Forward and Backward Propagation in Deep Learning

Forward Propagation:

Forward propagation refers to the process of computing the output of a neural network for a given input. It involves passing the input data through the network’s layers in a sequential manner, with each layer performing two main operations: linear transformation and activation.

1. Linear Transformation:
   • In each layer of the neural network (except for the input layer), the input data is transformed using a linear operation. This operation involves computing the dot product of the input data (or activations from the previous layer) with a set of weights, and adding a bias term.
   • Mathematically, this can be represented as: 𝑧=𝑊𝑥+𝑏z=Wx+b, where 𝑧z is the output of the linear transformation, 𝑊W is the weight matrix, 𝑥x is the input data, and 𝑏b is the bias vector.
2. Activation Function:
   • After the linear transformation, the output 𝑧z is passed through an activation function, which introduces non-linearity into the network.
   • Common activation functions include ReLU (Rectified Linear Unit), sigmoid, tanh (hyperbolic tangent), and softmax (used in the output layer for classification).
   • The output of the activation function becomes the input to the next layer in the network.
3. Output Prediction:
   • The process of linear transformation followed by activation is repeated for each layer of the network until the final output layer is reached.
   • The output of the final layer represents the predicted output of the network for the given input data.

Backward Propagation:

Backward propagation, also known as backpropagation, is the process of computing gradients of the loss function with respect to the parameters (weights and biases) of the network. It involves propagating the error backwards through the network and updating the parameters to minimize the loss.

1. Compute Loss:
   • First, the loss between the predicted output and the true target is computed using a loss function such as mean squared error (MSE) for regression or cross-entropy loss for classification.
2. Backpropagate Error:
   • Starting from the output layer, the gradient of the loss with respect to the output activations is computed using the chain rule of calculus.
   • The gradient is then propagated backwards through the network, layer by layer, computing the gradients of the loss with respect to the activations and parameters of each layer.
3. Update Parameters:
   • Once the gradients of the loss with respect to the parameters of the network are computed, the parameters are updated using an optimization algorithm such as gradient descent.
   • The parameters are adjusted in the direction that minimizes the loss, with the learning rate controlling the size of the updates. (Machine Learning Course in Pune)
4. Iterate:
   • The process of forward and backward propagation is repeated for multiple iterations (epochs), with the parameters gradually adjusted to minimize the loss on the training data.

Training Process:

During the training process, forward and backward propagation are alternated to iteratively update the parameters of the network and improve its performance on the training data. The goal is to minimize the loss function by learning the optimal parameters that best fit the training data while generalizing well to unseen data. After training, the network can be used to make predictions on new input data. (Machine Learning Training in Pune)

Overall, forward and backward propagation are fundamental processes in training neural networks and are key components of deep learning algorithms. They enable the network to learn from data and make accurate predictions on a wide range of tasks.