A practical overview of backpropagation

Multilayer perceptrons learn from training data through a process called backpropagation. The process can be described as a way of progressively correcting mistakes as soon as they are detected. Let's see how this works.

Remember that each neural network layer has an associated set of weights that determines the output values for a given set of inputs. In addition to that, remember that a neural network can have multiple hidden layers.

In the beginning, all the weights have some random assignment. Then the net is activated for each input in the training set: values are propagated forward from the input stage through the hidden stages to the output stage where a prediction is made (note that we have kept the following diagram simple by only representing a few values with green dotted lines, but in reality, all the values are propagated forward through the network):

Since we know the true observed value in the training set, it is possible to calculate the error made in prediction. The key intuition for backtracking is to propagate the error back and use an appropriate optimizer algorithm, such as a gradient descent, to adjust the neural network weights with the goal of reducing the error (again for the sake of simplicity, only a few error values are represented):

The process of forward propagation from input to output and backward propagation of errors is repeated several times until the error gets below a predefined threshold. The whole process is represented in the following diagram:

The features represent the input and the labels are here used to drive the learning process. The model is updated in such a way that the loss function is progressively minimized. In a neural network, what really matters is not the output of a single neuron but the collective weights adjusted in each layer. Therefore, the network progressively adjusts its internal weights in such a way that the prediction increases the number of labels correctly forecasted. Of course, using the right set features and having a quality labeled data is fundamental to minimizing the bias during the learning process.