Learning and Remapping in the Sensory Motor System. F.A. Mussa-Ivaldi Northwestern University. In natural arm movements, complex motions of the joints lead to simple hand kinematics. From Morasso 1981. Is the shape of trajectories the byproduct of dynamic optimization?.
From Morasso 1981
Is the shape of trajectories the byproduct of dynamic optimization?
(Uno, Kawato and Suzuky, 1989)
Shadmehr & Mussa-Ivaldi, 1994
The shape of trajectories is not a by-product of dynamic optimization.
It reflects and is consistent with the Euclidean properties of ordinary space
Geometry, from a physical standpoint is the totality of the laws according to which rigid bodies mutually at rest can be placed with respect to each other… “Space” in this interpretation is in principle an infinite rigid body – or skeleton - to which the position of all other bodies is related.”
A. Einstein, 1949
Signals spaces, configuration spaces, state spaces, feature spaces, etc...
It is a common misconception that the visual system provides the primal information about this symmetry.
Glove Talk. Sidney Fels and Geoffrey Hinton, 1990
2 Screen Coordinates
F.A. Mussa-Ivaldi, S. Acosta, R. Scheidt, K.M. Mosier
The subjects learn to solve an ill-posed inverse problem (from cursor location to hand gesture) and in doing so, they learn the geometrical structure of the map, i.e. a specific partition of degrees of freedom.
A better map
A bad map
The interaction of human and machine learning: Co-Adaptation by Least Mean Squares
1)Set an arbitrary starting map:
Endpoint vector dim(x) =2
“Body” vector dim(h)=20
2) Collect movements toward a set of K targets:
Movements (endpoint coordinates)
Movements (body coordinates)
3) Calculate the error (in endpoint coordinates)
For each movement
For a whole test epoch
4) Calculate the gradient of the error (w.r.t. A)
5) Update the A-matrix in the direction of the gradient
4) Repeat from step 2 until convergence.
Sensory-Motor Cognition IS NOT an oxymoron !