feed-forward neural networks training neural network let' now look at how neural network is trained figure - illustrates training neural network assuming the same notation as earlierwe denote by th the collection of all the weights and bias terms of all the layers of the network let us assume that th has been initialized with random values we denote by fnn the overall function representing the neural network as previously mentionedwe can take single data point and compute the output of the neural network as we can also compute the disagreement with the actual output using the loss function yy that islfnn(xth)ylet' now compute the gradient of this loss function and denote it by lfnn(xth)ywe can now update th using steepest descent as ths ths lfnn(xth) )where denotes single step note that we can take many such steps over different data points in our training set over and over again until we have reasonably good value for lfnn(xth)ynote for nowwe will stay away from the computation of gradients of loss functions (fnn(xth)ythese can be generated using automatic differentiation (covered elsewhere in the bookquite easily (even for arbitrary complicated loss functionsand need not be derived manually