Monkeying Around the Null Space: An Investigation of Preparatory Neural Activity Using Reduced Rank Ridge Regression

Abstract

Preparatory neural activity underlies every voluntary movement we make, yet somehow it does not lead to premature muscle activation. The dorsal premotor cortex (PMd) and the primary motor cortex (M1) are regions that map directly to the spinal cord and exhibit preparatory neural activity. The null space theory attempts to explain the lack of downstream motion, claiming that there is a theoretical space in which any changes will result in muscle activation which the preparatory activity avoids (Kaufman et al., 2014). This means that preparatory neural activity operates in dimensions that are not recognized as task-relevant and are therefore output-null. Essentially, there is coordinated population cancelation behavior that does not result in muscle readouts. This study uses neural and muscle data from Kaufman et al., 2014 to assess whether the presence of preparatory activity in the null space and the low dimensional communication subspace can be better captured through reduced rank ridge regression, compared to the ridge regularized principal component regression. The results of this study indicate that the reduced rank ridge regression preserves more output variance through the communication space with the same rank as that of Kaufman et al., 2014. Additionally, it appears that the preparatory activity is strongly constrained to the null space when evaluating the degree of tuning that the preparatory activity has to this space. This means that the brain is essentially able to perform unseen computations to prepare for movement through utilizing the many dimensions in the null space.