Neural Population Dynamics during Reaching Are Better Explained by a Dynamical System than Representational Tuning
Fig 5
Representational tuning in an RNN for center-out reaching.
(a) Preferred movement direction in Cartesian space of all units, corresponding to the magnitude of bi,2 and bi,3 in Eq 9. (b) Summary of contribution vectors of all individual neurons (one vector each) over the entire movement, with black population vector showing the overall predicted movement direction. (c) Integrating the population vectors in panel b over time traces out a predicted trajectory (solid) that largely matches the actual trajectory (translucent). (d) Mean correlation between condition tuning order at neural movement onset compared to later time points during movement (in steps of 10 ms) for the RNN model and an example PMd/M1 data set presented in Churchland et al. [22]. Insets show full correlation histograms for two time points. (e) Adjusted R-Square obtained by regressing the activity of each neuron (from the go cue to the end of movement 300 ms after go) on a representational cosine model of velocity tuning (Methods). (f) Movement activity of three example neurons and the corresponding velocity based regression fits. The overall fit performance to these units is high (Adjusted R-Square above 0.8), but the regression fails to capture the multiphasic and varied nature of the underlying signal. (g) Time lag between neural activity and velocity, per neuron, obtained from the velocity tuning regression in panel e, showing a large range of values.