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Summary: Supplementary Note
Perceptron Learning and Capacity.
The perceptron13
is a node that makes a binary decision by thresholding a weighted sum of its
N inputs. For convenience, in this Supplementary Note we denote the decision variables by
{0, 1} and not by and as in the paper. The inputs are given by a vector x = (x1, . . . , xN ),
where each component is a single scalar that can be interpreted as the firing rate of an afferent
neuron. Thus, the decision of the perceptron is given by
=
N
i=1
ixi - , (1)
where is the Heaviside step function, i denotes the weight of the i-th input component and is
the decision threshold.
A labeled pattern consists of an input vector x and a scalar y {0, 1} that denotes the desired
output for this input. Given a set of p labeled patterns {(xµ
, yµ
)|µ = 1, . . . , p}, the perceptron
learning rule consists of the following synaptic changes: For each input pattern xµ
for which the
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