Topological Structure of Population Activity in Mouse Visual Cortex Encodes Visual Scene Rotations

The primary visual cortex is one of the most well understood regions supporting the processing involved in sensory computation. Historically, our understanding of this part of the brain has been driven by describing the features to which individual neurons respond. An alternative approach, which is rapidly becoming a staple in neuroscience, is to study and analyze the geometry and topology of the manifold generated by the neural activity of large populations of neurons. In this work, we introduce a rigorous quantification of the structure of such neural manifolds and address some of the problems the community has to face when conducting topological data analysis on neural data. We do this by analyzing publicly available two-photon optical recordings of primary mouse visual cortex in response to visual stimuli with a densely sampled rotation angle. Since the set of twodimensional rotations lives on a circle, one would hypothesize that they induce a circle-like manifold in neural activity. We confirm this hypothesis by discovering a circle-like neural manifold in the population activity of primary visual cortex. To achieve this, we applied a shortest-path (geodesic) approximation algorithm for computing the persistent homology groups of neural activity in response to visual stimuli. It is important to note that the manifold is highly curved and standard Euclidean approaches failed to recover the correct topology. Furthermore, we identify subpopulations of neurons which generate both circular and non-circular representations of the rotated stimuli, with the circular representations being better for angle decoding. We found that some of these subpopulations, made up of orientationally selective neurons, wrap the original set of rotations on itself which implies that the visual cortex also represents rotations up to 180 degrees. Given these results we propose that population activity can represent the angle of rotation of a visual scene, in analogy with how individual direction-selective neurons represent the angle of direction in local patches of the visual field. Finally, we discuss some of the obstacles to reliably retrieving the truthful topology generated by a neural population.