Geometry of spiking activity in early visual cortex: a Topological Data Analytic approach

In the brain, spiking patterns live in a high-dimensional space of neurons and time. Thus, determining the intrinsic structure of this state space for neural activity presents a theoretical and experimental challenge. To address this challenge, we introduce a new framework for applying topological data analysis (TDA) to spike train data to determine the geometry of neural activity space. Key to our approach is a parametrized family of distances based on the timing of spikes to determine the dissimilarity between neuronal responses. We applied TDA to visually driven single-unit and multiple single-unit spiking activity in macaque V1 and V2. TDA across timescales reveals a common geometry in V1 and V2 that is most consistent with a low-dimensional space endowed with Euclidean or hyperbolic geometry with modest curvature. Remarkably, the inferred geometry depends on timescale, and is most distinct for the timescales that are important for encoding contrast, orientation, and spatial correlations. ### Competing Interest Statement The authors have declared no competing interest.