To simplify the problem it is assumed that the network receives a set
of two-valued inputs, x₁, x₂, ..., xₙ, and is required to produce only
a single two-valued output, y. It is convenient to assign the numerical
quantities +1 and -1 to the two values of each variable.
The simplest network would consist of a single linear threshold
element with a set of weights, c₀, c₁, c₂, ..., cₙ. These determine
the output-input relation or function so that y is +1 or -1 according
as the quantity, c₀ + c₁x₁ + c₂x₂ + ... + cₙxₙ, is positive or not,
respectively. It is possible for such a single element to exhibit an
adaptive behavior as follows. If, for a given set, x₁, x₂, ..., xₙ, the
output, y, is correct, then make no changes to the weights. Otherwise
change the weights according to the equations