Understanding Automatic Differentiation
Automatic differentiation (AD), also known as algorithmic differentiation, is a technique used to efficiently compute the derivatives of mathematical functions. AD plays a crucial role in training neural networks by enabling efficient computation of gradients, which are essential for optimizing the network parameters. In the larger picture of neural network training, automatic differentiation facilitates the following key steps:
Forward Propagation: During forward propagation, the input data flows through the neural network layers, and intermediate activations are computed for each layer. Automatic differentiation captures and records the operations performed during this process, creating a computational graph.
Loss Calculation: After the forward propagation, the network’s output is compared to the true labels, and a loss function quantifies the discrepancy between them. The loss function provides a measure of how well the network is performing.
Backward Propagation: This is where automatic differentiation truly shines. It automatically computes the gradients of the loss function with respect to the network’s parameters. The chain rule is applied to efficiently calculate these gradients by traversing the computational graph in reverse order. This process is known as backward propagation or backpropagation.
Gradient Descent: Once the gradients are obtained, optimization algorithms like gradient descent are employed to update the network’s parameters. These updates nudge the parameters in a direction that minimizes the loss function and improves the network’s performance.
Iterative Training: The forward-backward-propagation cycle is iteratively repeated for a certain number of epochs or until convergence. In each iteration, the network’s parameters are adjusted based on the computed gradients, gradually improving the model’s accuracy.
Generalization and Evaluation: Once the model is trained, it is evaluated on unseen data to assess its performance and generalization ability. The gradients obtained during training using automatic differentiation are no longer necessary during this evaluation phase.
Overall, automatic differentiation simplifies the process of computing gradients in neural networks, enabling efficient training and optimization. It is a fundamental technique that underlies the success of deep learning and has greatly contributed to the advancement of the field.
