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

@article{Schneidman2006WeakPC, title={Weak pairwise correlations imply strongly correlated network states in a neural population}, author={Elad Schneidman and Michael J. Berry and Ronen Segev and William Bialek}, journal={Nature}, year={2006}, volume={440}, pages={1007-1012} }

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…

## 1,512 Citations

Spin glass models for a network of real neurons

- Mathematics, Biology
- 2009

It is shown that Pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent system.

When are correlations strong

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An expansion for the entropy of Ising systems in powers of the correlations is developed, carrying this out to fourth order, and it is shown that even though all pairwise correlations are weak, the fact that these correlations are widespread means that their impact on the network as a whole is not captured in the leading orders of perturbation theory.

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Overall, the findings identify circuit-level mechanisms that produce and fail to produce higher-order spiking statistics in neural ensembles.

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It is shown that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity and the consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.

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- Medicine, BiologyProceedings of the National Academy of Sciences
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It is concluded that a second- order maximum entropy model can predict correlated states, but not their evolution over time, which suggests that higher-order maximum entropy models incorporating temporal interactions will be needed to account for the sequences of correlated states that are often observed in the data.

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Surprisingly, despite the fact the firing pattern of neurons is controlled by brain state, the model based on pairwise interactions captures more than 90% of the structure in the detailed patterns of spiking observed during wakefulness and sleep.

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The properties of the neural vocabulary are explored by estimating its entropy, which constrains the population's capacity to represent visual information, and classifying activity patterns into a small set of metastable collective modes, showing that the neural codeword ensembles are extremely inhomogenous.

How fast can we learn maximum entropy models of neural populations

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Most of our knowledge about how the brain encodes information comes from recordings of single neurons. However, computations in the brain are carried out by large groups of neurons. Modelling the…

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- Mathematics, MedicineJournal of mathematical neuroscience
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