Is the information geometry of probabilistic population codes learnable?

John J. Vastola, Zach Cohen, Jan Drugowitsch
Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 197:258-277, 2023.

Abstract

One reason learning the geometry of latent neural manifolds from neural activity data is difficult is that the ground truth is generally not known, which can make manifold learning methods hard to evaluate. Probabilistic population codes (PPCs), a class of biologically plausible and self-consistent models of neural populations that encode parametric probability distributions, may offer a theoretical setting where it is possible to rigorously study manifold learning. It is natural to define the neural manifold of a PPC as the statistical manifold of the encoded distribution, and we derive a mathematical result that the information geometry of the statistical manifold is directly related to measurable covariance matrices. This suggests a simple but rigorously justified decoding strategy based on principal component analysis, which we illustrate using an analytically tractable PPC.

Cite this Paper

BibTeX
@InProceedings{pmlr-v197-vastola23a, title = {Is the information geometry of probabilistic population codes learnable?}, author = {Vastola, John J. and Cohen, Zach and Drugowitsch, Jan}, booktitle = {Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {258--277}, year = {2023}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Di Bernardo, Arianna and Miolane, Nina}, volume = {197}, series = {Proceedings of Machine Learning Research}, month = {03 Dec}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v197/vastola23a/vastola23a.pdf}, url = {https://proceedings.mlr.press/v197/vastola23a.html}, abstract = {One reason learning the geometry of latent neural manifolds from neural activity data is difficult is that the ground truth is generally not known, which can make manifold learning methods hard to evaluate. Probabilistic population codes (PPCs), a class of biologically plausible and self-consistent models of neural populations that encode parametric probability distributions, may offer a theoretical setting where it is possible to rigorously study manifold learning. It is natural to define the neural manifold of a PPC as the statistical manifold of the encoded distribution, and we derive a mathematical result that the information geometry of the statistical manifold is directly related to measurable covariance matrices. This suggests a simple but rigorously justified decoding strategy based on principal component analysis, which we illustrate using an analytically tractable PPC.} }
Endnote
%0 Conference Paper %T Is the information geometry of probabilistic population codes learnable? %A John J. Vastola %A Zach Cohen %A Jan Drugowitsch %B Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2023 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Arianna Di Bernardo %E Nina Miolane %F pmlr-v197-vastola23a %I PMLR %P 258--277 %U https://proceedings.mlr.press/v197/vastola23a.html %V 197 %X One reason learning the geometry of latent neural manifolds from neural activity data is difficult is that the ground truth is generally not known, which can make manifold learning methods hard to evaluate. Probabilistic population codes (PPCs), a class of biologically plausible and self-consistent models of neural populations that encode parametric probability distributions, may offer a theoretical setting where it is possible to rigorously study manifold learning. It is natural to define the neural manifold of a PPC as the statistical manifold of the encoded distribution, and we derive a mathematical result that the information geometry of the statistical manifold is directly related to measurable covariance matrices. This suggests a simple but rigorously justified decoding strategy based on principal component analysis, which we illustrate using an analytically tractable PPC.
APA
Vastola, J.J., Cohen, Z. & Drugowitsch, J.. (2023). Is the information geometry of probabilistic population codes learnable?. Proceedings of the 1st NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 197:258-277 Available from https://proceedings.mlr.press/v197/vastola23a.html.

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