Tracking the topology of neural manifolds across populations

Yoon, Iris H. R.; Henselman-Petrusek, Gregory; Yu, Yiyi; Ghrist, Robert; Smith, Spencer LaVere; Giusti, Chad

doi:10.1073/pnas.2407997121

Title: Tracking the topology of neural manifolds across populations

Journal Article · 07 November 2024 · Proceedings of the National Academy of Sciences of the United States of America

DOI: https://doi.org/10.1073/pnas.2407997121 · OSTI ID:2480424

^[1]; Henselman-Petrusek, Gregory ^[2]; Yu, Yiyi ^[3]; Ghrist, Robert ^[4]; Smith, Spencer LaVere ^[3];

^[5]

Wesleyan University, Middletown, CT (United States)
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
Univ. of California, Santa Barbara, CA (United States)
Univ. of Pennsylvania, Philadelphia, PA (United States)
Oregon State Univ., Corvallis, OR (United States)

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

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Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 2480424

Report Number(s):: PNNL-SA--204895

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 46 Vol. 121; ISSN 0027-8424

Publisher:: National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
analogous cycles
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computational topology
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neuroscience
persistent homology
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Title: Tracking the topology of neural manifolds across populations

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