Gradient Descent: Optimizing the Weights

Once backpropagation calculates gradients (the direction and magnitude of error), gradient descent uses this information to update the network's weights. It's the algorithm that actually implements learning by taking small, carefully calibrated steps toward better performance.

Imagine being blindfolded in hilly terrain and trying to reach the lowest point. Gradient descent works by feeling which direction is downhill (the gradient) and taking a step in that direction. This process repeats until you reach a valley where no direction leads further down.

The learning rate controls how large each step should be – too large and you might overshoot the valley, too small and training becomes painfully slow. Several variations of gradient descent exist, including Batch Gradient Descent (using all examples before updating), Stochastic Gradient Descent (SGD, updating after each example), and Mini-batch Gradient Descent (updating after small batches, combining the benefits of both).

Modern optimizers like Adam, RMSprop, and AdaGrad enhance basic gradient descent by incorporating adaptive learning rates and momentum. These sophisticated algorithms help navigate the complex error landscapes of deep networks, avoiding local minima and accelerating convergence toward optimal solutions.