Identifying Feedforward and Feedback Controllable Subspaces of Neural Population Dynamics

Ankit Kumar, Loren M. Frank, Kristofer E. Bouchard

Keywords: Control Theory, Systems Neuroscience, Dimensionality Reduction

Abstract: There is overwhelming evidence that cognition, perception, and action rely on feedback control. However, if and how neural population dynamics are amenable to different control strategies is poorly understood, in large part because machine learning methods to directly assess controllability in neural population dynamics are lacking. To address this gap, we developed a novel dimensionality reduction method, Feedback Controllability Components Analysis (FCCA), that identifies subspaces of linear dynamical systems that are most feedback controllable based on a new measure of feedback controllability. We further show that PCA identifies subspaces of linear dynamical systems that maximize a measure of feedforward controllability. As such, FCCA and PCA are data-driven methods to identify subspaces of neural population data (approximated as linear dynamical systems) that are most feedback and feedforward controllable respectively, and are thus natural contrasts for hypothesis testing. We developed new theory that proves that non-normality of underlying dynamics determines the divergence between FCCA and PCA solutions, and confirmed this in numerical simulations. Applying FCCA to diverse neural population recordings, we find that feedback controllable dynamics are geometrically distinct from PCA subspaces and are better predictors of animal behavior. Our methods provide a novel approach towards analyzing neural population dynamics from a control theoretic perspective, and indicate that feedback controllable subspaces are important for behavior.

Primary Area: applications to neuroscience & cognitive science

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 7747