Post on 28-Mar-2015
Learning and Remapping in Learning and Remapping in the Sensory Motor Systemthe Sensory Motor System
F.A. Mussa-Ivaldi Northwestern University
In natural arm movements, complex In natural arm movements, complex motions of the joints lead to simple motions of the joints lead to simple hand kinematicshand kinematics
From Morasso 1981
Is the shape of trajectories the byproduct of dynamic optimization?
(Uno, Kawato and Suzuky, 1989)
Kinematic AdaptationKinematic Adaptation
Flanagan and Rao (1995)
Dynamic AdaptationDynamic Adaptation
Unperturbed movements
Shadmehr & Mussa-Ivaldi, 1994
Perturbing fieldPerturbing field
rF
1.112.11
2.111.10
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Note: there is no force at rest 0)r(
AdaptationAdaptation
After-effects
Transport of a spring-mass Transport of a spring-mass objectobject
Dingwell, Mah and Mussa-Ivaldi (2004)
Post-adaptation kinematics
Baseline
Initial response
The shape of trajectories is not a by-product of dynamic optimization.
It reflects and is consistent with the Euclidean properties of ordinary space
What is space ?What is space ? Intuitive Concept
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 Less Intuitive
ConceptsSignals spaces, configuration spaces, state spaces, feature spaces, etc...
Ordinary SpaceOrdinary Space
Euclid
Pythagoras
Two equivalent statements
?180o
x
yd 222 yxd
Euclidean SymmetryEuclidean SymmetryAmong all possible norm only the L2 (Euclidean) norm is invariant under rigid transformations (e.g. rotations, translations).
Size does not depend upon position and orientation.
xxx T 2Euclidean (L2) Norm
1AATOrthogonal transformation
Axy
21
2
xxxAxAx
AxAxyyy
TT
TTT
Signal spacesSignal spaces
Neither the visual nor the motor signals spaces are Euclidean.
Yet, we perceive Euclidean symmetry and we coordinate motor commands to control independently movement amplitude and direction
•It is a common misconception that the visual system provides the primal information about this symmetry.
•In fact it is likely for the opposite to be true: we learn the properties of space through active perception
Is the bias toward Euclidean symmetry a guiding principle for the emergence of new motor programs?
The motor system can reassign The motor system can reassign degrees of freedom to novel tasksdegrees of freedom to novel tasks
Glove Talk. Sidney Fels and Geoffrey Hinton, 1990
Vocabulary Sam-I-am
The properties of space are captured by the motor system when forming novel motor programs whose purpose is to control the motion of an endpoint
19 SIGNALS (Hand Configuration)
2 Screen Coordinates
F.A. Mussa-Ivaldi, S. Acosta, R. Scheidt, K.M. Mosier
Remapping Remapping SpaceSpace
The taskThe task The subject must place the cursor
corresponding to the hand inside a circular target
Experiment begins with the cursor inside a target.
New target is presented – Cursor is suppressed.
The subject must try to make a single rapid movement of the fingers so as to place the (invisible) cursor inside the new target and stop.
As the hand is at rest after this initial movement, the cursor reappears
The subject corrects by moving the cursor under visual guidance inside the target
Only the initial open loop movement is analyzed
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Some examplesSome examples
Weird task. Cannot be represented before the experiment
Body and task endpoint are physically uncoupled
Only feedback pathway is vision Dimensional imbalance Metric imbalance
Some observationsSome observations
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or
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Single Subject
Endpoint errorEndpoint error
LinearityLinearity
S
E
A
B
Aspect-Ratio: AB/SE
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Asp
ect
Ratio
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0.65 EnsembleSingle Subject
•Cursor movements DO NOT become straighter !
Extended training Extended training 4 consecutive days 2 groups of subjects No-Vision subjects (P2) just engage in the
task for 4 days Vision subjects (P3) train with continuous
visual feedback trials. But they are tested in the same no-vision condition as the other group.
The two groups receive the same amount of training
Extended Training ResultsExtended Training Results Both group have the same learning trend. Continuous visual feedback of endpoint movements
facilitates the formation of straighter open-loop trajectories
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Err
or (
cm)
P2 (No Vision)P3 (Vision)
1 2 3 4
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ect R
atio
•Error reduction and straightening of motion are independent processes
•Straightening of motion is facilitated when vision and movement execution are concurrent
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.
Decomposition of Glove Decomposition of Glove SignalsSignals
CFBCBF
PQA
BF
)()(
)(
)( 1
ATIAN
AAAT
AAAA
n
TT
0
Component" Space-Task")(
Component" Space-Null")(
TNT
TN
T
N
hh
hhh
hATh
hANh
1 2 3 4140
160
180
200
220
240
Day
Nu
ll M
otio
n (
G.S
.U.)
1 2 3 460
70
80
90
100
110
120
Day
Ta
sk M
otio
n (
G.S
.U.)
P2 (No Vision)P3 (Vision)
Task-space and Null-space Task-space and Null-space MotionMotion
↓19%↓24%
↓20% ↓23%
Importing a metric Importing a metric structurestructure
•Identify Residual Control Signals (Movements, EEG, EMG, Multiunit…)
•Form a first “vocabulary” of commands (faster, slower, right, left, MIDI, etc…)
•Machine learns to respond appropriately
•Patient practice and leans new commands
Practical Applications:Practical Applications:Body-Machine Interfaces Body-Machine Interfaces (BMI)(BMI)
Interface
DUAL LEARNING
Sensing garments (Smartex -Pisa)
•52 smeared sensors on lycra
•No metallic wires
•External connection realized by metallic press stud
Calibration: Find optimally Calibration: Find optimally controlled DOFs (synergies) controlled DOFs (synergies) by dimensionality reductionby dimensionality reduction
Natural Synergies -> Control Natural Synergies -> Control ParametersParameters
A bad map A better map
Tonal SpacesTonal Spaces
The interaction of human and machine learning: Co-Adaptation by Least Mean Squares
The interactive LMS procedure - The interactive LMS procedure - 1 1
1) Set an arbitrary starting map:
hAx
Endpoint vector dim(x) =2 “Body” vector dim(h)=20
The interactive LMS procedure - The interactive LMS procedure - 2 2
2) Collect movements toward a set of K targets:
Kxxx ˆ,,ˆ,ˆ 21
Kxxx ,,, 21
Khhh ,,, 21
Targets
Movements (endpoint coordinates)
Movements (body coordinates)
The interactive LMS procedure - The interactive LMS procedure - 3 3
3) Calculate the error (in endpoint coordinates)
iii xAxe ˆ)(
K
i
iTi eeE1
2 )(
For each movement
For a whole test epoch
The interactive LMS procedure - The interactive LMS procedure - 4 4
4) Calculate the gradient of the error (w.r.t. A)
k
i
Tii heA
E
1
2
)(2
5) Update the A-matrix in the direction of the gradient
A
EAA
2
4) Repeat from step 2 until convergence.
An ExampleAn Example
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Training Epoch #
Nor
mal
ized
End
poin
t E
rror
Per
Mov
emen
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Updated mappings do not occuruntil after the dashed linebetween epochs 5 and 6
ConclusionConclusion
Sensory-Motor Cognition IS NOT
an oxymoron !