Are Internal Models of the Entire Body Learnable?
Aaron D'Souza, Sethu Vijayakumar and Stefan Schaal
Abstract of poster presented at the Annual Meeting of the Society for
Neuroscience, Vol. 27, Program No. 406.2, (2001).
Recent research has provided increasingly more evidence for the existence
of internal models in biological motor control - either as forward models
or inverse models. In the most visionary theories, internal models of the
entire body dynamics and kinematics are required to accomplish motor competence.
However, from a statistical learning viewpoint, the acquisition of such large
internal models is very complex due to the hundreds of (possibly irrelevant/redundant)
input dimensions from various afferent and efferent sources - a similar
problem as faced by the cerebellum. To assess the learnability of such large-scale
internal models, we used a variety of advanced statistical tools, including
mixtures of factor analyzers, local singular value decomposition, and local
projection regression, to analyze full-body human movement data from several
subjects collected using a special full-body exoskeleton that records 35
joint angles of the human body at 100Hz. Our analyses of the local dimensionality
of the human data in the context of a full-body inverse dynamics model
confirmed that the 105-dimensional input space (35 position, velocity,
and acceleration dimensions) could be locally compressed to about 5 to
10 dimensions. Such locally low dimensional distributions can be efficiently
exploited by neural network learning, suggesting that full-body internal
models are indeed learnable. We discuss reasons for the existence of low
dimensional distributions of movement data in the context of known invariances
of movement behavior, including the minimum jerk/torque-change hypothesis,
the 2/3 power law, smoothness of movement, and rhythmic pattern generation.