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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
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When do correlations increase with firing rates in recurrent networks?

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Neural networks use noisy firing patterns for information transmission. Stronger excitatory coupling in recurrent networks drives a positive relationship between neural firing rate and pairwise correlations.

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Area of Science:

  • Computational Neuroscience
  • Neural Coding
  • Network Dynamics

Background:

  • Understanding how noisy neural firing patterns transmit information is a key neuroscience challenge.
  • Neural spiking is inherently noisy, often analyzed using pairwise correlations.
  • Experimental observations show correlations can increase with firing rate, potentially benefiting information coding.

Purpose of the Study:

  • To investigate the circuit mechanisms underlying the relationship between pairwise correlations and firing rates in spiking neural networks.
  • To determine how recurrent excitatory-inhibitory coupling influences this correlation-firing rate relationship.

Main Methods:

  • Studied conductance-based, recurrently coupled excitatory-inhibitory spiking networks.
  • Employed linear response theory to predict the correlation matrix and decompose correlations.
  • Analyzed correlations in terms of graph motifs to understand emergence in recurrent networks.

Main Results:

  • A positive relationship between pairwise correlations and firing rates emerged with stronger excitatory coupling.
  • Linear response theory successfully predicted the correlation matrix and explained the emergence of this relationship.
  • Covariation of correlations with firing rate, when present, was linked to low-rank structure in the correlation matrix.

Conclusions:

  • Stronger excitatory coupling in recurrent networks can generate the observed positive correlation-firing rate relationship.
  • Graph motif decomposition explains why this relationship appears in some recurrent networks but not others.
  • The correlation-firing rate relationship is associated with low-rank structure in neural network correlation matrices.