In artificial neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of the primary building blocks of convolutional neural networks (CNNs), a class of neural network most commonly applied to images, video, audio, and other data that have the property of uniform translational symmetry.

The convolution operation in a convolutional layer involves sliding a small window (called a kernel or filter) across the input data and computing the dot product between the values in the kernel and the input at each position. This process creates a feature map that represents detected features in the input.

Kernels, also known as filters, are small matrices of weights that are learned during the training process. Each kernel is responsible for detecting a specific feature in the input data. The size of the kernel is a hyperparameter that affects the network's behavior.

For a 2D input ${\displaystyle x}$ and a 2D kernel ${\displaystyle w}$, the 2D convolution operation can be expressed as:$${\displaystyle y[i,j]=\sum _{m=0}^{k_{h}-1}\sum _{n=0}^{k_{w}-1}x[i+m,j+n]\cdot w[m,n]}$$where ${\displaystyle k_{h}}$ and ${\displaystyle k_{w}}$ are the height and width of the kernel, respectively.

This generalizes immediately to nD convolutions. Commonly used convolutions are 1D (for audio and text), 2D (for images), and 3D (for spatial objects, and videos).

Stride determines how the kernel moves across the input data. A stride of 1 means the kernel shifts by one pixel at a time, while a larger stride (e.g., 2 or 3) results in less overlap between convolutions and produces smaller output feature maps.

Padding involves adding extra pixels around the edges of the input data. It serves two main purposes:

Common padding strategies include: