Modeling the diverse effects of divisive normalization on noise correlations

Divisive normalization, a prominent descriptive model of neural activity, is employed by theories of neural coding across many different brain areas. Yet, the relationship between normalization and the statistics of neural responses beyond single neurons remains largely unexplored. Here we focus on noise correlations, a widely studied pairwise statistic, because its stimulus and state dependence plays a central role in neural coding. Existing models of covariability typically ignore normalization despite empirical evidence suggesting it affects correlation structure in neural populations. We therefore propose a pairwise stochastic divisive normalization model that accounts for the effects of normalization and other factors on covariability. We first show that normalization modulates noise correlations in qualitatively different ways depending on whether normalization is shared between neurons, and we discuss how to infer when normalization signals are shared. We then apply our model to calcium imaging data from mouse primary visual cortex (V1), and find that it accurately fits the data, often outperforming a popular alternative model of correlations. Our analysis indicates that normalization signals are often shared between V1 neurons in this dataset. Our model will enable quantifying the relation between normalization and covariability in a broad range of neural systems, which could provide new constraints on circuit mechanisms of normalization and their role in information transmission and representation. Cortical responses are often variable across identical experimental conditions, and this variability is shared between neurons (noise correlations). These noise correlations have been extensively studied to understand how they impact neural coding and what mechanisms determine their properties. Here we show how correlations relate to divisive normalization, a mathematical operation widely adopted to describe how the activity of a neuron is modulated by other neurons via divisive gain control. We introduce the first statistical model of this relation. We extensively validate the model and investigate parameter inference in synthetic data. We find that our model, when applied to data from mouse visual cortex, outperforms a popular model of noise correlations that does not include normalization, and it reveals diverse influences of normalization on correlations. Our work demonstrates a framework to measure the relation between noise correlations and the parameters of the normalization model, which could become an indispensable tool for quantitative investigations of noise correlations in the wide range of neural systems that exhibit normalization.