Abstract
Observable structure of variability presents a window into the underlying processes of skill acquisition, especially when the task affords a manifold of solutions to the desired task result. This study examined skill acquisition by analyzing variability in both its distributional and temporal structure. Using a virtual throwing task, data distributions were analyzed by the Tolerance, Noise, Covariation-method (TNC); the temporal structure was quantified by autocorrelation and detrended fluctuation analysis (DFA). We tested four hypotheses: (1) Tolerance and Covariation, not Noise, are major factors underlying long-term performance improvement. (2) Trial-to-trial dynamics in execution space exhibits preferred directions. (3) The direction-dependent organization of variability becomes more pronounced with practice. (4) The anisotropy is in directions orthogonal and parallel to the solution manifold. Results from 13 subjects practicing for 6 days revealed that performance improvement correlated with increasing Tolerance and Covariation; Noise remained relatively constant. Temporal fluctuations and their directional modulation were identified by a novel rotation method that was a priori ignorant about orthogonality. Results showed a modulation of time-dependent characteristics that became enhanced with practice. However, this directionality was not coincident with orthogonal and parallel directions of the solution manifold. A state-space model with two sources of noise replicated not only the observed temporal structure but also its deviations from orthogonality. Simulations suggested that practice-induced changes were associated with an increase in the feedback gain and a subtle weighting of the two noise sources. The directionality in the structure of variability depended on the scaling of the coordinates, a result that highlights that analysis of variability sensitively depends on the chosen coordinates.
Highlights
The past decade has seen a number of studies on motor control and learning that used variability as a window into the underlying processes of skill acquisition
Using the well-established mathematical concept of null space, the Uncontrolled Manifold (UCM) approach showed that variations in direction parallel to the solution manifold, that are deemed irrelevant to task achievement and, “uncontrolled,” were larger than variability in direction orthogonal to the manifold (Scholz and Schöner, 1999)
We venture the speculation that such results may provide clues about the relative scaling of the coordinates inside the nervous system. In summary, this experimental and modeling work demonstrated that the acquisition of a complex motor skill with a redundant task space is associated with an increasing anisotropy in data distributions and a corresponding increase in directionality in their temporal structure
Summary
The past decade has seen a number of studies on motor control and learning that used variability as a window into the underlying processes of skill acquisition This approach is promising when the task is redundant and affords a manifold of solutions that achieve the desired task result. Such mathematically infinite set of equivalent solutions may be advantageous as the complex sensorimotor system abounds with noise arising at all levels, ranging from variations in ion channel kinetics to amplitudes of action potentials (Faisal et al, 2008). The same concept has been part of the stochastic optimal feedback control framework, where only errors in directions irrelevant for task achievement are penalized by the cost function (Todorov and Jordan, 2002; Todorov, 2004)
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