Rates of learning and the dynamic pattern approach

One of the interesting features of coordinated rhythmic movement is that people start out with a particular pattern to their performance - there is pre-existing structure to our attempts to coordinate these movements. This structure affects our ability to learn new coordinations, and the pattern of the effects reveals a lot about the cause of this pre-existing structure. 

However, the literature is split into two incompatible accounts of learning, and trying to fix this is part of my ongoing interest in this task. The first account is the dynamic pattern approach, which was pioneered by JAS Kelso, and championed by modelling (Gregor Schöner) and behavioural studies (Pier Zanone). I'm more interested in the latter aspect, because it's the motivation for the former. I've already reviewed how this account fails, but it's still alive and well thanks to some creative history, and needs to be tackled again. The second account, which I prefer, is the perception-action account (Bingham) which developed from empirical work on visual and proprioceptive perception as well as action measures, and embodied in a model.

We haven't explicitly tackled the rate of learning issue, although we will and there is already support for our account in the literature (Wenderoth et al, 2002). But it comes up regularly in the dynamic pattern behavioural work, so it's time to work out what's going on in their data.

Predictions of the dynamic pattern approach

Zanone & Kelso (1994) published a book chapter summarising the work so far and laying out the dynamic pattern approach. In it, they made a specific prediction:

...learning rate should vary inversely with the stability of the closest intrinsic attractor to the required pattern.

Zanone & Kelso, 1994, pp 482

In other words, learning a novel coordination closer to 0° should be harder than learning one close to 180°, because the stronger attractor at 0° will interfere more with the learning process. This is not what occurs; in fact, Fontaine et al (1997) and Wenderoth et al (2002) found the exact opposite pattern and suggested that this reflects people's ability to perceive the required information - the region around 0° is more readily discriminated, which is the root cause of it being so stable.

It seems straight-forward: the dynamical pattern hypothesis makes a clear and straight forward prediction and two papers have shown the prediction is incorrect, plus the perception-action account can readily explain the result. Case closed, surely. 

Well, no. The dynamic pattern approach is still motivating empirical work. Zanone now frames the discussion of learning in terms of stability: learning a novel coordination near a stable state (e.g. 0°) is more likely to persist in memory because stable is better than unstable. Zanone now regularly replicates the result that learning, say, 45° is easier than learning 135° but claims it supports the predictions of the dynamic pattern approach, based in stability.

This move happened, as far as I can tell, in a paper by Kostrubiec & Zanone (2002). The authors first claim (incorrectly) that the dynamic pattern approach predicts that competition between stable states and novel coordinations being learned varies with distance such that competition is weakest when the distance is small. This is the exact opposite of the actual prediction, quoted above and which they cite as if it supports the claim. It also makes no sense: a stable state is, in dynamical systems terms, an attractor, and the ability of an attractor to influence a system's behaviour can only decrease with distance. This misrepresentation of their past work is a real concern, although later papers acknowledge the original prediction (and then claim the dynamic pattern approach still explains what actually happens).
 

As an initial attempt to attack this empirically, Kostrubiec & Zanone (2002) attempted to measure learning, memory and interference using three different tasks during training:

1. Learning: this involved attempting to move at the target relative phase, paced by a visual metronome (either 90°, 135° or 158°, which are 90°, 45° and 22° away from 180°, respectively). This assessed the effect of distance from an attractor (although it ignores the asymmetry in attractor strength between 0° and 180°).
2. Memory: this task was called synchronisation-continuation, and involved moving for 10s with the metronome on then 20s with it off; the latter part tests memory for the pattern being learned.
3. Interference: this involved moving at a currently stable relative phase other than the one being learned. If you were currently learning 135°, you were prompted (with an 8s demo) to move at, say, 90°. I think this is the case; the methods are entirely unclear at this point. I believe the idea was to measure how hard it was to produce a recently learned phase in the middle of learning another one. 

The results of this messy fishing trip were, predictably, an incoherent mess.

1. Effects of the various manipulations on movement accuracy (absolute error, AE) were confounded with variation in movement stability (standard deviation of the AE). This is a problem with these studies, because movement stability is not independent of mean performance, and you can produce a stable movement by not accurately producing the difficult condition you are being asked to make. We fixed this by moving to a 'time-on-task' measure of movement stability; I'll blog the details of that measure soon as it will come in handy later.
2. Training continued until people's movement stability with the metronome on reached a criterion. However, it's clear from the data that in the absence of the metronome performance was terrible, so it's not at all clear anyone has learned anything. While pre- and post-training performance across a wide range of relative phases was measured, only the baseline data are reported.
3. Rate of learning was longest for 135°, so it was not linearly related to distance from 180°. This makes little sense, and possibly comes from the fact that people had to learn the three different relative phases in order. 

The interpretation of the data is all framed within the incorrect description of the dynamic pattern predictions, and the model fit presented in Figure 2 is, I'm pretty certain, a data fitting exercise, not a prediction of the model. This is only an educated guess because the model fit procedure is not described, but the HKB model doesn't really have any way to produce that figure without data. 

Summary

There's more results to go over in future posts, but while the methods get tighter and the reporting of past work less shoddy, the pattern is going to be the same as here: with no actual mechanism at work, there is nothing constraining the explanation of the data and everything, no matter how it works out, fits the model.  'Stability' doesn't explain anything, because it can be used to explain everything. Without a mechanism, these experiments are just data-fitting exercises; my goal is, of course, to explain the data with reference to the model.

References

Fontaine, R., Lee, T., & Swinnen, S. (1997). Learning a new bimanual coordination pattern: Reciprocal influences of intrinsic and to-be-learned patterns. Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale, 51 (1), 1-9 DOI: 10.1037/1196-1961.51.1.1

Kostrubiec, V., & Zanone, P. (2002). Memory dynamics: distance between the new task and existing behavioural patterns affects learning and interference in bimanual coordination in humans. Neuroscience Letters, 331 (3), 193-197 DOI: 10.1016/S0304-3940(02)00878-9

Wenderoth N, Bock O, & Krohn R (2002). Learning a new bimanual coordination pattern is influenced by existing attractors. Motor control, 6 (2), 166-82 PMID: 12122225

Zanone, P.G., & Kelso, J.A.S. (1994). The coordination dynamics of learning: Theoretical structure and experimental agenda. In S.P. Swinnen, H. Heuer, J. Massion, & P. Casaer (Eds.), Interlimb coordination: Neural, dynamical, and cognitive constraints (pp. 461-490). San Diego, CA: Academic Press.