18.1. Backpropagation and Neural Network Training: What is Backpropagation
Backpropagation is a fundamental method in training neural networks, especially in deep learning architectures. This method is responsible for adjusting the synaptic weights of a neural network in order to minimize the difference between the output predicted by the network and the expected output, that is, the error. Backpropagation is applied after forward propagation, where input signals are passed through the network to generate an output.
To understand backpropagation, it is important to first understand the concept of gradient. The gradient is a vector that points in the direction of the greatest increase in a function. In terms of neural networks, we are interested in the gradient of the error in relation to the network weights, as we want to know how to adjust the weights to reduce the error. Backpropagation actually calculates these gradients efficiently using differential calculus, in particular the chain rule.
The backpropagation process begins with calculating the error at the network output. This error is generally calculated as the difference between the network's predicted output and the actual (or expected) output, often using a cost function such as Cross Entropy or Mean Square Error. Once the error has been calculated, the next step is to propagate it back through the network, from the last layer to the first, updating the weights in each layer as the error passes through them.
Weights are updated according to the gradient descent update rule, where the current weight is adjusted in the opposite direction to the gradient of the error with respect to that weight. Mathematically, this is expressed as:
W = W - η * (∂E/∂W)
Where W is the current weight, η is the learning rate, and ∂E/∂W is the gradient of the error E with respect to the weight W. The learning rate is a hyperparameter that determines the size of the step we take towards the minimum error. If the learning rate is very large, we may exceed the minimum; if it is too small, training may be very slow or stuck in local minima.
The calculation of the gradient of the error in relation to the weights is where the chain rule comes in. For a network with multiple layers, the error of a layer depends on the weights of that layer, but also on the weights of subsequent layers. The chain rule allows you to calculate these dependencies in order to determine how the error in one output layer affects the weights in a previous layer.
An important aspect of backpropagation is the concept of automatic differentiation, which is a technique that allows you to calculate gradients efficiently. Instead of manually calculating the partial derivatives of each weight, modern deep learning libraries like TensorFlow and PyTorch use automatic differentiation to calculate these gradients quickly and accurately.
In addition, there are several variants and improvements of the gradient descent method, such as stochastic gradient descent (SGD), Moment, Adagrad, RMSprop, and Adam. These methods seek to accelerate convergence and avoid problems such as local minima and saddle points.
In summary, backpropagation is an essential algorithm for learning neural networks. It allows us to adjust the weights of a network in a way that minimizes output error, and is one of the reasons why deep learning has been so successful in a variety of complex tasks, from image recognition to natural language processing. even games and robotics. A deep understanding of backpropagation is crucial for anyone who wants to work seriously with neural networks and deep learning.
