Evaluating state space discovery by persistent cohomology in the spatial representation system

Kang, Louis; Xu, Boyan; Morozov, Dmitriy

doi:10.1101/2020.10.06.328773

Cited by 3 publications

(4 citation statements)

References 52 publications

(67 reference statements)

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“…The findings suggest that network dynamics during OF foraging resides on a low-dimensional manifold with the same barcode as a torus. We noted the appearance of additional short bars in the barcodes for all modules, but these are expected for toroidal point clouds 56 , as we confirmed with simulated data from several CAN models 15,16 and point clouds sampled from idealized tori, in each case exhibiting similar features (see Extended Data Fig. 6).…”

Section: Mainsupporting

confidence: 82%

“…Each grid module cluster contained a mixture of nondirectional (pure) grid cells and conjunctive grid × direction cells 55 . We limited our analyses to the subset of pure grid cells because (i) the expected toroidal topology might be distorted by additional directional modulation, and (ii) detection of topology in conjunctive cells may require a larger number of cells than recorded here 56 .…”

Section: Mainmentioning

confidence: 99%

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Toroidal topology of population activity in grid cells

Hermansen

Pachitariu

et al. 2021

Preprint

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The medial entorhinal cortex (MEC) is part of a neural system for mapping a subject's position within a physical environment. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations, and are organized in modules which collectively form a population code for the animal's allocentric position1. The invariance of the correlation structure of this population code across environments and behavioural states, independently of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained elusive due to the small samples of cells obtained to date. Here we show, with simultaneous recordings from many hundreds of grid cells, and subsequent topological data analysis, that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to the moving animal's position in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained, with minimal distortion, between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feed-forward models where grid patterns are created from external inputs by Hebbian plasticity. This demonstration of network dynamics on a toroidal manifold provides the first population-level visualization of CAN dynamics in grid cells.

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Section: Mainsupporting

confidence: 82%

Section: Mainmentioning

confidence: 99%

Toroidal topology of population activity in grid cells

Hermansen

Pachitariu

et al. 2021

Preprint

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“…We thank Francesco Fumarola for insightful and helpful discussions. This manuscript has been released as a preprint on bioRxiv (Kang et al, 2020 ).…”

mentioning

confidence: 99%

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

Kang

Morozov

2021

Front. Comput. Neurosci.

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Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

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“…(Hatcher, 2002 ). An implication of this construction is that if the place fields cover the environment sufficiently densely, then their overlaps encode the topology of

, which provides a link between the place cells' spiking pattern and the topology of the represented space (De Silva and Ghrist, 2007 ; Curto and Itskov, 2008 ; Chen et al, 2012 ; Dabaghian et al, 2012 ; Kang et al, 2020 ).…”

Section: Topological Modelmentioning

confidence: 99%

From Topological Analyses to Functional Modeling: The Case of Hippocampus

Dabaghian

2021

Front. Comput. Neurosci.

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Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

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Evaluating state space discovery by persistent cohomology in the spatial representation system

Cited by 3 publications

References 52 publications

Toroidal topology of population activity in grid cells

Toroidal topology of population activity in grid cells

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

From Topological Analyses to Functional Modeling: The Case of Hippocampus

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