Definition: Gradient descent is an optimization algorithm used to minimize the loss function in machine learning models, including neural networks.

Purpose: It aims to find the optimal set of model parameters (weights and biases) that minimize the error or loss.

How It Works:

1. Initialization: Start with an initial set of parameters.
2. Compute Gradients: Calculate the gradient of the loss function with respect to each parameter. This involves computing the partial derivatives of the loss function.
3. Update Parameters: Adjust the parameters in the direction opposite to the gradient to reduce the loss. The update rule is typically: $$ \theta := \theta - \eta \nabla L(\theta) $$ where ( \theta ) represents the parameters, ( \eta ) is the learning rate, and ( \nabla L(\theta) ) is the gradient of the loss function with respect to the parameters.
4. Iteration: Repeat the process until the parameters converge to the minimum loss or for a fixed number of iterations.

Variants:

• Batch Gradient Descent: Uses the entire dataset to compute the gradient.
• Stochastic Gradient Descent (SGD): Uses one training example at a time to compute the gradient.
• Mini-Batch Gradient Descent: Uses a subset of the dataset (mini-batch) to compute the gradient.

Relationship Between Gradient Descent and Backpropagation

• backpropagation is used to efficiently compute the gradients of the loss function with respect to the network parameters.

• Gradient Descent uses these gradients to update the parameters in order to minimize the loss function.