A computational graph is a graphical representation of a mathematical function that allows us to track gradients. It is commonly used in deep learning and optimization algorithms, such as backpropagation.

  In a computational graph, nodes represent mathematical operations or functions, and edges represent the flow of data. Each node takes one or more inputs and produces an output. The output of one node becomes the input of another node, creating a directed acyclic graph (DAG).

  To track gradients in a computational graph, we need to apply the chain rule of calculus. The chain rule allows us to calculate the gradients of complex functions by decomposing them into simpler functions.

  When computing the gradient of a function with respect to a particular variable, we initialize the gradient of that variable as 1. Then, we traverse the computational graph in a reverse order, starting from the output node and moving towards the input nodes. At each node, we calculate the local gradient, which represents the effect of that node on the overall function.

  To calculate the local gradient, we take the derivative of the node's output with respect to its inputs. This can typically be obtained through symbolic differentiation or automatic differentiation techniques. The local gradient is then multiplied by the gradient of the variable that flows into the node, which represents the effect of the overall function on that variable.

  As we traverse the computational graph, we accumulate the gradients by multiplying the local gradients with the incoming gradients. This process is known as backpropagation, and it allows us to efficiently compute the gradients of the entire function with respect to all the variables.

  Once we have obtained the gradients, we can use them for various purposes, such as updating the parameters of a neural network during training using gradient descent optimization.

  In summary, a computational graph allows us to track gradients by applying the chain rule and performing reverse-mode automatic differentiation. By traversing the graph in a reverse order, we can efficiently compute the gradients of a mathematical function with respect to its inputs.