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Integral expressing the amount of overlap of one function as it is shifted over another
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f {\displaystyle f} and g {\displaystyle
Convolution
Theorem in mathematics
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the
Convolution_theorem
Type of feedforward neural network
A convolutional neural network (CNN) is a type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep
Convolutional_neural_network
Topics referred to by the same term
mathematics, convolution is a binary operation on functions. Circular convolution Convolution theorem Titchmarsh convolution theorem Dirichlet convolution Infimal
Convolution_(disambiguation)
Mathematical operation on arithmetical functions
In mathematics, Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory
Dirichlet_convolution
Neural network technology
neural networks, a convolutional layer is a type of network layer that applies a convolution operation to the input. Convolutional layers are some of
Convolutional_layer
Mathematical operation
Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that
Circular_convolution
Type of error-correcting code using convolution
represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates
Convolutional_code
Matrix used in image processing to alter an image
In image processing, a kernel, convolution matrix, or mask is a small matrix used for blurring, sharpening, embossing, edge detection, and more. This
Kernel_(image_processing)
Mathematical concept
space of convolution quotients is a field of fractions of a convolution ring of functions: a convolution quotient is to the operation of convolution as a
Convolution_quotient
Probability distribution of the sum of random variables
The convolution/sum of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that
Convolution of probability distributions
Convolution_of_probability_distributions
scale convolution of two functions s ( t ) {\displaystyle s(t)} and r ( t ) {\displaystyle r(t)} , also known as their logarithmic convolution or log-volution
Logarithmic_convolution
Mathematical operation in signal processing
discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space. It is also a special case of convolution on
Multidimensional discrete convolution
Multidimensional_discrete_convolution
Algorithm to smooth data points
distorting the signal tendency. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree
Savitzky–Golay_filter
Method for visualizing vector fields
In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field (such as fluid motion) at high spatial resolutions
Line_integral_convolution
Mathematical inequality about the convolution of two functions
In mathematics, Young's convolution inequality is a mathematical inequality about the convolution of two functions, named after William Henry Young. In
Young's convolution inequality
Young's_convolution_inequality
Convolution
category theory, Day convolution is an operation on functors that can be seen as a categorified version of function convolution. It was first introduced
Day_convolution
Method in signal processing
the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal x [ n ] {\displaystyle x[n]} with a finite impulse
Overlap–add_method
The Titchmarsh convolution theorem describes the properties of the support of the convolution of two functions. It was proven by Edward Charles Titchmarsh
Titchmarsh convolution theorem
Titchmarsh_convolution_theorem
Function in discrete mathematics
partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since the DFT deals with a finite amount
Discrete_Fourier_transform
Method in signal processing
is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal x [ n ] {\displaystyle x[n]} and a finite
Overlap–save_method
Artificial reverberation effect
electromechanical transducers to create vibrations in large plates of sheet metal. Convolution reverb uses impulse responses to record the reverberation of physical
Reverb_effect
Free convolution is the free probability analog of the classical notion of convolution of probability measures. Due to the non-commutative nature of free
Free_convolution
convolution is a special subset of convolution operations in which the convolution kernel is symmetric across its zero point. Many common convolution-based
Symmetric_convolution
Mathematical concept
In mathematics, the convolution power is the n-fold iteration of the convolution with itself. Thus if x {\displaystyle x} is a function on Euclidean space
Convolution_power
In mathematics, negacyclic convolution is a convolution between two vectors x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\dots ,x_{n})} and
Negacyclic_convolution
Class of artificial neural networks
implement different flavors of message passing, started by recursive or convolutional constructive approaches. A 2022 position paper argued that many architectures
Graph_neural_network
Convolutional neural network structure
LeNet is a series of convolutional neural network architectures created by a research group at AT&T Bell Laboratories between of the period of 1988 to
LeNet
Family of computer vision models designed for efficient inference on mobile devices
MobileNet is a family of convolutional neural network (CNN) architectures designed for image classification, object detection, and other computer vision
MobileNet
Extension of cubic spline interpolation
accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing, bicubic interpolation is often chosen
Bicubic_interpolation
science, a convolutional deep belief network (CDBN) is a type of deep artificial neural network composed of multiple layers of convolutional restricted
Convolutional deep belief network
Convolutional_deep_belief_network
Decodes a bitstream with the Viterbi algorithm
that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example
Viterbi_decoder
Influential 2012 deep convolutional neural network
AlexNet is a convolutional neural network architecture developed for image classification tasks, notably achieving prominence through its performance
AlexNet
section of the beam. However, convolution can be used in certain cases to improve computational efficiency. In order for convolution to be used to calculate
Convolution for optical broad-beam responses in scattering media
Convolution_for_optical_broad-beam_responses_in_scattering_media
Discrete Fourier transform for prime sizes
a cyclic convolution (the other algorithm for FFTs of prime sizes, Bluestein's algorithm, also works by rewriting the DFT as a convolution). Since Rader's
Rader's_FFT_algorithm
2026 Marvel Studios film
focus on Peter, though he criticized occasional pacing issues and plot convolutions. David Ehrlich at IndieWire gave the film a C−, describing it as a "dull
Spider-Man:_Brand_New_Day
Type of artificial neural network
consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e
Residual_neural_network
Family of convolutional neural networks
Inception is a family of convolutional neural network (CNN) for computer vision, introduced by researchers at Google in 2014 as GoogLeNet (later renamed
Inception (deep learning architecture)
Inception_(deep_learning_architecture)
Function which maps a tuple of sequences into a sequence of tuples
In computer science, zipping is a function which maps a tuple of sequences into a sequence of tuples. This name zip derives from the action of a zipper
Zipping_(computer_science)
Mathematical transform
of graph structured learning algorithms, such as the widely employed convolutional networks. Given an undirected weighted graph G = ( V , E ) {\displaystyle
Graph_Fourier_transform
Gyrus of the primary auditory cortex of the brain
temporal gyrus, also called Heschl's gyrus (/ˈhɛʃəlz ˈdʒaɪrəs/) or Heschl's convolutions, is a gyrus found in the area of each primary auditory cortex buried
Transverse_temporal_gyrus
Function whose graph is 0, then 1, then 0 again, in an almost-everywhere continuous way
{\sin(\pi af)}{\pi af}}=a\ \operatorname {sinc} _{\pi }{(af)}.} The self convolution of the dis-continuous rectangular function results in the triangular
Rectangular_function
Integral transform and linear operator
The Hilbert transform is given by the Cauchy principal value of the convolution with the function 1 / ( π t ) {\displaystyle 1/(\pi t)} (see § Definition)
Hilbert_transform
Mathematical model which is both linear and time-invariant
found directly using convolution: y(t) = (x ∗ h)(t) where h(t) is called the system's impulse response and ∗ represents convolution (not to be confused
Linear_time-invariant_system
Topics referred to by the same term
products, bounding the product of two quantities Young's convolution inequality, bounding the convolution product of two functions Young's inequality for integral
Young's_inequality
Series of convolutional neural networks for image classification
The VGGNets are a series of convolutional neural networks (CNNs) developed by the Visual Geometry Group (VGG) at the University of Oxford. The VGG family
VGGNet
Reconstruction of a filtered signal
In mathematics, deconvolution is the inverse of convolution. Both operations are used in signal processing and image processing. For example, it may be
Deconvolution
Aspect of probability theory
distribution. Addition of random variables, on the other hand, are the convolution of their probability distributions. Let X and Y be independent random
Sum of normally distributed random variables
Sum_of_normally_distributed_random_variables
Generalization of the Legendre transformation
functions. The infimal convolution of two functions has a geometric interpretation: The (strict) epigraph of the infimal convolution of two functions is
Convex_conjugate
Directional cubic convolution interpolation (DCCI) is an edge-directed image scaling algorithm created by Dengwen Zhou and Xiaoliu Shen. By taking into
Directional cubic convolution interpolation
Directional_cubic_convolution_interpolation
Objects that generalize functions
possible to define the convolution of a function with a distribution, or even the convolution of two distributions. Convolution of a test function with
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Concept in machine learning
parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights
Tensor_(machine_learning)
In statistics, the Hájek–Le Cam convolution theorem states that any regular estimator in a parametric model is asymptotically equivalent to a sum of two
Hájek–Le Cam convolution theorem
Hájek–Le_Cam_convolution_theorem
distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact
List of convolutions of probability distributions
List_of_convolutions_of_probability_distributions
Signal (re-)construction algorithm
theorem article, which points out that it can also be expressed as the convolution of an infinite impulse train with a sinc function: x ( t ) = ( ∑ n =
Whittaker–Shannon interpolation formula
Whittaker–Shannon_interpolation_formula
Transformation of a mathematical sequence
under the binomial convolution. There is also another binomial convolution in the mathematical literature. The binomial convolution of arithmetical functions
Binomial_transform
of the symbol so the linear convolution of a frequency-selective multipath channel can be modeled as circular convolution, which in turn may transform
Cyclic_prefix
Square matrix of cyclically shifted rows
operations. Algebraically, multiplication by a circulant matrix is circular convolution on the cyclic group Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z}
Circulant_matrix
Fitting an approximating function to data
a matrix transformation is called convolution. Thus the matrix is also called convolution matrix or a convolution kernel. In the case of simple series
Smoothing
Type of convolutional neural network
U-Net is a convolutional neural network that was developed for image segmentation. The network is based on a fully convolutional neural network whose
U-Net
Deep learning model structure
multilayer perceptron networks, these layers are stacked together. The Convolutional layer is typically used for image analysis tasks. In this layer, the
Layer_(deep_learning)
Integration kernels for smoothing out sharp features
smooth functions approximating nonsmooth (generalized) functions, via convolution. Intuitively, given a (generalized) function, convolving it with a mollifier
Mollifier
Concept in the solution of linear partial differential equations
the most important case, directly linked to the possibility of using convolution to solve an arbitrary right hand side — was shown by Bernard Malgrange
Fundamental_solution
Response of an optical system to a point source of light
everywhere in the imaging space, the image of a complex object is then the convolution of that object and the PSF. The PSF can be derived from diffraction integrals
Point_spread_function
Computational model used in machine learning
weight patterns of multiple nodes. Architectural innovations such as convolutional neural networks (CNNs) significantly improved performance in computer
Neural network (machine learning)
Neural_network_(machine_learning)
Mathematical theorem on convolved binomial coefficients
In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients: ( m + n r ) = ∑ k = 0 r (
Vandermonde's_identity
Type of parallel computing architecture of tightly coupled nodes
convolution. Similarly, n-dimensional convolution can be computed by an n-dimensional array of PEs. Many other implementations of the 1D convolutions
Systolic_array
Concept in mathematics
specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis
Cauchy_product
Computer scientist (born 1986)
With Alex Krizhevsky and Geoffrey Hinton, he co-created AlexNet, a convolutional neural network. One of the most highly cited computer scientists in
Ilya_Sutskever
Covariance and correlation
and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation
Cross-correlation
Formal power series
integral transformations Knuth's article "Convolution Polynomials" defines a generalized class of convolution polynomial sequences by their special generating
Generating_function
Device for suppressing part of a signal
the behavior of the filter as a convolution of the time-domain input with the filter's impulse response. The convolution theorem, which holds for Laplace
Filter_(signal_processing)
Distance function defined between probability distributions
y ) {\displaystyle f(x)=\inf _{y}d(x,y)-g(y)} , making it an infimal convolution of − g {\displaystyle -g} with a cone. This implies f ( x ) − f ( y )
Wasserstein_metric
Mathematical algorithm
obtain the convolution of a and b, according to the usual convolution theorem. Let us also be more precise about what type of convolution is required
Chirp_Z-transform
Rational mathematical function indexed by integer partitions
In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of products of matrix
Weingarten_function
Matrix with shifting rows
be represented by such a matrix. Similarly, one can represent linear convolution as multiplication by a Toeplitz matrix. Toeplitz matrices are asymptotically
Toeplitz_matrix
Fourier analysis technique applied to sequences
} The significance of this result is explained at circular convolution and fast convolution algorithms. S 2 π ( ω ) {\displaystyle S_{2\pi }(\omega )}
Discrete-time Fourier transform
Discrete-time_Fourier_transform
Neurological factors responsible for intelligence
[dubious – discuss] The folding of the brain's surface, known as cortical convolution, has become more pronounced throughout human evolution. It has been suggested
Neuroscience_and_intelligence
Type of machine learning model
Yanming (2021). "Review of Image Classification Algorithms Based on Convolutional Neural Networks". Remote Sensing. 13 (22): 4712. Bibcode:2021RemS..
Large_language_model
Branch of machine learning
connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and
Deep_learning
Filter in electronics and signal processing
systems. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass
Gaussian_filter
Serial concatenated convolutional codes (SCCC) are a class of forward error correction (FEC) codes highly suitable for turbo (iterative) decoding. Data
Serial concatenated convolutional codes
Serial_concatenated_convolutional_codes
Deep learning framework
Caffe (Convolutional Architecture for Fast Feature Embedding) is a deep learning framework, originally developed at University of California, Berkeley
Caffe_(software)
Functions in harmonic analysis mathematics
1)} estimates. A singular integral of convolution type is an operator T {\displaystyle T} defined by convolution with a kernel K {\displaystyle K} that
Singular_integral
Object detection system
Once (YOLO) is a series of real-time object detection systems based on convolutional neural networks. First introduced by Joseph Redmon et al. in 2015, YOLO
You_Only_Look_Once
Study of the properties of codes and their fitness
the output of the system convolutional encoder, which is the convolution of the input bit, against the states of the convolution encoder, registers. Fundamentally
Coding_theory
Signal-processing procedure
without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input
Blind_deconvolution
Type of imaging sensor
arbitrary convolution kernel around the event coordinate in an array of integrate-and-fire pixels. Extension to multi-kernel event-driven convolutions allows
Event_camera
distributions says that every probability distribution P admits (in the convolution semi-group of probability distributions) a factorization P = P 1 ⊗ P
Khinchin's theorem on the factorization of distributions
Khinchin's_theorem_on_the_factorization_of_distributions
idempotent measure on a metric group is a probability measure that equals its convolution with itself; in other words, an idempotent measure is an idempotent element
Idempotent_measure
Family of functions in mathematics
{\displaystyle F_{n}(x)\geq 0} with average value of 1 {\displaystyle 1} . The convolution F n {\displaystyle F_{n}} is positive: for f ≥ 0 {\displaystyle f\geq
Fejér_kernel
Mathematical form
\mathrm {d} \tau } is well defined and is called the convolution. Under the Fourier transform, convolution becomes point-wise function multiplication. The
Product_(mathematics)
American mathematician (b. 1949)
doctoral dissertation was titled "Inequalities for strongly singular convolution operators". Fefferman achieved a full professorship at the University
Charles_Fefferman
2017 research paper by Google
generate the output. Since the Transformer does not rely on recurrence or convolution of the text in order to perform encoding and decoding, the paper relied
Attention_Is_All_You_Need
Image edge detection algorithm
∗ {\displaystyle *} here denotes the 2-dimensional signal processing convolution operation. In his text describing the origin of the operator, Sobel shows
Sobel_operator
1884 paper "Observations on the relation of the principal fissures and convolutions of the cerebrum to the outer surface of the scalp" introduced what would
Robert_William_Reid
Neural network coding model
The convolutional sparse coding paradigm is an extension of the global sparse coding model, in which a redundant dictionary is modeled as a concatenation
Convolutional_sparse_coding
Image scaling algorithm
and other types of photos. waifu2x was inspired by Super-Resolution Convolutional Neural Network (SRCNN). It uses Nvidia's CUDA for computing, although
Waifu2x
High-performance forward error correction codes
processing. The first class of turbo code was the parallel concatenated convolutional code (PCCC). Since the introduction of the original parallel turbo codes
Turbo_code
Image dataset
created, students were paid to label all of the images. Various kinds of convolutional neural networks tend to be the best at recognizing the images in CIFAR-10
CIFAR-10
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