Backpropagation is a widely used algorithm for computing the gradient of a loss function with respect to the parameters of a computational graph. It allows us to efficiently update the parameters during the training process of a neural network.

  In a computational graph, each node represents an operation or function, and the edges represent the flow of computations between nodes. Each node takes inputs from its parent nodes, performs a specific operation on them, and produces an output.

  During forward propagation, the inputs are fed through the graph, and each node computes and passes its output to the next nodes until the final output is obtained. This process allows us to compute the loss or error between the network's predictions and the true labels.

  During backpropagation, the derivatives of the loss function with respect to the parameters are calculated by propagating the gradients backwards through the graph. The key idea is to use the chain rule of derivatives to compute these gradients efficiently.

  We start by initializing the gradients of the parameters to zero. Then, we traverse the graph in the reverse order of the forward propagation, from the output to the input nodes. At each node, we compute the derivative of the output with respect to its inputs and accumulate the gradients of the parameters.

  The derivative of the output with respect to the inputs of a node can be obtained by multiplying the gradient flowing from the following nodes (computed during the previous backpropagation step) with the derivative of the node's operation.

  This process continues until we reach the input nodes, where we have computed the gradients of the loss function with respect to the parameters. These gradients are then used to update the parameters of the graph using an optimization algorithm such as stochastic gradient descent.

  By iteratively performing forward and backward propagation, the graph's parameters are updated, gradually reducing the loss function and improving the performance of the model.

  Overall, backpropagation in a computational graph efficiently computes the gradients of the parameters using the chain rule and enables the training of complex models like neural networks.