Chapter 2. Prehension

Appendix C - Computational Neural Modelling 3 8 5
Figure C.l McCulloch-Pitts neuron vs Leaky Integrator.
Activation is on the X axis and output is on the Y axis. For the
leaky integrator, several values of t are shown. See text for
details
u(t+l) = u(t) + du = u(t) + (-u(t) + I) = I (2)
which is precisely the McCulloch-Pitts unit. The advantage of using
the leaky integrator model is that it provides a continuous time model
of the neural network.
Each neuron has a state, or activation level. An activation function
is a deterministic function that computes a neuron’s state as a function
of the neuron’s input. The strength of the connection from one neuron
to another can be attenuated or enhanced through the use of a weight,
which represents the synaptic strength. Weights on the inputs adjust
the influence of the input. The activation function for a McCulloch-
Pitts neuron is:
where the activity of each input into neuron i is multiplied by an
associated weight wij (the strength of connection between neuron i
and neuron j) and these products are summed to produce the activation
of that neuron. Positive weights represent excitatory connections;
negative weights inhibitory ones. The state of activation is actually
time-varying (i.e., ai(t)), so that the state of the system can be
represented at any time t. An activation of zero usually means that the
neuron is inactive. Activation functions can be discrete (mapping the
inputs to a binary value or a small and limited set of values) or