title: 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 parametrized 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.
authors.affiliation: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA.
authors.forename: Joel
authors.initials: J
authors.lastname: Zylberberg
authors.affiliation: Department of Applied Mathematics, Program in Neuroscience, Department of Physiology and Biophysics, University of Washington, Seattle, Washington 98195, USA.
authors.forename: Eric
authors.initials: E
authors.lastname: Shea-Brown
mesh_terms: D000465:Algorithms; D000069550:Machine Learning; D008959:Models, Neurological; D009474:Neurons / Q000166:cytology*; D017711:Nonlinear Dynamics