Convolutional neural network (CNN)

A convolutional layer slides a set of learned kernels, typically 3 × 3 or 5 × 5 spatially and spanning all input channels, across the input and computes a dot product at each position, producing one feature map per kernel. Strictly, deep-learning libraries implement cross-correlation rather than flipped convolution, which makes no difference once the weights are learned. The output width follows (W − K + 2P) / S + 1 for input width W, kernel size K, padding P and stride S. Two structural priors make the design efficient: local connectivity (each output depends only on a small receptive field) and weight sharing (the same kernel is used at every position), which gives translation equivariance and cuts the parameter count by orders of magnitude compared with a fully connected layer. Pooling or strided convolution downsamples the maps, adding a limited degree of translation invariance and letting deeper layers see larger regions; stacking two 3 × 3 layers gives a 5 × 5 receptive field with fewer parameters, the insight behind VGG (2014).

The lineage runs from LeCun et al.'s 1989 zip-code reader trained with backpropagation, through LeNet-5 (1998) for cheque reading, to AlexNet (Krizhevsky, Sutskever and Hinton, 2012), which won ILSVRC 2012 with a top-5 error of 15.3 % against 26.2 % for the runner-up, using ReLU activations, dropout and training on two GPUs. ResNet (He et al., 2015) added identity shortcut connections so that networks of 152 layers could be trained without degradation, and batch normalisation (2015) stabilised training. MobileNet-style depthwise separable convolutions reduce cost for phones and embedded devices, and U-Net (2015) introduced the encoder-decoder with skip connections that became standard for medical segmentation and later for the denoising network in many diffusion models.

Since the Vision Transformer (Dosovitskiy et al., 2020), which splits an image into 16 × 16 patches and applies self-attention, the relationship has been one of trade-offs rather than replacement. CNNs build in locality and so learn well from smaller datasets; ViTs have weaker inductive bias, need more data or pretraining, but model global context from the first layer. ConvNeXt (2022) showed that a CNN modernised with transformer-era training recipes is competitive again, and many production systems use hybrids.

Known failure modes include sensitivity to small adversarial perturbations, a documented bias towards texture rather than shape on ImageNet-trained models, and poor transfer when camera, lighting or scanner differs from training data, which matters in medical imaging and road inspection alike. Convolutions are also used in one dimension for audio and time series and in three for volumetric scans, so "CNN" describes the weight-sharing operation, not the image domain.