Convolutional Neural Networks, or CNNs, are specialized deep learning models designed for processing grid-like data, particularly images. They use mathematical operations including convolution, activation functions, pooling, and matrix multiplication to automatically extract features from input data and make accurate predictions.
The convolution operation is the mathematical foundation of CNNs. A small filter or kernel slides across the input image, performing element-wise multiplication with the overlapping region, then summing the results. This process extracts local features like edges, corners, and textures from the input data.
After convolution, activation functions like ReLU introduce non-linearity by setting negative values to zero. This allows the network to learn complex, non-linear patterns. Pooling operations then reduce the spatial dimensions by taking the maximum or average value from small regions, providing computational efficiency and translation invariance.
The final stage involves fully connected layers. First, the 2D feature maps are flattened into a 1D vector. This vector is then processed through dense layers using matrix multiplication and bias addition. The final layer often uses softmax activation to produce probability distributions for classification tasks.
Training CNNs involves backpropagation and gradient descent. The network makes predictions in the forward pass, then calculates error using a loss function. Gradients are computed through calculus, flowing backward through the network. Finally, weights are updated using these gradients to minimize the loss and improve accuracy.