Tuesday 7 September 2010

Learning a Novel Coordination - The Dynamic Pattern Hypothesis

Other coordination posts are here.

Recall this image:
The HKB potential function, ~1Hz
This basic layout is supposed to describe an intrinsic state of affairs, namely that only 0°and 180°are stable coordinations (+/- 180° are identical except for which limb is lagging and which is leading). If you look at this function, you will see that potential energy is a maximum at +/90; this suggests that 90°is a maximally unstable coordination (i.e. it takes the most energy to maintain and is susceptible to perturbations which will make behaviour 'run off' towards one or other attractor). This is indeed the case, empirically; people can do it but fail to respond to the inevitable errors that accumulate and they lose the coordination very rapidly.

The question then is: can you learn to move at 90°? Is this dynamic pattern modifiable by experience?
If you're a drummer of any kind, you'll already know the answer: yes, but it's hard. The first people to look at learning were Pier Zanone and Scott Kelso, and they were interested in the consequences of learning across the space of possible coordinations. How is this dynamic modified by experience? 

They developed a straight-forward methodology. First, they needed a feedback method, because people can't maintain 90° without help long enough to learn anything about it. They settled on the visual metronome, two displays of pairs of LEDs which flashed in the required pattern (e.g. the two top LEDs would light at the same time, and then the bottom two at the same time, to pace 0°). The participant's job was to match the flexion and extension of their fingers to these metronomes (one per finger) and thus reproduce the requested relative phase at a requested frequency.

This then enabled them to pace any given relative phase, which allowed them to a) train one relative phase (e.g. 90°) and then b) scan through all relative phases from 0° to 180° to see whether stability there had changed. These scans would provide them with a snapshot of the current actual shape of the potential function at various moments during training.

What they found was the following:
  1. Training at 90° seemed to 'drain' resources from the entire landscape, but especially from 180°. Movement stability there decreased during training but then recovered by the end. 
  2. The effect of training at 90° was the creation of a third attractor centred there. Zanone & Kelso described this as a phase transition, a qualitative change in the underlying dynamics. They hypothesised that this phase transition required resources from the existing dynamic to be created, hence the temporary loss of stability at 180° while the system reorganised itself.
  3. This new-found ability to move at 90° only generalised to -90° (or 270°), the symmetry partner of the trained location that only differs in terms of which limb is leading or lagging. Zanone & Kelso took this to be evidence that what was being learned was an abstract control dynamic, not a specific pattern of limb movement.
They then tested some variants. For example, some participants come to the lab already able to do 90° - Zanone & Kelso trained these people to do, for example, 135° and scanned the resulting dynamic. This experiment revealed that the attractor at 90° moved to centre itself over 135°; three attractors seems to be the limit! They also tested their hypothesis about the abstract nature of the control dynamic being learned, by showing that learning a 90° phase relation between an arm and the opposite leg generalised to the other combination - this supported their hypothesis, that what was learned was an abstract control dynamic that could simply be plugged into any limb combination.

The Dynamic Pattern Hypothesis
These results lead to what has been the dominant theoretical approach to coordinated rhythmic movement, the dynamic pattern hypothesis. This approach claims the following:
  1. The HKB model describes the intrinsic dynamic of this task; this layout exists in the background and structures all attempts to produce a coordination. This structure in behaviour is a function of relative phase, which can thus be treated as an order parameter.
  2. 0° and 180° are attractors, i.e. preferred states of the system that draw other states towards them.0° is a stronger attractor than 180°.
  3. Learning these other states involves competing against these preferred states. 
    1. PREDICTION: learning close to 0° will be harder than learning close to 180° because the stronger pull of 0° will interfere more with the process of learning.
  4. The result of learning is a new attractor; this qualitative change in the shape of the intrinsic dynamics is a phase transition.
Next time...
There remains a problem that this approach has failed to address: why is the intrinsic dynamic the shape that it is? And what happens when you test the prediction in 3.1?


  1. Do you have any opinions on the Amazeen work suggesting that the preferred coordination mode is shifted from 0° as a function of handeness? So lefties prefer (or default to) a slight left hand lead, while righties prefer a slight right hand lead.

  2. The basic phenomena emerge from the coordination requirement, specifically, but the final stability of any given movement emerges from the interplay between this and the limb dynamics, etc. I don't know the specific paper you're mentioning, but there are certainly effects on the stability of a specific movement from things like handedness, etc. The other literature from this UConn group is the effect of detuning: coordinating pendulums with different preferred frequencies moves the layout around without altering the basic shape, for example.

    Spoiler alert - I think the dynamic pattern approach is entirely wrong :) These posts are just laying out the groundwork. I certainly want to get to these sorts of details because they help motivate a fully perception-action approach, which is of course what I will advocate.

  3. Why do you think the dynamic pattern approach is entirely wrong? I can't specifically find your arguments against it other than that it is a description rather than an explanation.

    1. The next posts in this series address this. The dynamic pattern description makes incorrect predictions about learning rates which reveal that the attractor dynamics emerge from a system in which perception of relative phase provides most of the structure (see the model post).