Optimal packing of attractor states in neural representations

John Vastola
Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 228:425-442, 2024.

Abstract

Animals’ internal states reflect variables like their position in space, orientation, decisions, and motor actions—but how should these internal states be arranged? Internal states which frequently transition between one another should be close enough that transitions can happen quickly, but not so close that neural noise significantly impacts the stability of those states, and how reliably they can be encoded and decoded. In this paper, we study the problem of striking a balance between these two concerns, which we call an ‘optimal packing’ problem since it resembles mathematical problems like sphere packing. While this problem is generally extremely difficult, we show that symmetries in environmental transition statistics imply certain symmetries of the optimal neural representations, which allows us in some cases to exactly solve for the optimal state arrangement. We focus on two toy cases: uniform transition statistics, and cyclic transition statistics. Code is available at \url{https://github.com/john-vastola/optimal-packing-neurreps23}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v228-vastola24a, title = {Optimal packing of attractor states in neural representations}, author = {Vastola, John}, booktitle = {Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {425--442}, year = {2024}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Miolane, Nina}, volume = {228}, series = {Proceedings of Machine Learning Research}, month = {16 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v228/main/assets/vastola24a/vastola24a.pdf}, url = {https://proceedings.mlr.press/v228/vastola24a.html}, abstract = {Animals’ internal states reflect variables like their position in space, orientation, decisions, and motor actions—but how should these internal states be arranged? Internal states which frequently transition between one another should be close enough that transitions can happen quickly, but not so close that neural noise significantly impacts the stability of those states, and how reliably they can be encoded and decoded. In this paper, we study the problem of striking a balance between these two concerns, which we call an ‘optimal packing’ problem since it resembles mathematical problems like sphere packing. While this problem is generally extremely difficult, we show that symmetries in environmental transition statistics imply certain symmetries of the optimal neural representations, which allows us in some cases to exactly solve for the optimal state arrangement. We focus on two toy cases: uniform transition statistics, and cyclic transition statistics. Code is available at \url{https://github.com/john-vastola/optimal-packing-neurreps23}.} }
Endnote
%0 Conference Paper %T Optimal packing of attractor states in neural representations %A John Vastola %B Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2024 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Nina Miolane %F pmlr-v228-vastola24a %I PMLR %P 425--442 %U https://proceedings.mlr.press/v228/vastola24a.html %V 228 %X Animals’ internal states reflect variables like their position in space, orientation, decisions, and motor actions—but how should these internal states be arranged? Internal states which frequently transition between one another should be close enough that transitions can happen quickly, but not so close that neural noise significantly impacts the stability of those states, and how reliably they can be encoded and decoded. In this paper, we study the problem of striking a balance between these two concerns, which we call an ‘optimal packing’ problem since it resembles mathematical problems like sphere packing. While this problem is generally extremely difficult, we show that symmetries in environmental transition statistics imply certain symmetries of the optimal neural representations, which allows us in some cases to exactly solve for the optimal state arrangement. We focus on two toy cases: uniform transition statistics, and cyclic transition statistics. Code is available at \url{https://github.com/john-vastola/optimal-packing-neurreps23}.
APA
Vastola, J.. (2024). Optimal packing of attractor states in neural representations. Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 228:425-442 Available from https://proceedings.mlr.press/v228/vastola24a.html.

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