Chapter 2. Prehension

Appendix C - Computational Neural Modelling 399
object ‘key’ was seen by this network, it would compute what posture
to form as follows:
[ ;:; : 1.8 4 E] [ 2.4
-0.6 gOR] [i] =
From our list of vectors representing firing rates of the output
neurons, we see that this is side opposition. The reader can check to
see that the other input patterns will produce the desired output
patterns. These input patterns were chosen because the vectors are
orthonormal. Vectors that are orthogonal have a dot product equal to
zero. Orthonomal vectors are orthogonal and also have a magnitude
of 1. We can see that the number of stimulus/response vector pairs is
limited by the size of the weight matrix. Nonlinear networks are more
powerful, robust, and don’t have the orthonormal constraint.
C.5 Summary
The power of a computational model using a neural network
architecture is that the model can generalize from a few sample points.
With a distributed representation, graceful degradation can occur; as
well, local computations can be performed.
Adaptive models can learn. Using supervised learning, it would
be similar to a child learning to grasp: the fist time the child tries to
grasp a heavy toy, some posture is chosen, and the toy drops from her
hand. Failure in the task tells the brain that parameters, such as
muscle set or the chosen posture, were chosen incorrectly, and
adjustments are made so that success is more likely the next time.
Modification can be made to either the parameter values or to the
selection of the parameters; e.g., using more fingers to provide more
force, or realizing that the texture of the object surface is important in
choosing a grasp. Repeated trials allow the correct setting of
parameters, until a successful grasp is selected, and even generalized
from. This allows the child to eventually start picking up objects that
she has never intereacted with before.
Artificial neural networks can be trained on real-world examples,
and then they can generalize to solving arbitrary instances within their
problem space. In adaptive neural nets, invariances can be learned,
and encoded within the network, both in its topology and within the
strengths of synaptic connections between the neurons. Other types