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

Guidolin, Andrea; Desroches, Mathieu; Victor, Jonathan D.; Purpura, Keith P.; Rodrigues, Serafim

doi:10.1101/2022.03.16.484568

Cited by 2 publications

(1 citation statement)

References 56 publications

(136 reference statements)

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“…al. [43], in which the authors try to understand the geometry of visual space by combining spiking metrics [44] with topological methods. Nevertheless, the reduction methods used in these examples rely on visual inspection and remove structural properties of the data, due to the fact that the data has to be projected to a low-dimensional subspace.…”

Section: Previous Work On the Topology Of Neural Manifolds In Visionmentioning

confidence: 99%

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

Beshkov

Einevoll

2023

Preprint

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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.

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Section: Previous Work On the Topology Of Neural Manifolds In Visionmentioning

confidence: 99%

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

Beshkov

Einevoll

2023

Preprint

View full text Add to dashboard Cite

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Geometry of spiking patterns in early visual cortex: a topological data analytic approach

Guidolin

Desroches

Victor

et al. 2022

J. R. Soc. Interface.

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In the brain, spiking patterns live in a high-dimensional space of neurons and time. Thus, determining the intrinsic structure of this space 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 and use it to determine the geometry of spiking patterns in the visual cortex. Key to our approach is a parametrized family of distances based on the timing of spikes that quantifies 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 for spiking patterns in V1 and V2 which, among simple models, is most similar to that of a low-dimensional space endowed with Euclidean or hyperbolic geometry with modest curvature. Remarkably, the inferred geometry depends on timescale and is clearest for the timescales that are important for encoding contrast, orientation and spatial correlations.

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

Cited by 2 publications

References 56 publications

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

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

Geometry of spiking patterns in early visual cortex: a topological data analytic approach

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