convolutional

Convolutional refers to the convolution operation, a fundamental mathematical tool used to combine two functions to produce a third function. In continuous time, the convolution involves integrating the product of one function with a shifted version of another. In discrete settings, it becomes a sum over products of input samples and a kernel or filter. Convolution is commutative, associative, and linear, and it links to Fourier analysis through the convolution theorem.

In signal processing, convolution is used to apply linear time-invariant systems to signals. A finite impulse response filter or kernel is convolved with a signal to emphasize certain features, such as smoothing, sharpening, or edge detection. In image processing, two-dimensional convolutions apply kernels across height and width to produce feature maps that reflect local patterns in the data.

In machine learning and computer vision, convolutional commonly refers to convolutional neural networks (CNNs). A CNN uses convolutional layers that apply learnable filters to input data, producing feature maps that capture local patterns. The filters slide, or convolve, across the input with a defined stride and padding, enabling local connectivity and parameter sharing. These properties provide translation equivariance and reduced parameter counts, aiding learning on high-dimensional data. Nonlinear activation functions and pooling layers often follow convolutional layers to introduce nonlinearity and reduce spatial resolution.

History and variants: the underlying convolution operation originated in mathematical analysis and became central to signal processing in the 20th century. In deep learning, CNNs were popularized in the 1990s and have since become foundational for image, audio, and video tasks. Variants include dilated, depthwise separable, and transposed convolutions, each addressing specific architectural goals.