A sub-Riemannian model of neural states in the primary motor cortex

TL;DR

This paper introduces a neurogeometric sub-Riemannian model of motor cortex activity that captures neural states through a hierarchical, geometric framework based on kinematic parameters and cortical connectivity.

Contribution

It develops a novel sub-Riemannian geometric model for neural states in motor cortex, linking kinematic variables to neural activity patterns and confirming their sufficiency in explaining neural state formation.

Findings

Successfully recovers neural states from cortical activity data

Demonstrates the sufficiency of kinematic variables and metrics in modeling neural states

Reflects the brain's hierarchical processing through modular geometric modeling

Abstract

We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more complex patterns known as neural states (Georgopoulos, Hatsopoulos, Kadmon-Harpaz et al). Based on the sub-riemannian framework introduced in 2023, we model the space of fragments as a set of short curves defined by kinematic parameters. We then introduce a geometric kernel that serves as a model for cortical connectivity and use it in a differential equation to describe cortical activity. By applying a grouping algorithm to this cortical activity model, we successfully recover the neural states observed in Kadmon-Harpaz et al, which were based on measured cortical activity. This confirms that the choice of kinematic variables and the distance metric used here are sufficient to explain the phenomena of neural state formation. The modularity of our model reflects the brain's hierarchical structure, where initial groupings in the kinematic space $\mathcal{M}$ lead to more abstract representations. This approach mimics how the brain processes stimuli at different scales, extracting both local and global properties.