Recurrent neural network model inputs and outputs.

(a) RNNs receive a 17-dimensional input signal consisting of the location of the movement target in Cartesian coordinates, a “visual” feedback signal giving the arm’s endpoint position delivered with a 70 ms delay, a “proprioceptive” feedback signal consisting of the length and velocity of each of the 6 limb muscles delivered with a 20 ms delay, and a binary go cue. RNNs output 6 motor stimulation commands (between 0 and 1) to drive each muscle: SF (shoulder flexors), SE (shoulder extensors), EE (elbow extensors), EF (elbow flexors), BE (bi-articular extensors), and BF (bi-articular flexors). (b) The 17-dimensional input signal was mapped to the recurrent network using linear weights Win. RNN output was transformed into motor commands by linear weights Wout. The vector ht is the activity of hidden units at time t. (c) Task-related RNN inputs in a reach toward the rightmost target depicted in (a). For the purpose of illustration in this Figure, we translated the starting and target positions such that the start position is at the coordinates 0, 0. The simulation duration was 1 s, with 10 ms time steps. The goal (dashed lines) was set to the hand’s starting position before the go signal changed to 1, to the movement target position after that. (d) Sample endpoint trajectories after training RNNs on reaches to random target locations. Reaching trajectories are indicated in orange, and small gray dots show target positions. The large gray circle indicates the position of the centre-out reaches within the workspace. (e) Reaching trajectories and hidden unit activity over time at the end of training in the centre-out task. colours indicate each of 8 targets. The go-cue switches from 0 to 1 at time t = 0.

Networks learn to compensate for curl force fields without any contextual input.

(a) Lateral deviation averaged over 8 centre-out reaches for each batch. Black indicates null-field phases (NF1 and NF2), green indicates the first phase of the force field (FF1), and purple indicates the second phase of the force field (FF2). Positive values indicate deviation in the direction of the force field, which is clockwise relative to the line connecting the starting and target positions. (b) Simulated reaching trajectories at the beginning and end of each phase, grouped in different columns. (c) Motor commands during reaching toward the rightmost target for NF1 and FF1.

RNN models exhibit behavioural characteristics of savings.

(a) Averaged learning curves shown in Figure 3a are overlaid. Sub-panels indicate (left) the lateral deviation at batch 0 (before training in the corresponding phase) and (right) the learning rate r after fitting an exponential curve to the lateral deviations over training for each network. (b) The percentage of networks (40 total) with savings is plotted against the number of RNN hidden units. The dashed line indicates the percentage of networks with savings, defined as the learning rate in FF2 being larger than in FF1. The solid line shows percentage of networks showing savings defined by lateral deviation at batch 0 being smaller in FF2 than FF1. Error bars indicate the 95% confidence interval.

Changes in the preparatory activity of RNN hidden units following FF learning.

a: Projection of the hidden preparatory activity (340 ms before the go-cue) of an example trained model performing 8 centre-out reaches on the force-predictive subspace acquired with targeted dimensionality reduction (TDR). Different reaching targets are indicated with different colours, and different adaptation phases are indicated with different shapes: circle for NF1, triangle for FF1, square for NF2, and star for FF2. b: A schematic illustration of the uniform shift. Each cross indicates the centre of the hidden preparatory activity for NF1 and FF1, and the arrow indicates the uniform shift. c: Projection of the hidden preparatory activity of all phases onto the uniform shift after orthogonalizing the uniform shift with respect to TDR. The data are scaled so that the projection of NF1 onto the uniform shift is zero and the projection of FF1 is one.

Uniform shift in RNN hidden unit activity is related to savings.

A: Lateral deviation in FF2 (purple) when the hidden preparatory activity was perturbed in the positive (+) and negative (−) directions of the uniform shift with different magnitudes. Arrows point to the trajectories of an example model when the hidden unit activity was perturbed (red trajectories) or not (blue trajectories). The lateral deviation hand trajectories for FF1 are illustrated in green. B: Motor commands of the same model performing the same reach as shown in panel A when the hidden unit activity was perturbed with a magnitude of 2.0. The vertical dashed line indicates the time at which the perturbation was delivered. The lower sub-panel shows the difference from the unperturbed motor command. C: The activity of 128 RNN hidden units after being perturbed (dashed line). The lower sub-panel shows the difference between the unperturbed and perturbed RNN hidden unit activity.