Neural manifold under plasticity in a goal driven learning behaviour
Fig 4
Learning the feedback signal is possible for within- but not for outside-manifold perturbations.
(A) Regression is used to learn feedback weights. (B-C) Result of feedback learning for a within-manifold perturbation (WMP) (B) and an outside-manifold perturbation (OMP) (C). Accuracy of predicting neural dynamics from cursor dynamics is measured by R2. Similarity between inferred and correct feedback weights is measured by calculating the correlation coefficient between both. (D) Feedback learning results depend on the number of trials used for regression. Dashed lines show the feedback learning result for taking 50 trials. Compared is feedback learning after the initial training phase (where BCI readout and internal manifold completely overlap) (black), after within-manifold perturbation (red) and after outside-manifold perturbation (blue). (E) Recurrent relearning using the learned feedback weights. As before, task performance is quantified by calculating the mean squared error (MSE) between target cursor velocity and produced cursor velocity. Compared is task performance after within- (WMP) or outside-manifold (OMP) perturbation to performance after relearning with inferred feedback weights (WMR and OMR respectively) (F) Accuracy in the feedback learning, measured by the correlation coefficient between correct and inferred feedback weights, affects recurrent relearning performance, measured by mean squared error. (G) Alignment of internal manifold and readout determines feedback learning performance. To take into account variance in feedback learning for within-manifold perturbations, we calculate the manifold overlap only up to a network-specific dimension, not up to 10 dimensions as done in the rest of the paper. The specific dimension is defined as where λi are the Eigenvalues of the covariance matrix. The data points show feedback learning results for 20 simulations, whereas the black lines are interpolations between OMP and initial BCI mappings for which we evaluated feedback learning.