The Delta Rule, also known as the Widrow-Hoff rule, is a fundamental principle in the field of artificial intelligence and neural networks. It is a method used to minimize the error between the predicted output and the actual target output during the training of a model. The Delta Rule is particularly important in supervised learning, where a model learns from labeled input data.
In essence, the Delta Rule updates the weights of a neural network by calculating the difference, or ‘delta’, between the expected output (target value) and the actual output produced by the network. This error is then used to adjust the weights of the connections in the network to improve accuracy. Mathematically, the weight update can be expressed as:
wnew = wold + η * δ * x
where:
wnewis the updated weight.woldis the current weight.η(eta) is the learning rate, which determines how much the weights should be adjusted.δis the error term, calculated as the difference between the actual output and the target output.xis the input value associated with the weight being updated.
The Delta Rule emphasizes the importance of adjusting weights in the direction that reduces the error, thereby improving the model’s performance over time. This process is repeated iteratively across many training samples, allowing the neural network to learn complex patterns and make accurate predictions.