Summary
Across a range of motor and cognitive tasks, cortical activity can be accurately described by low-dimensional dynamics unfolding from specific initial conditions on every trial. These “preparatory states” largely determine the subsequent evolution of both neural activity and behaviour, and their importance raises questions regarding how they are — or ought to be — set. Here, we formulate motor preparation as optimal anticipatory control of future movements, and show that the solution requires a form of internal feedback control of cortical circuit dynamics. In contrast to a simple feedforward strategy, feedback control enables fast movement preparation and orthogonality between preparatory and movement activity, a distinctive feature of peri-movement activity in reaching monkeys. We propose a circuit model in which optimal preparatory control is implemented as a thalamo-cortical loop gated by the basal ganglia.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
This revision follows two rounds of peer-review and brings many changes. In particular, we now show that optimal feedback control does not only benefit the inhibition-stabilized network studied in the first submission, but benefits universally any (linear) network that solves the same task. Moreover, we conducted further statistics analysis of trial-by-trial variability (former Figure 6). Although variability suppression was consistently stronger in the combined CS+ECS than in the LCS, it was not significant in the monkey analyzed in the original submission. We went back to perform the same analysis in another monkey for which more trials were available, and the effect did reach significance. However, a Reviewer had alerted us to another potential source of confound: our estimation of the LCS subspace is necessarily noisy, and there was the possibility that noise correlations in this estimate might spuriously explain the effect that we reported. We performed a control that strongly suggested this might have been the case. Overall, we felt that the link between across-trial variability and optimal preparatory control is tenuous, and our model prediction cannot yet be tested conclusively given only recordings of an M1 population. As of now, we do not see any other way of reliably estimating prospectively potent and null directions than by direct perturbation of M1 dynamics and corresponding observations of subsequent movements. We therefore decided to remove these results in this revision, but have enhanced Figure 8 to suggest a way of more directly testing for optimal preparatory control in future experiments.
↵1 This result is central to the theory of linear quadratic control, where cost functions are often of the form of integrated squared functions of the state, output, or input, under linear dynamics. It allows one to manipulate these integrals algebraically, and compute them numerically by solving a linear matrix equation (e.g. Bartels and Stewart, 1972). Indeed we will use this result again several times below in different contexts.
