Chapter 2. Prehension

Chapter 4 - Planning of Prehension 97
Information from each retina is converted into four orientation maps
using a convolution functions. By convolving the retinal map with
one of four orientation masks (0", 45", 90°, 135 ), raw intensity values
are converted into orientation responses similar to the occular domi-
nance columns that have been noted in visual cortex (Hubel & Wiesel,
1968). A disparity map, in the middle of Figure 4.13, is created by
using a simple function that combines pairs of orientation maps, creat-
ing a layer of binocular neurons like those found in visual cortex
(Poggio & Fischer, 1977). Together, the left and right orientation
maps and the disparity map become part of the inputs to Kuperstein's
adaptive neural network.
On the bottom right of Figure 4.13, the rest of the inputs into the
network are seen. These come from the twelve eye muscles, six for
the left eye and six for the right eye. Kuperstein recodes these propri-
oceptive signals into a unimodal distribution of activity over 100 neu-
rons, creating a gaze map for each eye and one for disparity. In each
of the three gaze maps, 600 neurons encode the eye-muscle signal into
a representation that has a peak at a different place depending on the
activity of the muscles. This conversion puts the inputs into a higher
dimensional space, one that is linearly independent.
The top half of Figure 4.13 shows the hetero-associative memory.
This part of the network associates the visual inputs (disparity and ori-
ent maps) and eye-muscle activation (gaze maps) with an arm configu-
ration. At the top of the figure, the arm is represented by ten muscles
(three pairs of shoulder muscles and two pairs of elbow muscles).
For this adaptive computation, Kuperstein uses the delta learning rule
(see Appendix C) to adjust the weights by comparing the arm muscle
values computed by the current settings of the weights to the actual
arm muscle values. Using the delta learning rule, he computes the dif-
ference between these and adjusts the weights so that the difference
will be reduced. It took 3000 trials to learn the inverse kinematics to
within a 4% position error and 4" orientation error. On each trial, the
arm was place in a random configuration.
Kuperstein used supervised learning for modifying the weights in
the adaptive neural network. Kuperstein generated arm muscle set-
tings and compared them to the values produced by the network.
When they did not agree, he modified the weights so that the next time
the eyes saw that arm configuration, the computed arm muscle settings
5A convolution function simulates the response of a system in which the local
effects of inputs may be spread over time and space in the output, e.g., blurring of
a lens, echoing of sounds in a room.