Chapter 2. Prehension

384 A pp e n dic e s
C.2 Artificial Neural Networks
Artificial neural networks consist of processing units. Each unit
has an activation state and are connected together through synapses’ in
some pattern of connectivity. Rules govern how information is
propated and how learning occurs in the network. The processing
units can represent individual neurons or else concepts (that can either
be individual cells themselves or groups of cells). The issue, more
importantly, for these models is how a computation is performed
without regard so much as to at level it is working. In the next
subsections, we describe some of the decisions that a network
designer must make, and what are the reasons and advantages for
doing so.
C.2.1 Activation functions and network topologies
Different models are used within neural network models for the
processing units. The most common is the McCulloch-PittS type
neuron, where each unit simultaneously takes a weighted sum of its
inputs (dendrites) at each network time step At, and if threshold is
reached, the cell body discharges at a certain firing frequency. The
output of such a neuron is seen in the left side of Figure C.l. If we
consider the weighted sum of a neuron’s incoming signals to be its
input, I, and its state to be u, then a McCulloch-Pitts neuron operates
according to the assignment u = I. The result is then thresholded to
produce its output. An alternative to this discrete model is the leakv
interrrator model, where the neuron’s behavior is described by a frrst-
order linear differential equation:
where z is the unit’s time constant. In simulating such a neuron, z
must be greater than the simulation time step At. As the time constant
approaches the simulation time step, this rule approaches the
McCulloch-Pitts rule. The output of such a neuron is seen in the right
side of Figure C.l. If z = dt, we see that du = -u + I. So, in the
simulation,
‘A synapse is a small separation between the axon (output fiber) of one neuron and the
cell body or fibers of another neuron. A neuron can synapse onto itself as well.