Learning, Motor Skill, and Long-Range Correlations

Nourrit-Lucas et al (2015) compare expert and novice performance on a ski-simulator, a complex task which is often used by human movement scientists. Acquiring skilled performance on the ski-simulator requires you to learn a particular form of control as you shift your weight from side to side (van der Pol form of damped oscillations).

Their main result involved comparing the autocorrelations (which they call serial correlations) of participants’ performance. The participants were instructed to move from side to side as fast, and widely, as possible and these movements were motion tracked. The period of the oscillations was extracted and the autocorrelation for different lags calculated (other complexity measures were also calculated, which I ignore here). The autocorrelations for novices were positive for lag 1 and possibly for other short lags, but dropped to zero for longer range lags (5-30). Expert’s autocorrelations were higher for shorter lags and did not drop to zeros for any of the lags examined (showing positive long-range correlations in performance).

Figure 3, Nourrit-Lucas et al (2015)
Figure 3, Nourrit-Lucas et al (2015)

Nourrit-Lucas et al put an impressive interpretation on their result. It undermines, they say, that motor learning involves merely a process of simplification, unification or selection of a single efficient motor programme. Instead, they say “Expert performance seems characterized by a more complex and structured dynamics than that of novices.”

They link this interpretation to the idea of degeneracy, in which learning is the coordination of a complex network so that multiple functional units become linked to all support given outcomes. “This enrichment of neural networks could explain the property of robustness of motor skills, essentially revealed in retention tests, but also the properties of generalizability and transfer”

They cite modelling by Delignieres & Mermelat (2013) which links level of degeneracy to extent of long-range correlations. Whilst they admit that other complex networks are also capable of producing the long-range correlations observed, I would go further and say that a “simple-unitary” model of motor learning might also produce long-range correlations if there was some additional structured noise on performance (e.g. drift in attention or some such). Novices of course, would also have this influence on their performance, but perhaps it is swamped by the larger variability of their yet to be optimised motor system. I don’t see why the analysis of Nouritt-Lucas excludes this interpretation, but I may be missing something.

I also note that their result contrast with that of van Beers et al (2013), who showed that lag 1 autocorrelations in experts at at an aiming task tended towards zero. They interpreted this as evidence of optimal learning (ie neither under- nor over- correction of performance based on iterated error feedback). The difference may be explained by the fact that van Beers’ task used an explicit target whilst Nourrit-Lucas’ task lacked any explicit target (merely asking participants to, in effect, “do their best” in making full and fast oscillations).

The most impressive element of the Nouritt-Lucas study is not emphasised in the paper – the expert group are recruited from a group that was trained on the task 10 years previously. In Nourrit-Lucas et al (2013) she shows that despite the ten year gap the characteristic movement pattern of experts (that damped van der Pol oscillation) is retained – a truly impressive lab demonstration of the adage that you “don’t forget how to ride a bike [or equivalently complex motor task]”.


Delignieres, D., & Marmelat, V. (2013). Degeneracy and long-range correlations. Chaos: An Interdisciplinary Journal of Non-linear Science, 23, 043109.

Nourrit-Lucas, D., Tossa, A. O., Zélic, G., & Delignières, D. (2015). Learning, Motor Skill, and Long-Range Correlations. Journal of motor behavior, (ahead-of-print), 1-8.

Nourrit-Lucas, D., Zelic, G., Deschamps, T., Hilpron, M., & Delignieres, D. (2013). Persistent coordination patterns in a complex task after 10 years delay: How validate theold saying “Once you have learned how to ride a bicycle, you never forget!” Human Movement Science, 32, 1365–1378. doi:10.1016/j.humov.2013.07.005

van Beers, R. J., van der Meer, Y., & Veerman, R. M. (2013). What autocorrelation tells us about motor variability: Insights from dart throwing. PloS one, 8(5), e64332.

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