Learning algorithm for multi-layered networks:

Furthermore details we see that  if S is too high, the contribution from w_i * x_i is reduced. It means that t(E) - o(E) is multiplied by x_i after then if x_i is a big value as positive or negative so the change to the weight will be greater. Here to get a better feel for why this direction  correction works so it's a good idea to do some simple calculations by hand. 

Here η simply controls how far the correction should go at one time that is usually set to be a fairly low value, e.g., 0.1. However the weight learning problem can be seen as finding the global minimum error which calculated as the proportion of mis-categorised training examples or over a space when all the input values can vary. Means it is possible to move too far in a direction and improve one particular weight to the detriment of the overall sum: whereas the sum may work for the training example being looked at and it may no longer be a good value for categorising all the examples correctly. Conversely for this reason here η restricts the amount of movement possible. Whether large movement is in reality required for a weight then this will happen over a series of iterations by the example set. But there sometimes η is set to decay as the number of that iterations through the entire set of training examples increases it means, can move more slowly towards the global minimum in order not to overshoot in one direction.

However this kind of gradient descent is at the heart of the learning algorithm for multi-layered networks that are discussed in the next lecture. 

Further Perceptrons with step functions have limited abilities where it comes to the range of concepts that can be learned and as discussed in a later section. The other one way to improve matters is to replace the threshold function into a linear unit through which the network outputs a real value, before than a 1 or -1. Conversely this enables us to use another rule that called the delta rule where it is also based on gradient descent.