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

TL;DR

This paper demonstrates that input nonlinearities can generate higher-order correlations in neural populations, which can enhance information transmission depending on stimulus statistics and firing rate constraints.

Contribution

It reveals how input nonlinearities lead to higher-order correlations and their role in improving population coding and information transmission.

Findings

Higher-order correlations arise from input nonlinearities in neural models.

Performance improvements depend on stimulus distribution and firing rate constraints.

Including beyond-pairwise interactions can enhance machine learning models like Boltzmann machines.

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.