise [2,3]
It is widely agreed that neural activity in the brain is more than the sum of its parts—coherent percepts, thoughts, and actions require the coordinated activity of many neurons in a network, not the independent activity of many individual neurons
Summary
Physicists have long hoped that the functional behavior of large, highly interconnected neural networks could be described by statistical mechanics [1,2,3]. The goal of this effort has been not to simulate the details of particular networks, but to understand how interesting functions can emerge, collectively, from large populations of neurons. The hope, inspired by our quantitative understanding of collective behavior in systems near thermal equilibrium, is that such emergent phenomena will have some degree of universality, and that one can make progress without knowing all of the microscopic details of each system. Precisely because of these abstractions, it has not always been clear how to bring the predictions of the models into contact with experiment
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