Simple mathematical model
for a neuron
Invented by Rosenblatt in the 1960
A perceptron is a function
defined by 2 functions g: Rn
and t: R
per f(x) = t(g(x)). R
is the set
of real numbers
g is called the summation function and t is called the activation/transfer function.
Usually g(x) is the inner product of x with a weight vector w minus a real threshold value theta; g(x) = < x,w> - threshold
t can be any monotonic
function, but usually bounded
ness is demanded. Very often the sign
function is used.
Perceptrons were believed to be very powerful in the 1960s, until Minsky and Papert proved in their book "Perceptrons" that a single perceptron (with the sign function) can't solve the XOR problem.
Note that often authors use the above example for g, the sign function for t and regard other functions for t as non-perceptrons.