Weak pairwise correlations imply strongly correlated network states in a neural population

By Elad Schneidman, Michael J. Berry, R. Segev, William Bialek. 2005

1,789 citations recorded by the source corpus.

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Statistical and Nonlinear Physics

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Citations in the corpus

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Neurophysiological and Computational Principles of Cortical Rhythms in Cognition (2010, background): “network’s state (851) and may be important for various”
Inverse statistical problems: from the inverse Ising problem to data science (2017, background): “This raises the possibility that the correlations described by the pairwise model (1) in [196] and related works originate from a confounding factor (connections to a neuron other than those whose signal is measured), rather than from connections between recorded neurons [121].”
Statistical mechanics of complex neural systems and high dimensional data (2013, methodology): “It has been employed as a simple model of spin glasses [7, 8], as well as neural networks [58], and has made a recent resurgence in neuroscience within the context of maximum entropy modeling of spike trains [59, 60].”
Small-World Brain Networks Revisited (2016, background): “In an inﬂuential paper published in 2006 with Bialek and colleagues, Schneidman demonstrated that weak pairwise correlations implied strongly correlated network states in a neural population, suggesting the presence of strong collective behaviour [102].”
From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction (2012, neutral): “MaxEnt has been used to analyze many types of biological data, ranging from multi-electrode recording of neural activities [25,26], gene concentrations in genetic networks [27], bird flocking [28] etc.”
A Small World of Neuronal Synchrony (2008, methodology): “…are correlated positively because strongly correlated units are more likely to interact strongly, but this relation, as in previous studies (Schneidman et al. 2006; Tang et al. 2008), is not straightforward: Some neuronal pairs with strong correlations have weak interactions and vice versa.”
Principles of maximum entropy and maximum caliber in statistical physics (2013, methodology): “Schneidman et al. (2006) speak of the rate of a firing pattern as its probability of occurrence within the small time interval t.”
Spatio-temporal correlations and visual signalling in a complete neuronal population (2008, methodology): “The statistics of such patterns have been studied in a variety of brain areas, and their significance in the processing and representation of sensory information has been debated extensively [1, 2, 3, 4, 5, 6, 7, 8, 9].”