Preliminaries ‘An Introduction to Backpropagation and Multilayer Perceptrons’ ‘The Backpropagation Algorithm’ Speed Backpropagation up 1 BP algorithm has been described in ‘An Introduction to Backpropagation and Multilayer Perceptrons’. And the implementation of the BP algorithm has been recorded at ‘The Backpropagation Algorithm’. BP has worked in many applications for many years, but there are too many drawbacks in the process. The basic BP algorithm is too slow for most practical applications that it might take days or even weeks in training....

Preliminaries Calculus 1,2 Linear Algebra Batch v.s. Incremental Training1 In both LMS and BP algorithms, the error in each update process step is not MSE but SE \(e=t_i-a_i\) which is calculated just by a data point of the training set. This is called a stochastic gradient descent algorithm. And why it is called ‘stochastic’ is because error at every iterative step is approximated by randomly selected train data points but not the whole data set....

Preliminaries An Introduction to Backpropagation and Multilayer Perceptrons Culculus 1,2 Linear algebra Jacobian matrix Architecture and Notations1 We have seen a three-layer network is flexible in approximating functions(An Introduction to Backpropagation and Multilayer Perceptrons). If we had a more-than-three-layer network, it could be used to approximate any functions as accurately as we want. However, another trouble that came to us is the learning rules. This problem almost killed neural networks in the 1970s....

Preliminaries Performance learning Perceptron learning rule Supervised Hebbian learning LMS Form LMS to Backpropagation1 The LMS algorithm is a kind of ‘performance learning’. And we have studied several learning rules(algorithms) till now, such as ‘Perceptron learning rule’ and ‘Supervised Hebbian learning’. And they were based on the idea of the physical mechanism of biological neuron networks.
Then performance learning was represented. Because of its outstanding performance, we go further and further away from natural intelligence into performance learning....