convolutional layer

A convolutional layer is the basic building block of a CNN: a bank of many small learnable filters that all slide over the same input, each producing its own output grid. If one filter is a single pattern detector, a convolutional layer is a whole committee of detectors — one might fire on horizontal edges, another on a particular color blob, another on a corner — and the layer stacks all their answers together. Early layers learn simple patterns (edges, textures); deeper layers, fed by the answers of earlier ones, learn compound patterns (eyes, wheels, text).

Precisely, a 2D convolutional layer maps an input tensor of shape (C_in, H, W) — C_in channels, height H, width W — to an output of shape (C_out, H_out, W_out). It holds C_out filters, each of shape (C_in, k, k), plus one bias per filter. Each filter spans all input channels and produces exactly one output channel (one feature map). The number of learnable parameters is C_out times (C_in times k times k) plus C_out biases — crucially independent of H and W, because the same filter is reused at every spatial position. The spatial output size follows H_out = floor((H + 2P - d(k-1) - 1) / S) + 1, where P is padding, S is stride, and d is dilation (same formula for width).

A layer's behaviour is set by a handful of hyperparameters: kernel size k (how big a neighbourhood each filter sees), number of output channels C_out (how many distinct features to learn), stride S (how far the filter hops, which downsamples), padding P (border handling, which controls output size), and dilation d (gaps in the kernel, which enlarge the receptive field). A convolutional layer is almost never used alone: it is typically followed by a normalization step (such as batch normalization) and a nonlinearity (such as ReLU), and this conv-norm-activation triple is the unit that gets stacked dozens or hundreds of times in architectures like VGG and ResNet.