The effects of training breadth on motor generalization

Abstract

To generate new movements, we have to generalize what we have learned from previously practiced movements. An important question, therefore, is how the breadth of training affects generalization: does practicing a broad or narrow range of movements lead to better generalization? We address this question with a force field learning experiment. One group adapted while making many reaches in a small region (narrow group), and another group adapted while making reaches in a large region (broad group). Subsequently, both groups were tested for their ability to generalize without visual feedback. Not surprisingly, the narrow group exhibited smaller adaptation errors, yet they did not generalize any better than the broad group. Path errors during generalization were indistinguishable across the two groups, whereas the broad group exhibited reduced terminal errors. These findings indicate that overall, practicing a variety of movements is advantageous for performance during generalization; movement paths are not hindered, and terminal errors are superior. Moreover, the evidence suggests a dissociation between the ability to generalize information about a novel dynamic disturbance, which generalizes narrowly, and the ability to locate the limb accurately in space, which generalizes broadly.

to make new movements, we generalize what we have learned from previously practiced movements. Our ability to generalize is important on two counts. First, it allows us to perform new movements we have yet to attempt, something crucial for skilled motor behavior. Second, it demonstrates how much we have learned from the movements that we have practiced, something especially informative for movement science (Berniker and Kording 2008; Shadmehr 2004). A natural question is what kind of training leads to maximal generalization? For instance, practicing a variety of reaches provides a broad experience of movement dynamics. This may be beneficial when attempting to generalize to a new, as yet unpracticed, movement (Krakauer et al. 2000). Alternatively, practicing the same movement repeatedly maximizes our familiarity with a particular behavior. This, too, may be beneficial when generalizing (Yarrow et al. 2009). We want to understand this trade-off between a narrow or broad focus of training, i.e., the breadth of training.

Many researchers have examined how training affects our ability to generalize. These studies have explored the influences of movement amplitude (Goodbody and Wolpert 1998; Mattar and Ostry 2010), movement direction (Donchin et al. 2003; Gandolfo et al. 1996; Krakauer et al. 2000; Mattar and Ostry 2007; Smith 2001; Thoroughman and Shadmehr 2000; Thoroughman and Taylor 2005), movement speed (Goodbody and Wolpert 1998), workspace location (Criscimagna-Hemminger et al. 2003; Hwang et al. 2003; Malfait et al. 2002; Shadmehr and Moussavi 2000), and dominant vs. nondominant limb (Bagesteiro and Sainburg 2002; Criscimagna-Hemminger et al. 2003; Sainburg and Kalakanis 2000; Wang and Sainburg 2004). However, none of these studies explicitly examined how the breadth of training movements affects the ability to generalize.

We designed a force field learning experiment wherein subjects trained with either broad or narrow breadth. In the narrow breadth training group, subjects made center-out, point-to-point reaches. In the broad training group, subjects made reaches over a larger region to randomly drawn targets. All subjects were then tested for generalization under identical conditions. During practice, subjects in the narrow group outperformed those in the broad group with all error metrics examined. However, these benefits did not result in improved trajectories during generalization; when examining path errors, both groups were indistinguishable during generalization. Surprisingly, however, when examining movements made without visual feedback, the broad group had smaller terminal errors during generalization, bringing their hands closer to the target than the narrow group. These findings demonstrate that practicing a variety of movements is advantageous for generalization. Furthermore, training-related errors are not necessarily representative of performance during generalization. Finally, the differences in generalization errors suggest a possible dissociation between the ability to generalize information about a novel dynamic disturbance (as measured through path errors) and the ability to locate the limb in space accurately (as measured through the terminal errors).

METHODS

Twenty-two right-handed subjects (26.0 ± 4.8 yr, 16 males) took part in this experiment. Fourteen subjects took part in the regular experiment, and eight in the control group. All experimental protocols were approved by the Northwestern University Institutional Review Board and were in accordance with Northwestern University's policy statement on the use of humans in experiments. All participants were naïve to the goals of the experiment, signed consent forms before participating, and were paid to participate. Subjects were paid based on performance with a minimum of $10 and a maximum of $24.

Experimental protocol.

Fourteen subjects participated in a 2-day adaptation experiment. On the 1st day, each subject made reaches in a curl field in one of two possible training regions. On a 2nd day, they then made reaches in a curl field with the opposite orientation and in the other training region. In the narrow region, subjects made center-out point-to-point reaches, whereas in the large region targets were drawn pseudorandomly from 1 of 8 directions, forming a random walk. Both groups made 1,000 reaches, 35% of which were made without visual feedback. Afterward, all subjects were tested for generalization in the testing region on a center-out pattern of targets without visual feedback. Ten percent of these test reaches were catch trials.

Subjects sat in a height-adjustable chair with their elbow in a suspended sling to reduce fatigue and ensure their limb was approximately in a horizontal plane aligned with their shoulder (Fig. 1A). All reaches were made while grasping a robotic manipulandum in one of three workspaces. In the broad training group, subjects made reaches in a rectangular region, 22 cm high and 35 cm wide (Fig. 1B, dark blue traces). In the narrow training group, subjects made reaches in a 20-cm-diameter circular region (Fig. 1B, purple traces). The generalization workspace, identical for both groups, was also a 20-cm-diameter region. To control for the anisotropy of the robot dynamics, the chair the subject sat in was moved relative to the robot such that the center of the workspace was in an approximately similar location for all subjects based on their respective limb lengths and shoulder widths. In both broad and narrow training, a subject's shoulder was ∼15 cm to the left and 40 cm in front of the center of the workspace of the robot. In the generalization workspace, the subject's shoulder was translated ∼30 cm to the right.

Fig. 1.

Experimental setup. A: subjects sat in front of a robotic manipulandum that rendered either a null or a curl field while they made reaches to targets presented on a monitor. B: subjects in the narrow group made point-to-point reaches with the center-out star pattern of targets (example reaches are shown, purple traces). Subjects in the broad group made reaches in 8 directions pseudorandomly chosen in a region more than twice as large as the narrow group (example reaches are shown, dark blue traces). All subjects were then tested for generalization, making point-to-point reaches in the same region with the same star pattern of targets (light blue traces).

Visual feedback was provided on a computer monitor, calibrated to display accurate displacements, sitting above the robot and in front of the subjects (Fig. 1A). A cursor displayed on the screen (a white circle 4 mm in diameter) depicted the location of their hand. Each trial began with the display of a new target (yellow circle 10 mm in diameter) randomly drawn from one of eight directions (0, 45, 90, … 315°) and at a distance of 10 cm. If subjects came to a halt (velocity <0.1 m/s) within the target, within 700 ± 100 ms of the trial onset, then the target turned green, a tone was emitted, and their running score was advanced by 1. If they made the reach too slowly, the target turned blue, and if too fast, red. After a brief pause (500 ms), the target was extinguished and a new target was displayed.

In the broad training group, the target (in 1 of 8 directions) was drawn randomly such that it still remained within the region. In this group, few reaches were made to the same target twice. In the narrow training group, the subsequent target was always the origin (Fig. 1B, compare purple and blue traces). Thus subjects made center-out reaches to randomly drawn targets. In this group, reaches were made to each of the 8 target locations repeatedly.

At various trials during the experiment, the robot would render either a null field or a velocity-dependent curl field. The null field rendered zero forces at the handle, attempting to compensate for the inertia of the manipulandum (see below). The curl field was defined in terms of the Cartesian velocity of the subject's hand as F = BẊ, where the matrix B = [0 −c; c 0], where c = ±15 Ns/m and Ẋ = [ẋ,ẏ]^T is the hand velocity (the ± values for c result in counterclockwise and clockwise curl fields, respectively). Since this field is defined in terms of the hand velocity, the forces it produces for identical hand displacements, made with different arm postures, are equivalent; e.g., forces a subject would experience in the broad, narrow, and generalization workspaces would be identical.

Subjects were randomly assigned to 1 of 2 groups, broad or narrow, and participated in 5 blocks of reaching trials. In the 1st block, subjects made 250 reaches in the training workspace (either broad or narrow region) while the robot generated a null field. In 35% of these trials, randomly chosen, the cursor was extinguished at the start of the trial and the subjects reached without visual feedback. After 400 ms, the cursor was displayed again, allowing them to bring their hand within the target. Once the block was concluded, the chair was moved to the 2nd position so that the subject's limb was in the configuration appropriate for the generalization workspace. The 2nd block consisted of another 250 trials in the null field, again with 35% randomly chosen trials wherein the cursor was extinguished. These 2 initial blocks were used to ascertain the subjects' baseline performance in the 2 workspaces.

In the 3rd and 4th blocks, subjects adapted to the force fields in the training workspace. Each block consisted of 500 trials in the force field. In between blocks 3 and 4, subjects were allowed to rest for approximately 3–5 min. Of these 1,000 trials, a random 350 had the cursor extinguished. In 100 of these trials without visual feedback, the robot generated a null field, producing a catch trial. These catch trials allowed us to characterize each subject's ability to predict the perturbing forces while they trained.

In the final block, subjects were tested for their ability to generalize in the generalization workspace. The chair was quickly moved to the appropriate location, and subjects made another 72 reaches. In all trials, the cursor was extinguished and random target directions were chosen. Each subject made 9 reaches in each of the 8 directions. In ∼90% (65) of the trials, the robot rendered the same curl field the subjects trained in, whereas 7 randomly drawn trials were null fields.

Each subject returned for the 2nd part of the experiment on a 2nd day between 24 h and 7 days later. They then performed the same protocol described above but in the other training group and with the opposite orientation curl field.

Eight subjects took part in a control experiment performed to quantify naïve performance during the generalization task (the 5th block of trials). The protocol for these subjects was identical to that described above with the following exception: the subjects did not perform blocks 3 and 4 of adaptation; that is, subjects performed blocks 1 and 2, measuring baseline performance, and then performed block 5, making reaches in the force field. Thus their reaches in the generalization task were naïve to the force field and quantify performance without the benefit of practice.

Data analysis.

Cartesian position data of the endpoint of the robot was collected at 1,000 Hz. These data were used to compute a velocity signal (discretely differentiated and filtered with a 20-Hz, 3rd-order Butterworth filter). For each trial, path errors (errors made while moving) and terminal errors (errors relative to target location) were computed. The path errors were the maximum perpendicular error and angular error. The angular error for each trial was computed as the angle between a ray from the subject's starting position to the target and the ray from the same starting position to the point on the path where velocity was maximal. The terminal perpendicular and angular errors were also computed (note that these errors are only meaningful in trials without visual feedback). The terminal angular error was found as the angle between a ray from the subject's starting position to the target and the ray from the same starting position to the location where the subject stopped.

To visualize performance during adaptation, errors were binned into 50-trial intervals (Fig. 3). Early and late errors were further averaged across the 1st and last 100 trials, respectively. Tests for significance were performed using paired t-tests. A Bonferroni correction was made for 4 comparisons, and significance levels were set to 0.05/4 = 0.0125.

Fig. 3.

Summary of errors. The perpendicular and angular errors for movement paths (A and B) and movement termination errors (C and D) for reaches made without visual feedback. In each panel, for both experimental groups (blue and purple for the broad group and narrow group, respectively), the across-subject average measures (± SE) are displayed. For baseline blocks 1 and 2 (null field), averages are over the entire block. For the training blocks 3 and 4 (force field), averages are computed over 50-trial bins with additional averages computed during the 1st and last 100 trials (shaded regions). For the generalization block 5, averages are computed over all force field trials. Also displayed are the generalization results for the matching broad and narrow control groups (labeled control). deg, Degrees.

To compare training errors across groups, exponential fits [y = a × exp(b × trial) + c] were bootstrapped on the data. The data during training were sampled with replacement to obtain 2,000 of these curves. These samples were used to compute median values and the 95% confidence intervals. Similarly, the samples were used to find the bootstrapped differences in these curves and their 95% confidence intervals.

Experimental apparatus.

The robotic apparatus used is an updated version of that used in Shadmehr and Mussa-Ivaldi (1994). The manipulandum has two torque motors (model JR24M4CH; PMI Motor Technologies) used to generate forces at the handle. Two position encoders were used to record the angular position of the two robotic joints with a resolution exceeding 20 arcsec of rotation (model 25/045-NB17-TA-PPA-QAR1S; Teledyne-Gurley). The position, velocity, and acceleration of the handle were derived from these two signals. Endpoint forces and torques were monitored with a six-degrees-of-freedom load cell fixed to the handle of the robot (model F/T Gamma 30/100; Assurance Technologies). Software written for this experiment was run in the real-time xPC platform of MATLAB at 1,000 Hz. On each sample, the subject's kinematics were calculated and used to compute any endpoint forces (curl field or null field). A model of the robot (τ_robot) was used to cancel partially its inertial mechanics. In addition, a low-gain force-feedback loop was also used to help cancel the difference between the forces measured at the robot handle, F_measured, and those commanded. The gains on the inertial and force-feedback torques/forces were chosen to keep the robot stable while maximizing the fidelity of the rendered forces. The commanded torques were as follows:

$$\tau =J^T\text{F}+0.3\hspace{0.17em}{\tau }_{\text{robot}}+0.4\hspace{0.17em}{J}^T\left(\text{F}-{\text{F}}_{\text{measured}}\right)\text{.}$$

RESULTS

To study how training affects generalization, we conducted a force field adaptation study wherein we altered the breadth of training movements. On their 1st day, each subject was randomly assigned to a group (narrow or broad) and a curl field orientation (clockwise or counterclockwise). Subjects in the narrow training group made center-out reaches in eight directions. Subjects in the broad training group made reaches within a rectangular region more than twice the area of the narrow region (see methods and Fig. 1). In contrast with the narrow group, targets were drawn at random from one of eight directions, forming a random walk. On the 2nd day, each subject participated in the other group with the opposite orientation curl field. Although each subject performed the experiment on 2 separate days, analyses performed on the 1st and 2nd days alone found the same basic results. For the analysis presented below, the data for each training group were pooled together across days to analyze the effect of breadth on generalization.

To quantify movement errors, we chose the commonly used maximum perpendicular error and angular error (abbreviated as perp-error and ang-error below). In addition to these path errors, we also computed these same metrics at the terminal location of a reach (term-perp-error and term-ang-error, respectively). Not surprisingly, these terminal errors were ∼0 when the subjects had visual feedback. However, when feedback was extinguished, these errors were indicative of subjects' ability to position their limb in space accurately. Our aim was to use these path and terminal errors to examine how subjects learn to compensate for the force field in a predictive manner. To mitigate possible confounds associated with corrective feedback commands, we limit the analysis we present here to those trials in which visual feedback was absent.

All subjects initially performed a block of 250 trials in the training workspace to characterize baseline trajectories. These movements were in a null field and included random trials without visual feedback of the cursor. Reaches in both groups exhibited straight paths and approximately bell-shaped velocity profiles as is typical for such reaching trials (Fig. 2, block 1). Path and terminal movement errors in the broad group were consistently larger (Fig. 3, block 1 errors). With the exception of the terminal angular errors, these increases in error were statistically significant (perp-error: P < 0.001, ang-error: P = 0.001, term-perp-error: P = 0.002, term-ang-error: P = 0.131, where the significance level was defined as 0.0125). This was our 1st indication that a fixed amount of practice over a broad region was detrimental to performance.

Fig. 2.

Example reaches for a representative subject across the 5 blocks and 2 conditions (on 2 separate days). All reaches shown have their starting location translated to the same central location and were made without visual feedback. Reach colors are shaded according to target. For blocks 1 and 2, reaches were made in the training and generalization workspaces, respectively, in a null field (the last 5 reaches are displayed). For blocks 3 and 4, reaches were made in a curl field in their respective training workspaces (the 1st and last 5 are displayed). For the generalization block 5, all subjects made reaches in the same generalization workspace with the curl field they trained on (the last 5 reaches are displayed). Note that the reaches in the curl field are curved in opposite directions when the subject switches from the narrow group to the broad.

To establish a baseline for the generalization tests, all subjects subsequently performed a block of 250 trials in the generalization workspace. In this workspace, as in the narrow workspace, all subjects made center-out reaches to targets drawn randomly from 1 of 8 directions. Movements were in a null field and included random trials wherein vision of the cursor was absent (Fig. 2, block 2). Interestingly, in this block, movement errors, regardless of group, were smaller than in the training workspace (Fig. 3, compare blocks 1 and 2). For the narrow group, only the angular errors did not significantly decrease (perp-error: P = 0.001, ang-error: P = 0.391, term-perp-error: P < 0.001, term-ang-error: P < 0.001). For the broad group, each error significantly decreased (P < 0.001). Furthermore, unlike the errors in the training workspace of block 1, all errors during this block were nearly identical and statistically indistinguishable when comparing across training groups (Fig. 3, block 2; P > 0.5). This finding suggested that there was no a priori reason to believe that training in the narrow or broad workspace would lead to fundamentally different behavior in the generalization workspace.

Before we could probe generalization, subjects 1st had to learn. The next 2 blocks were for training reaches in the force field. Each block had 500 trials with a 3- to 5-min rest period in between blocks. As is typical in force field adaptation studies, early reaches in the force field veered off a straight path and missed the target (Fig. 2, blocks 3 and 4). With repeated trials, the reaches became straighter and the subjects' ability to land on target in the specified time improved. Catch trials, lacking visual feedback or the force perturbation, produced typical aftereffects progressively deviating from straight paths. These general findings were the same for both the narrow and broad group, evidencing subjects' general ability to adapt by learning a predictive model of the influences of the force field.

We quantified these improvements by comparing subject performance during early and late training. First, we note that relative to baseline errors, all early training errors, in both groups, increased (Fig. 3, shaded gray regions). As the trials continued, the errors progressively decreased, whereas catch trial errors increased (catch trials not shown). By the end of the second training block, all errors had decreased relative to their early values, many significantly so (Fig. 3, compare left shaded regions with the corresponding right shaded regions). For the narrow group, all errors were significantly smaller (perp-error: P < 0.001, ang-error: P = 0.004, term-perp-error: P = 0.003, term-ang-error: P = 0.005). For the broad group, only the angular errors did not display a significant decrease (perp-error: P = 0.003, ang-error: P = 0.043, term-perp-error: P = 0.004, term-ang-error: P = 0.004). Therefore, subjects in both groups had their reaches strongly perturbed by the force field but were able to adapt and improve their performance relative to early errors in the field.

Next, we quantified subject performance during adaptation relative to that during baseline. For the narrow group, the late training path errors were indistinguishable from baseline (perp-error: P = 0.161, ang-error: P = 0.317), whereas the late training terminal errors decreased relative to their baseline values, although only the terminal angular error did so significantly (compare the left shaded regions with the corresponding block 1, term-perp-error: P = 0.037, term-ang-error: P = 0.007). With the broad group, all late training errors were statistically indistinguishable from their baseline values (each P > 0.03). These results confirmed that subjects in both training groups were able adapt and bring their performance to baseline levels and below.

Although both training groups displayed similar amounts of relative reductions in errors during adaptation, there were clear differences in the values of these metrics. Subjects in the narrow training group, repeatedly practicing the center-out reaches, consistently produced smaller errors (Fig. 3). This was generally true throughout both training blocks. To quantify the differences in these error curves, we bootstrapped an exponential curve to the data and then used these samples to compute a bootstrapped difference. Ninety-five percent confidence intervals for all bootstrapped curves were computed. With the notable exception of the initial portion of the curves, where both groups were similarly unpracticed in the force field, the differences fell outside of the 95% confidence intervals shortly into the 3rd block (the confidence interval on the bootstrapped differences fell outside 0, indicating P < 0.05; Fig. 4). These results, combined with the findings from block 1, demonstrate that both path and terminal movement errors are larger when training in a broad region.

Fig. 4.

Bootstrapped exponential learning curves and their differences for the perpendicular and angular errors (A and B) and movement termination errors (C and D) for reaches made without visual feedback. Displayed are the median value curves (solid lines) and the 95% confidence intervals (shaded regions). Overlaid are the mean values (shaded lines) of the data. All groups began with indistinguishable error curves; the confidence intervals overlapped, and the 95% confidence interval for the bootstrapped differences overlapped 0. Soon thereafter, the errors diverged, and performance in the narrow group improved relative to the broad group.

As a final comparison of adaptation, we wanted to eliminate the possibility that any changes observed across groups were due to movement speed and not the breadth of training. The maximum speed for each trial was computed, and averages were found for the broad and narrow groups at different stages of training. There were no significant differences across groups during either early or late training periods. This offered further support that the differences across groups were due to the narrow and wide training protocols.

Our next step was to probe the ability of subjects to generalize. With their arm again in the generalization workspace, all subjects made 72 reaches in the curl field. All trials were made without vision of the cursor, and a small number of randomly chosen trials had a null field (see methods). As in the initial trials of the 1st training block, subjects' reaches were clearly perturbed by the fields (Fig. 2, block 5). However, before presenting a quantitative examination, we note the following observations. First, generally speaking, the average errors in the generalization trials were smaller than the early training errors. Second, both groups had very similar path errors, but the broad group had relatively smaller terminal errors. Therefore, all subjects demonstrated evidence of generalization, yet initial observations indicated the broad training group performed better despite their performance during training.

We proceed by comparing errors during generalization with those during late training to look for relative changes. For the narrow group, errors during generalization were consistently and significantly larger than those during late training (perp-error: P = 0.008, ang-error: P = 0.002, term-perp-error: P = 0.001, term-ang-error: P < 0.001). For the broad group, however, the path errors during generalization and late training were indistinguishable (perp-error: P = 0.673, ang-error: P = 0.371). Similarly, the terminal errors, although smaller during generalization, were still indistinguishable (term-perp-error: P = 0.40, term-ang-error: P < 0.271). These findings demonstrate that despite their relatively larger errors during training, subjects in the broad group exhibited more complete transfer, generalizing relatively more than the narrow group.

Next, we compared performance during generalization across training groups. When examining path errors (perpendicular and angular errors), the error metrics conventionally used to analyze adaptation and generalization, we found that training groups were statistically indistinguishable during generalization (Fig. 3, A and B; perp-error: P = 0.981, ang-error: P = 0.594). When examining terminal errors, we found that the broad group's errors were significantly smaller (Fig. 3, C and D; term-perp-error: P = 0.007, term-ang-error: P = 0.006). Thus, by directly comparing the broad and narrow groups, we again found that the broad group's performance during generalization was superior.

To examine these generalization errors in absolute terms, we compared them with those of a control group that performed an identical block of generalization reaches without the benefit of training (see methods). As can be seen, subjects in this control group performed uniformly worse than the regular subjects, indicating some benefits due to practice. To quantify this, an ANOVA was performed to test for an effect of the training group (narrow or broad) or the experiment (main or control). For the perpendicular errors, there was a significant effect for experiment [F_(1,35) = 11.587, P = 0.002, accounting for the large reductions in errors of the main group] but no effect for training group or interaction. For the angular errors, there were no significant effects. Regarding the terminal errors, although there was an obvious qualitative improvement in performance for the broad group, here, too, an ANOVA found no significant effect after correcting for multiple comparisons. In summary, subjects in the broad group generalized just as well as the narrow training group relative to their respective control groups.

Finally, in the interest of pursuing a thorough examination of generalization, we examined catch trials. Catch trials are generally used as a proxy for a subject's intended motor plan; that is, large catch trial errors indicate the subject was prepared to counter large disturbing forces. Therefore, a relative decrease in catch trial errors from training to the generalization trials would indicate a lack of generalization (Fig. 5). An ANOVA was performed for each of the four errors to examine the catch trials for the effects of group (narrow or broad) and stage of performance (late training or generalization). Interestingly, no significant effects were found for any of the four errors, suggesting once again that despite the relatively poor performance of the broad groups during training, performance did not suffer during generalization.

Fig. 5.

Catch trial errors. The perpendicular and angular errors for movement paths (A and B) and movement termination errors (C and D) for reaches made without visual feedback. In each panel, for both experimental groups (blue and purple for the broad group and narrow group, respectively), the across-subject average measures (± SE) are displayed. For baseline blocks 1 and 2 (null field), averages are over the entire block. For the training blocks 3 and 4 (force field), averages are computed over 50-trial bins with additional averages computed during the 1st and last 100 trials (shaded regions). For the generalization block 5, averages are computed over all force field trials.

DISCUSSION

Here, we presented findings from an adaptation and generalization study exploring how the breadth of training affects generalization. Two groups adapted under conditions designed to provide narrow or broad training breadth. Not surprisingly, we found that the narrow training group, repeatedly practicing the same movements to the same targets, exhibited superior performance while adapting. This was true for both path and terminal errors. When probed for generalization, however, the two groups were indistinguishable in terms of the conventional perpendicular and angular path errors. This was true for both errors in the force field and during catch trials. Considering the disparity in performance during training and the lack of a difference in control subjects, the broad group may have exhibited a more complete transfer of the adapted behavior. Furthermore, when examining movement termination errors (without visual feedback), we found that the broad training group outperformed the narrow group during generalization. On the whole, the findings demonstrate that training over a broad workspace results in superior performance: path errors are unaffected, and terminal errors improve.

One possible issue with our experimental design was that both generalization and narrow training movements were based on center-out movements, whereas broad training is used on a random walk approach. This decision was based on a practical compromise for providing two maximally distinct training protocols within the limits of experimental apparatus. However, if generalization relied heavily on the similarity between reaching protocols (i.e., center-out vs. random walk), then we would expect greater generalization from the narrow training to the generalization workspace, something we did not find. Still, designing a task that would sidestep this issue, perhaps by using equipment supporting larger workspaces, would be exciting.

The apparent dissociation between the effects of training breadth on path and terminal errors may suggest that different movement features are encoded with distinct representations. Consider that path errors (perpendicular and angular errors) during generalization reaches were not influenced by the size of the training workspace, whereas termination errors were superior after training in a broad workspace. Whether movement variables have local or global representations may account for this discrepancy. If movement variables have local representations, then new information is learned and represented specifically in the context experienced. In this case, repeated practice of similar movements benefits learning, but generalization to new, distant reaches is poor. If, however, movement variables have global (or very broad) representations, learning benefits from the wide variety of movements necessary to “reverse engineer” a new motor behavior. In this case, newly learned information generalizes broadly to very different movements. With these distinctions in mind, we can speculate that the information necessary to compensate for a novel dynamic disturbance (as measured through the path errors) appears to be represented locally, since both groups generalized equally well, to a new generalization workspace equally distant from their respective training areas. The information necessary to locate the limb in space accurately (as measured through the terminal errors) appears to be represented globally, since the broad group had the benefit of more varied reaches.

If there are distinct representations, what are the implications for previous generalization studies? Interestingly, previous work on visuomotor adaptation has already found differences in how people adapt and generalize reach trajectories and terminal positions (Ghez et al. 2007; Scheidt and Ghez 2007). There is the possibility that some experimental findings on generalization may have inadvertently entangled these two processes, and errors in the ability to localize the limb in space relative to a target may have been implicated in force field learning. Considering that many different studies of the motor system are not in agreement [e.g., Krakauer et al. (1999) vs. Tong et al. (2002)], future studies may need to be designed to probe force field learning carefully relative to other factors such as the ability to localize the limb in space.

Building off of this idea, an interesting possibility is that the broad group's reduced terminal errors are merely due to the range of reaches they made, completely independent of the force field; that is, an adaptation process independent of force field adaptation. This possibility is backed by a relatively recent body of computational and behavioral evidence suggesting subjects simultaneously adapt to their own bodies and the experimental perturbations (Berniker and Kording 2008, 2011; Haith et al. 2009; Kluzik et al. 2008; Torres-Oviedo and Bastian 2012). Although this would help explain the results, there is another series of studies that clearly demonstrate force field adaptation alone influences the proprioceptive sense of limb position (Darainy et al. 2013; Ostry et al. 2010). Thus, if there are multiple adaptation processes, they do not appear to be independent. Future studies can further explore this by comparing terminal errors after broad group training with and without force field adaptation.

With regard to novel force field learning, there is considerable evidence that sensorimotor adaptation is a form of local learning that does not generalize to very different circumstances (Berniker et al. 2013, 2014; Donchin et al. 2003; Gandolfo et al. 1996; Krakauer et al. 2000; Lackner and Dizio 1994; Mattar and Ostry 2007, 2010; Thoroughman and Shadmehr 2000). These studies are in line with our finding that movement path errors during generalization were the same for the narrow and broad groups. Consistent with the behavioral evidence, there is also neural data that suggests localized tuning curves (Cohen and Andersen 2002; Coltz et al. 1999; Georgopoulos et al. 2007; Paz et al. 2003). The implication is that neural populations encode local features of learning and should have difficulty extrapolating to completely novel circumstances. Similarly, computational models that examine how movement errors generalize during learning have found narrow bases of representation (Donchin et al. 2003; Ingram et al. 2010; Kadiallah et al. 2012; Thoroughman and Shadmehr 2000; Thoroughman and Taylor 2005). Our findings add to this body of work and further argue that adaptation is a form of local learning.

Despite this relatively recent body of evidence arguing for local representations that generalize narrowly, there is a long history of experimental work that suggests broad practice results in superior behaviors under the schema theory (Schmidt 1975). Schema theory posits that variability in practice facilitates the learning of a motor program by providing rich, varied experiences. Early studies found that variability of practice during training improved both retention (Shea and Kohl 1991) and generalization (Catalano and Kleiner 1984; Kerr and Booth 1978; McCracken and Stelmach 1977). However, many of these studies examined relatively familiar tasks such as key turns and ball throws. None examined learning of novel dynamics (such as a force field). Therefore, one can speculate that the link between these studies and our findings is how information regarding control of the limb itself, independent of external forces and dynamics, generalizes (as measured through terminal errors) and not the generalization of novel, external dynamics (as measured through movement errors).

We want to emphasize the implications of this generalization study for individuals that want to learn, or recover, a broad set of motor skills. In the case of robot-assisted physical therapy, the objective is to generalize from a limited range of training to a wide range of functionally relevant movements. In this context, our study provides further evidence for the benefits of training over a broad set of tasks. This might be one of the reasons why recent evidence suggests that conventional physical therapy is as good or better than robotic therapy (Kahn et al. 2006; Kwakkel et al. 2008; Swinnen et al. 2010); robotic therapy does not offer the same range of movements that a physical therapist can. We can speculate that robot-based therapy could be improved by broadening the set of movements it supports.

Beyond our conclusions about possible varying representations and training regimens, we want to draw attention to the importance of the choice of error metric. Movements are inherently high-dimensional phenomena (e.g., neural firing patterns, muscle commands, joint trajectories, etc.) typically distilled down to a single number (e.g., perpendicular error, angular error, curvature, etc.) for the purposes of experimental documentation. Here, we see that the choice of this number is not inconsequential and that indeed different error metrics have an important influence on the conclusions drawn from generalization studies. A more careful study of the roles of error metrics in movement science seems warranted.

GRANTS

This work was supported by National Institute of Neurological Disorders and Stroke Grant 1R01-NS-063399.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

M.B., H.M., and K.P.K. conception and design of research; M.B. and H.M. performed experiments; M.B. and H.M. analyzed data; M.B. and K.P.K. interpreted results of experiments; M.B. prepared figures; M.B. drafted manuscript; M.B., H.M., and K.P.K. edited and revised manuscript; M.B., H.M., and K.P.K. approved final version of manuscript.