Input nonlinearities can shape beyond-pairwise correlations and improve information transmission by neural populations

Abstract

While recent recordings from neural populations show beyond-pairwise, or higher-order correlations (HOC), we have little understanding of how HOC arise from network interactions and of how they impact encoded information. Here, we show that input nonlinearities imply HOC in spin-glass-type statistical models. We then discuss one such model with parameterized pairwise- and higher-order interactions, revealing conditions under which beyond-pairwise interactions increase the mutual information between a given stimulus type and the population responses. For jointly Gaussian stimuli, coding performance is improved by shaping output HOC only when neural firing rates are constrained to be low. For stimuli with skewed probability distributions (like natural image luminances), performance improves for all firing rates. Our work suggests surprising connections between nonlinear integration of neural inputs, stimulus statistics, and normative theories of population coding. Moreover, it suggests that the inclusion of beyond-pairwise interactions could improve the performance of Boltzmann machines for machine learning and signal processing applications.

Matches the version to appear in Physical Review E. Main paper is 10 pages long with 4 figures. The .pdf includes a 14-page appendix with an additional figure

References in corpus (5)

• Searching for collective behavior in a network of real neurons
• A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields
• Stimulus-dependent maximum entropy models of neural population codes
• The sign rule and beyond: Boundary effects, flexibility, and noise correlations in neural population codes
• Dead leaves and the dirty ground: low-level image statistics in transmissive and occlusive imaging environments

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