Delta Learning Rule & Gradient Descent Neural Networks

The development of the perceptron was a big step towards the goal of creating useful connectionist networks capable of learning complex relations between inputs and outputs. In the late 1950's, the connectionist community understood that what was needed for further development of connectionist models was a mathematically-derived (and thus potentially more flexible and powerful) rule for learning. By early 1960's, the Delta Rule [also known as the Widrow & Hoff Learning rule or the Least Mean Square (LMS) rule] was invented by Widrow and Hoff. This rule is similar to the perceptron learning rule by McClelland & Rumelhart, 1988, but is also characterized by a mathematical utility and elegance missing in the perceptron and other early learning rules. The Delta Rule uses the difference between target activation (i.e., target output values) and obtained activation to drive learning.