Page 38 - Rapid Learning in Robotics

24 Artificial Neural Networks

x
x 1
1
w y
i1 1
w x
x i2 y 2
2 Σ i y
x 3 w i3 x 3 2
w
i
1 1
input hidden output
a) b) layer layer layer

Figure 3.1: (a) The McCulloch-Pitts neuron “fires” (output y i =1 else 0) if the
weighted sum P j w ij x j of its inputs x j reaches or exceeds a threshold w i . If this
binary threshold function is generalized to a non-linear sigmoidal transfer func-
tion g P j w ij x j w i (also called activation,or squashing function, e.g. g =tanh ),
the neuron becomes a suitable processing element of the standard (b) Multi-Layer
Perceptron (MLP). The input values x i are made available at the “input layer”.
The output of each neural unit is feed forward as input to all neurons of the next
layer. In contrast to the standard or single-layer perceptron, the MLP has typi-
cally one or several, so-called hidden layers of neurons between the input and the
output layer.