Implementing a neural network from scratch involves designing its architecture, defining the forward and backward propagation, and optimizing weights through gradient descent. Start by initializing weights and biases, ensuring proper initialization to prevent vanishing or exploding gradients.
Forward propagation computes predictions by passing inputs through layers, applying weights and biases, and using activation functions like ReLU or sigmoid. Backpropagation calculates gradients of the loss function with respect to weights using the chain rule, allowing updates through an optimization algorithm like gradient descent.
Libraries like NumPy can assist in matrix operations, but implementing the model manually helps understand the core principles. Testing on small datasets ensures correctness before scaling up to more complex problems.