A unifying theory of receptive field heterogeneity predicts hippocampal spatial tuning.

Neural populations exhibit receptive fields that vary in their sizes and shapes. Despite the prevalence of such tuning heterogeneity, we lack a unified theory of its computational benefits. Here, we present a framework that unifies and extends previous theories, finding that receptive field heterogeneity generally increases the information encoded in population activity. The information gain depends on heterogeneity in receptive field size, shape, and on the dimensionality of the encoded quantity. For populations encoding two-dimensional quantities, such as place cells encoding allocentric spatial position, our theory predicts that both size and shape receptive field heterogeneity are necessary to induce information gain, whereas size heterogeneity alone is insufficient. We thus turned to CA1 hippocampal activity to test our theoretical predictions-in particular, to measure shape heterogeneity, which has previously received little attention. To overcome limitations of traditional methods for estimating place cell tuning, we developed a fully probabilistic approach for measuring size and shape heterogeneity, in which tuning estimates were strategically weighted by explicitly measured uncertainty arising from biased or incomplete traversals of the environment. Our method furnished evidence that hippocampal receptive fields indeed exhibit strong degrees of size and shape heterogeneity, abiding by the normative predictions of our theory. Overall, our work makes novel predictions about the relative benefits of receptive field heterogeneities beyond our application to place cells, and provides a principled technique for testing them.