Dissociable cognitive strategies for sensorimotor learning

Computations underlying cognitive strategies in human motor learning are poorly understood. Here we investigate such strategies in a common sensorimotor transformation task. We show that strategies assume two forms, likely reflecting distinct working memory representations: discrete caching of stimulus-response contingencies, and time-consuming parametric computations. Reaction times and errors suggest that both strategies are employed during learning, and trade off based on task complexity. Experiments using pressured preparation time further support dissociable strategies: In response caching, time pressure elicits multi-modal distributions of movements; during parametric computations, time pressure elicits a shifting distribution of movements between visual targets and distal goals, consistent with analog re-computing of a movement plan. A generalization experiment reveals that discrete and parametric strategies produce, respectively, more localized or more global transfer effects. These results describe how qualitatively distinct cognitive representations are leveraged for motor learning and produce downstream consequences for behavioral flexibility.


Supplementary
: Separating fully random from "random + directed" reaches by RT bin for Experiment 2. There are several methods for determining when a circular distribution of angles deviates from being a uniform distribution (random) to a non-uniform distribution (having one or more significant clusters of values). Here we show converging results from multiple methods, pointing to the same RT bin (7th) as the critical point where reaches began to be directed rather than random. (A) Circular variance in reach angles. For each subject, the variance of movement angles at each RT bin was computed and normalized by the number of trials rendered in that bin. Serial t-tests were conducted and the first significant test (α = 0.05) denoted a "change" in variance. The 7th bin (150-175 ms) was found to be the initial point of significant change (p = 0.03). (B) Vector length at each RT bin. Similar to (A), the vector length at each bin was computed and normalized by number of trials. Serial t-tests revealed the first two significant changes after the 1st bin (p = 0.03) and 7th bin (p = 0.006), however, due to low numbers of trials in the early bins and known limits of human RT, the 1st bin result was considered spurious. Finally, we also performed a Rayleigh test for uniformity. The Rayleigh test uses vector length to indicate a unimodal deviation from uniformity in a distribution. The first significant deviation was found to be after the 7th bin (p = 0.02). Error bars represent 1 s.e.m. were correlated between tasks (right panel; R = 0.46; p = 0.008). (B) Given the subtle asymptote in the movement angle data in the FORCED task, we used a second method to derive the mental rotation parameter in the FORCED task. We fit a sigmoid to each subject's full data set (RT > 150 ms; left panel), with free parameters for the offset and rate, fixing the asymptote of the sigmoid function as the subject's mean reach angle in the long RT window trials (1200 ms of target appearance). The mean sigmoid fit (blue) is plotted over the arithmetic mean reach angles. A correlation between z-scored mental rotation paces from the FREE task and FORCED task was weaker though also statistically reliable when using this fitting method (right panel; R = 0.37, p = 0.036). Error bars represent 1 s.e.m. We adapted the response substitution model of tuned motor cortical neurons described by Cisek and Scott [1], which they used to argue that response substitution is a more parsimonious interpretation of the neural results of Georgopoulos et al. [2] than mental rotation. We also developed our own mental rotation variant of this model, and compared the behavioral predictions of the two models.
The model of cortical directionally-tuned neurons is formalized as follows [1]: where yi is the simulated activity of M1 neuron i, and xi reflects the input to that neuron. The parameter k represents a time constant, gi is a gain parameter, Γi is an activity threshold, and bi is baseline activity (which is set to 0 in this model, see [1] for details). During the simulations, if activity ever goes negative at any time point, it is reset to a value of 0. The rate of activity growth (Supplementary Equation 1) is driven by the amount of excitatory input, Ei. In the simulations, cosine-tuned cells are given input at the start of the trial, with direction ϕj and magnitude aj, where j indexes the details of the trial (target and goal directions): where θj is the cell's "preferred" direction and si is the offset of the tuning function. Preferred directions of the cells were uniformly distributed from 0 to 360˚. All model parameters (see table below) were set to the values reported in [1]. Moreover, the same number of neurons were simulated (300), though here the simulations were iterated 30 times (due to high noise in the parameter settings) to derive a range of responses.
Finally, rotation trials are simulated for each neuron, and the resulting population vector is computed as follows: where p i is the unit vector in each cell's preferred direction, which is summed to yield the population vector P. Much research has shown that movement speed is correlated with the motor cortical population vector length [3]; essentially, the more "confident" the population is of the planned movement direction, the faster the resulting movement tends to be. We converted the population vector lengths of both models to movement speeds (in cm/s) by scaling them by an arbitrary scaling parameter with a value of 0.76.
We modeled neural population activity as a result of either response substitution or mental rotation as follows: For response substitution, two distinct, independent inputs drive neural activity (as in [1]), one reflecting the target direction (e.g. 0˚) and one reflecting the solution direction (e.g. 90˚). For the first 150 ms, input represents solely the target direction, at a maximum magnitude of a = 1, and the magnitude of the solution direction (e.g. 90˚) at the minimum a = 0. During the next 200 ms, these two magnitudes linearly switch values, with the target direction signal decaying to zero and the solution direction signal increasing to 1. The two signals then remain at constant values for the final 150 ms of the simulation.
For mental rotation, only a single input is considered, and its direction is smoothly "rotated" during the RT. Like RS, for the first 150 ms the target direction drives the input at a magnitude of 1 (reflecting the subject processing the target location and anchoring where they need to rotate from). Then, the input angle (ϕ) linearly shifts from 0˚ to 90˚ for the following 200 ms, with no change in magnitude. The signal then remains at the solution direction for the remainder of time (150 ms). Finally, for both models, cell recruitment delays were drawn from a uniform distribution from 50 ms to 150 ms.
These two input schedules reflect the logic of response substitution and mental rotation, respectively: In response substitution, a prepotent response to reach toward the target drives activity at first, and is slowly replaced by a new motor plan directed toward the solution. In mental rotation, however, a single plan is directed toward the target and then smoothly rotated toward the solution. Figure 7: Gaussian fits in Experiment 4. For Experiment 4, we also assessed group differences in generalization by doing a more traditional Gaussian-fitting approach. We fit a composite function that was composed of two half-normals with means at the two respective extreme training targets (rotated in all subjects to 20˚ and 160˚, respectively), with free parameters for the width, height, and offset of the functions (i.e., all three parameters are shared between the two half-normals). Data in the area between the two extreme targets (8T condition) was not modeled. Free parameters were constrained Critically, because the generalization patterns could be captured by different combinations of the three free parameters, parameter correlations emerged that made interpretation of the results difficult; namely, the offset and height parameters were strongly negatively correlated (r = -0.80, p < 0.0001). This likely occurred because "flat" generalization patterns can be captured by either a function with a high offset but minimal height and width, or, alternatively, a high width and different combinations of height and offset.

Supplementary
We note that while this method did indeed produce the predicted difference in width parameters between the groups, with the 8T group showing a significantly larger width (t(30) = 2.13, p = 0.04), the fitting procedure was sensitive to different constraints and starting values. Thus, we opted for a more interpretable linear model of the difference in movement angle based on the generalization probe target's distance from the nearest training target ( Figure 10C, main text).