In a neural network, the weights and biases are updated through a process called backpropagation. Backpropagation is a supervised learning algorithm that allows the network to adjust its weights and biases in order to minimize the difference between the predicted output and the actual output.

  The update of weights and biases in a neural network is based on the gradient descent optimization algorithm. Here are the steps involved in updating weights and biases:

  1. Forward Propagation: The input data is fed through the network, and the computations are performed layer by layer. Each neuron in the network calculates its weighted sum of inputs, applies an activation function, and passes the output to the next layer. This process continues until the final output is obtained.

  2. Loss Calculation: The difference between the predicted output and the actual output is calculated using a cost function or loss function. The commonly used loss functions are mean squared error (MSE) for regression problems and cross-entropy loss for classification problems.

  3. Backward Propagation: The error or loss is propagated backward through the network. The partial derivatives of the loss with respect to each weight and bias are calculated using the chain rule of calculus. This information is used to determine the sensitivity of the loss to changes in the weights and biases.

  4. Gradient Calculation: The gradients of the loss with respect to the weights and biases are calculated for each neuron. These gradients indicate the direction and magnitude of the steepest ascent of the loss function.

  5. Weight and Bias Update: The weights and biases are updated using the gradients calculated in the previous step. The learning rate is multiplied by the gradient to determine the step size in the update. The weights and biases are adjusted in the opposite direction of the gradient, so as to minimize the loss function.

  6. Repeat: Steps 1 to 5 are repeated for each data point in the training set, allowing the network to learn from multiple examples and refine its weights and biases.

  The process of updating weights and biases is repeated over multiple iterations or epochs until the network converges to a satisfactory solution, where the loss is minimized. This optimization process ensures that the network learns to make more accurate predictions based on the training data.