Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

The activity of a neural population encodes information about the stimulus that caused it, and decoding population activity reveals how neural circuits process that information. Correlations between neurons strongly impact both encoding and decoding, yet we still lack models that simultaneously capture stimulus encoding by large populations of correlated neurons and allow for accurate decoding of stimulus information, thus limiting our quantitative understanding of the neural code. To address this, we propose a class of models of large-scale population activity based on the theory of exponential family distributions. We apply our models to macaque primary visual cortex (V1) recordings, and show they capture a wide range of response statistics, facilitate accurate Bayesian decoding, and provide interpretable representations of fundamental properties of the neural code. Ultimately, our framework could allow researchers to quantitatively validate predictions of theories of neural coding against both large-scale response recordings and cognitive performance.