Gradients play a central role in training neural networks by guiding the optimization process. During training, the goal is to adjust the network’s parameters (weights and biases) to minimize a loss function, which measures how well the model’s predictions match the actual data. Gradients—mathematical vectors representing the partial derivatives of the loss with respect to each parameter—indicate the direction and magnitude of changes needed to reduce the loss. Without gradients, there would be no systematic way to update the parameters effectively. For example, in a simple linear layer, the gradient for a weight tells you whether increasing or decreasing that weight would lower the prediction error for a given input.
Gradients are calculated using backpropagation, which efficiently computes the derivatives through the chain rule from calculus. Starting at the output layer, the algorithm computes the gradient of the loss with respect to the final layer’s parameters and works backward through the network. This process leverages the structure of the network to reuse intermediate computations, avoiding redundant calculations. For instance, in a convolutional neural network (CNN), gradients for the filters in early layers depend on gradients from deeper layers, propagating error signals backward to adjust edge detectors. Optimizers like stochastic gradient descent (SGD) or Adam then use these gradients to update the parameters, scaling them by a learning rate to control step sizes.
A key challenge in gradient-based training is handling vanishing or exploding gradients, which occur when gradients become too small or too large as they propagate backward. For example, in deep networks with sigmoid activations, repeated multiplication of small derivatives during backpropagation can cause gradients to vanish, stalling learning in early layers. Solutions include using activation functions like ReLU (which avoids squashing gradients for positive inputs), techniques like batch normalization (to stabilize layer outputs), or architectures like LSTMs (which use gating mechanisms to preserve gradient flow). Developers often monitor gradient magnitudes during training to diagnose issues—such as saturated neurons or unstable learning—and adjust the model or optimizer settings accordingly.