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Sensorimotor Learning and the Development of Position Invariance
Muhua Li and James J. Clark
Motivation
Learning Procedure
 Biological: the position invariance property of many higherlevel visual cortex neurons.
Simulation Results
Our techniques are applied to the invariant representation of images
of straight lines. The projection of straight lines in space onto the
spherical retinal surface will form 2D curvatures that vary with
eccentricity.
 Theoretical: the sensorimotor contingency theory of O’Regan
and Noe [1] which holds that perception is based on the laws
relating motor activity and the resulting sensory input.
Main Idea
The position invariance
recognition can be
achieved by learning
the sensorimotor
contingencies
associated with neural
responses from the
lower-level feature
detectors.
In cases with a 10% undershooting probability in the training data:
 Without feedback, the estimated canonical images associate the
undershot stimuli as well as the foveal stimuli with the input
peripheral feature stimuli.
 With feedback, the network is able to discard the disturbance
from the undershot stimuli and make the correct association.
Temporal Difference (TD) Learning Algorithm
Enhanced Algorithm
A TD reinforcement learning algorithm [2] can learn the
sensorimotor contingencies associated with saccadic eye
movements.
Once the association matrix V has been learned, the response of
the network given a peripherally located stimulus P is a
prediction M (the estimated canonical image) of what the
corresponding foveal stimulus would look like: M  V * P
A feedback from the higher-level layer is used to handle cases
where the saccade does not succeed in foveating the target, but
instead undershoots the target, at which point a small corrective
saccade is made.
Conclusion
 Position invariance of higher-level cortical neurons may arise
from a learning of sensorimotor contingencies.
 A TD network as we propose here is able to perform such
learning, and generate the estimated canonical response as would
occur after foveation of a physical stimuli from the activities of
the lower-level visual feature detectors.
Basic Learning Rules
Vij (t )   ( (t )  Vij (t  1)[X j (t )  X j (t  1)]) X j (t )
 X j (t )   ( X j (t )  X j (t  1))
V is the association matrix relating pre- and post-saccadic
stimuli.  is the foveal stimuli (post-motor) as the reinforcement
reward. The pre-motor stimulus X is held in a short-term
memory generating an eligibility trace X , which will be used to
enhance, in a Hebbian fashion, the association to the post-motor
stimulus.
References
The reinforcement reward is composed of both the post-saccade
stimulus and its estimated canonical image, which are weighted by a
confidence:
 (t )   (t )  Vij (t  1) *  (t )
[1] O’Regan, J.K. and Noe, A. “A sensorimotor account of vision
and visual consciousness”, submitted to Behavioral and Brain
Sciences.
[2] Clark, J.J. “Sensorimotor development of position invarianct
feature detectors”, ICPR2002