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

Abstract

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 two- dimensional 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.

Coherently Remapping Toroidal Cells but Not Grid Cells Are Responsible for Path Integration in Virtual Agents

“…Overall, our findings support the converging understanding in neuroscience that ensembles of cells collectively form units of functionality instead of single cells. 11,[41][42][43] Besides toroidal cells, our analysis identified two other clusters of cells that influence the decoding error significantly (clusters with identity 3 and 8 in Figure S1). However, due to their low cell count, we restricted our focus to toroidal cells.…”

Bridging tuning and invariance with equivariant neuronal representations

“…We chose to focus on planar rotations because they are among the simplest geometric transformations and much is already known about how individual neurons change their responses to rotations of a single image, [22][23][24] but little is known about the corresponding image manifolds, especially for multiple images. Such image manifolds must form loops, because a 360 degrees-rotated image is the same as an unrotated image, which was shown explicitly 25 for a single image using persistent homology-a computational technique that identifies topological aspects of image manifolds. However, a geometric approach is needed to study the linear separability of image manifolds.…”