define Gradient Descent ?

 Gradient descent is an optimization algorithm used in various fields, including machine learning and mathematical optimization, to minimize a function by iteratively adjusting its parameters. The goal of gradient descent is to find the values of the parameters that result in the lowest possible value of the function.

The key idea behind gradient descent is to update the parameters of a model or system in the direction that leads to a decrease in the function's value. This direction is determined by the negative gradient of the function at the current point. The gradient is a vector that points in the direction of the steepest increase of the function, and taking its negative gives the direction of steepest decrease.

Here's a simplified step-by-step explanation of how gradient descent works:

1. Initialize the parameters of the model or system with some initial values.

2. Compute the gradient of the function with respect to the parameters at the current parameter values.

3. Update the parameters by subtracting a scaled version of the gradient from the current parameter values. This scaling factor is called the learning rate, which determines the step size in each iteration.

4. Repeat steps 2 and 3 until convergence criteria are met (e.g., the change in the function's value or parameters becomes very small, or a predetermined number of iterations is reached).

There are variations of gradient descent, such as stochastic gradient descent (SGD), mini-batch gradient descent, and more, which use subsets of the data to compute gradients, making the process more efficient for large datasets.

Gradient descent is crucial in training machine learning models, where the goal is often to find the optimal values of the model's parameters that minimize a loss function. By iteratively adjusting the parameters based on the negative gradient of the loss function, gradient descent helps models learn from data and improve their performance over time.

What is Gradient descent in deep learning ?

 Gradient descent is an optimization algorithm commonly used in deep learning to train neural networks. It is an iterative method that adjusts the parameters of the network in order to minimize a given loss function. The basic idea behind gradient descent is to find the optimal values of the parameters by iteratively moving in the direction of steepest descent of the loss function.

Here's how the gradient descent algorithm works in the context of deep learning:

1. **Initialization**: The algorithm begins by initializing the weights and biases of the neural network with random values. These weights and biases represent the parameters that determine how the network processes and transforms the input data.

2. **Forward Propagation**: During the forward propagation step, the input data is fed through the network, and the output of each neuron is computed based on the current parameter values. The network's predictions are compared to the true labels using a loss function, which quantifies the error between the predicted and actual outputs.

3. **Backpropagation**: The key to gradient descent is the calculation of gradients, which represent the sensitivity of the loss function with respect to each parameter in the network. Backpropagation is a method used to efficiently compute these gradients. It involves propagating the error gradients from the output layer back to the input layer, while applying the chain rule of calculus to compute the gradients at each layer.

4. **Gradient Calculation**: Once the gradients have been computed using backpropagation, the algorithm determines the direction in which the parameters should be updated to reduce the loss function. The gradient of the loss function with respect to each parameter indicates the direction of steepest ascent, so the negative gradient is taken to move in the direction of steepest descent.

5. **Parameter Update**: The parameters of the network are then updated using the gradients and a learning rate hyperparameter. The learning rate determines the size of the step taken in the direction of the negative gradient. A larger learning rate can lead to faster convergence but risks overshooting the minimum, while a smaller learning rate may converge slowly. There are also variations of gradient descent, such as stochastic gradient descent (SGD) and mini-batch gradient descent, which use subsets of the training data to compute the gradients and update the parameters.

6. **Iteration**: Steps 2 to 5 are repeated iteratively for a specified number of epochs or until the loss function reaches a satisfactory value. Each iteration brings the network closer to finding the optimal set of parameter values that minimize the loss function.

By repeatedly updating the parameters using the computed gradients, gradient descent guides the neural network towards the region of the parameter space that corresponds to lower loss values. This iterative process continues until the algorithm converges to a set of parameters that yield satisfactory predictions on the training data.