Identifying Feedforward and Feedback Controllable Subspaces of Neural Population Dynamics

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.

• The paper introduces FCCA, a novel method that identifies feedback controllable subspaces using energy metrics from the controllability Gramian.
• FCCA outperforms PCA by revealing geometric differences in subspaces tied to non-normal dynamics enforced by Dale's Law.
• The method's application to high-dimensional neural recordings suggests significant potential for improving brain-machine interfaces.

Summary of "Identifying Feedforward and Feedback Controllable Subspaces of Neural Population Dynamics"

Introduction

The paper introduces Feedback Controllability Components Analysis (FCCA), a novel method for analyzing neural population dynamics. It addresses the challenge of assessing feedback and feedforward controllability within neural systems, extending the control theoretic perspective to neural data analysis. This is crucial as cognition, perception, and action are greatly influenced by feedback control mechanisms.

Theoretical Background

FCCA is designed to identify subspaces that are most feedback controllable using a specific feedback controllability measure. This contrasts with Principal Components Analysis (PCA), which identifies subspaces that maximize feedforward controllability. The divergence between FCCA and PCA solutions is shown to be influenced by the system dynamics, particularly their non-normality.

The measure of controllability involved here is defined in terms of the energy required to steer system states, which is quantifiable via the controllability Gramian derived from the linearized system dynamics. FCCA provides an innovative approach to analyzing recorded neural population data without needing explicit model fitting.

Analytical Approach

The paper elucidates various methods for dimensionality reduction that optimize controllability measures. It establishes the geometric distinction between FCCA and PCA subspaces using theoretical results and numerical simulations. This distinction emerges in neural systems due to Dale's Law, which enforces non-normal dynamics within cortical circuits.

Experimental Validation

Through empirical data from diverse neural recordings, FCCA subspaces are demonstrated to outperform PCA subspaces in predicting behavioral outcomes, underscoring the significance of feedback controllable dynamics in neural data analysis. The authors systematically apply FCCA, highlighting its ease of application to high-dimensional neural recordings.

Implications and Future Directions

FCCA provides a pathway for novel analyses in systems neuroscience, with potential applications in brain-machine interfaces, where optimizing feedback controllable subspaces could enhance prediction accuracy and calibration efficiency. Moreover, this study opens avenues for further methodology extension, possibly integrating explicit model fitting or expanding into nonlinear dynamics to deepen insights into neural population activity.

Conclusion

The study effectively bridges control theory and neuroscience, introducing FCCA as a potent method to analyze neural population dynamics. The findings assert the importance of distinguishing between feedforward and feedback controllable subspaces, revealing that feedback controllability significantly contributes to behaviorally relevant neural dynamics. This work sets the stage for more refined computational techniques in neuroscience and underscores the necessity to consider feedback mechanisms in neurophysiological data analysis.