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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
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
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
Triangular array of the binomial coefficients
limit. (The operation of repeatedly taking a convolution of something with itself is called the convolution power.) Pascal's triangle has many properties and
Pascal's_triangle
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
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
Functional relationship between two quantities
additive and reproductive convolution as well as under scale transformation. Consequently, these models all express a power-law relationship between the
Power_law
Data network that uses electrical wiring
rate is 128.6 kbit/s, while its most robust is 21.4 kbit/s. It uses a convolutional code for error detection and correction. The upper layer is usually
Power-line_communication
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
Family of random graph models
{\displaystyle u_{1}^{*n}} denotes the n {\displaystyle n} -fold convolution power. Moreover, explicit asymptotes for w n {\displaystyle w_{n}} are known
Configuration_model
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
Relative importance of certain frequencies in a composite signal
{x}}_{T}(f)|^{2}\,df,} where the integrand defines the power spectral density: The convolution theorem then allows regarding | x ^ T ( f ) | 2 {\displaystyle
Spectral_density
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
Family of computer vision models designed for efficient inference on mobile devices
The depthwise separable convolution decomposes a single standard convolution into two convolutions: a depthwise convolution that filters each input channel
MobileNet
Infinite sum that is considered independently from any notion of convergence
product of the two sequences of coefficients, and is a sort of discrete convolution. With these operations, R N {\displaystyle R^{\mathbb {N} }} becomes
Formal_power_series
Formal power series
function F with a power series expansion such that F(0) = 1. We say that a family of polynomials, f0, f1, f2, ..., forms a convolution family if deg fn
Generating_function
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 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)
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
Eigenvalue algorithm
A.; Allauzen, A. (2023), "Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration", Proceedings of the 40th International Conference
Power_iteration
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
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
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
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
Intelligence of machines
dependencies and are less sensitive to the vanishing gradient problem. Convolutional neural networks (CNNs) use layers of kernels to more efficiently process
Artificial_intelligence
Power spectrum of a noise signal
The sparse nature of velvet noise allows for efficient time-domain convolution, making velvet noise particularly useful for applications where computational
Colors_of_noise
as carrier modulation. To address averse power line channel properties, robustness mechanism convolutional encoding (optional), scrambling and interleaving
PRIME (power-line communication)
PRIME_(power-line_communication)
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
Image-generating machine learning model
models. The "zero convolution" is a 1×1 convolution with both weight and bias initialized to zero. Before training, all zero convolutions produce zero output
Stable_Diffusion
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
Mathematical concept
named after William Henry Young and should not be confused with Young's convolution inequality. Young's inequality for products can be used to prove Hölder's
Young's inequality for products
Young's_inequality_for_products
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
Topics referred to by the same term
the diagonal of a matrix Kernel density estimation, the width of the convolution kernel used in statistics Graph bandwidth, in graph theory Coherence
Bandwidth
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)
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)
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
Concept in Fourier analysis
signals combined by convolution (such as a source and filter) into sums of their cepstra, for linear separation. In particular, the power cepstrum is often
Cepstrum
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
Opposition that a system presents to an acoustic pressure
convolution operator; R is the acoustic resistance in the time domain; G = R−1 is the acoustic conductance in the time domain (R−1 is the convolution
Acoustic_impedance
Integral transform useful in probability theory, physics, and engineering
integral equations with algebraic polynomial equations, and by replacing convolution with multiplication. For example, through the Laplace transform, the
Laplace_transform
Canadian computer scientist
expand the limits in image recognition and classification. Building on Convolutional Neural Networks and Sutskever’s Deep Neural Network approach of deepening
Alex_Krizhevsky
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)
Probability distribution
(named after Woldemar Voigt) is a probability distribution given by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution. It is often
Voigt_profile
\left(\left(n+{\frac {1}{2}}\right)x\right)}{\sin \left({\frac {1}{2}}x\right)}}.} The convolution of any integrable function of period 2 π {\displaystyle 2\pi } with the
List of trigonometric identities
List_of_trigonometric_identities
refinement equation, dilation equation or two-scale equation. Using the convolution (denoted by a star, *) of a function with a discrete mask and the dilation
Refinable_function
Mapping involving integration between function spaces
integration kernels are then biperiodic functions; convolution by functions on the circle yields circular convolution. If one uses functions on the cyclic group
Integral_transform
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
Effect in signal processing
{\displaystyle s(t)} and a Dirac comb function. The spectrum of a product is the convolution between S ( f ) {\displaystyle S(f)} and another function, which inevitably
Spectral_leakage
distribution, a convolution of a normal distribution with an exponential distribution, and the Gaussian minus exponential distribution, a convolution of a normal
List of probability distributions
List_of_probability_distributions
{\phi }}=\sum \limits _{n=0}^{\infty }a_{n}{\frac {\zeta ^{n}}{n!}}} . Convolution in C { ζ } {\displaystyle \mathbb {C} \{\zeta \}} : Let ϕ ^ , ψ ^ ∈ C
Resurgent_function
Semiconductor light source
Stern, Maike Lorena; Schellenberger, Martin (March 31, 2020). "Fully convolutional networks for chip-wise defect detection employing photoluminescence
Light-emitting_diode
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
Branch of machine learning
connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and
Deep_learning
Power series with negative powers
may involve infinite sums which need not converge (one cannot take the convolution of integer sequences). Geometrically, the two Laurent series may have
Laurent_series
Mathematical transform that expresses a function of time as a function of frequency
Borel measures, with multiplication given by convolution of measures. With the convention above, convolution corresponds to operator multiplication with
Fourier_transform
Rational mathematical function indexed by integer partitions
method to systematically calculate the integrals over the unitary group as a power series in 1/d. Let σ = ( 123 ) ( 45 ) ( 6 ) ( 7 ) ( 8 ) {\displaystyle \sigma
Weingarten_function
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
Output of a dynamic system when given a brief input
the convolution of the input with the impulse response. When the transfer function and the Laplace transform of the input are known, this convolution may
Impulse_response
Series of GPUs by Nvidia
ghosting and greater image stability in motion compared to the previous convolutional neural network (CNN) model. DLSS 4 also allows a greater number of frames
GeForce_RTX_50_series
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
Recursive integer sequence
0) to (r,s) that never go above the line ry = sx. The Catalan k-fold convolution is: ∑ i 1 + ⋯ + i k = n i 1 , … , i k ≥ 0 C i 1 ⋯ C i k = k 2 n + k (
Catalan_number
Function whose domain is the positive integers
Here "convolution" does not mean "Dirichlet convolution" but instead refers to the formula for the coefficients of the product of two power series:
Arithmetic_function
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
Probability distribution
{\displaystyle F} , the convolution of F {\displaystyle F} with itself, written F ∗ 2 {\displaystyle F^{*2}} and called the convolution square, is defined
Heavy-tailed_distribution
Multiplication algorithm
n + 1 {\displaystyle 2^{n}+1} ) can be calculated by evaluating the convolution of A , B {\displaystyle A,B} . Also, with g = 2 2 M ′ {\displaystyle
Schönhage–Strassen_algorithm
backpropagation algorithm, as well as recurrent neural networks and convolutional neural networks, renewed interest in ANNs. The 2010s saw the development
History of artificial neural networks
History_of_artificial_neural_networks
Measure of energy loss as sound waves propagate through a medium
relaxation model considers the power law viscosity underlying different molecular relaxation processes. Szabo proposed a time convolution integral dissipative acoustic
Acoustic_attenuation
Arithmetic function related to the divisors of an integer
(s-a-b)}{\zeta (2s-a-b)}},} which is a special case of the Rankin–Selberg convolution. A Lambert series involving the divisor function is: ∑ n = 1 ∞ q n σ
Divisor_function
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
Function equal to the product of its values on coprime factors
function, so called because it is the multiplicative identity for Dirichlet convolution. Sometimes written as u ( n ) {\displaystyle u(n)} ; not to be confused
Multiplicative_function
Type of statistical measure over subsets of a dataset
cumulative, or weighted forms. Mathematically, a moving average is a type of convolution. Thus in signal processing it is viewed as a low-pass finite impulse
Moving_average
Measure of the shape of a function
_{i=0}^{n}{n \choose i}E\left[(x-a)^{i}\right](a-b)^{n-i}.} The raw moment of a convolution h ( t ) = ( f ∗ g ) ( t ) = ∫ − ∞ ∞ f ( τ ) g ( t − τ ) d τ {\textstyle
Moment_(mathematics)
Multiplicative function in number theory
Dirichlet convolution as: 1 ∗ μ = ε {\displaystyle 1*\mu =\varepsilon } where ε {\displaystyle \varepsilon } is the identity under the convolution. One way
Möbius_function
Decomposition of periodic functions
-periodic, and its Fourier series coefficients are given by the discrete convolution of the S {\displaystyle S} and R {\displaystyle R} sequences: H [ n ]
Fourier_series
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
Computational model used in machine learning
units (GPUs), and large datasets. Architectural innovations such as convolutional neural networks (CNNs) significantly improved performance in computer
Neural network (machine learning)
Neural_network_(machine_learning)
Discrete Fourier transform algorithm
algorithm; it also re-expresses a DFT as a convolution, but this time of the same size (which can be zero-padded to a power of two and evaluated by radix-2 Cooley–Tukey
Fast_Fourier_transform
Micro-electronic component
multiply-accumulate, Fast Fourier transform, fused multiply-add, and convolutions. As with other computer systems, SoCs require timing sources to generate
System_on_a_chip
Effect of a material on light
between electric and electric displacement field can be expressed as a convolution: D i ( t , r ) = E i ( t , r ) + ∫ 0 ∞ ∫ f i k ( τ ; r , r ′ ) E k (
Dispersion_(optics)
Study of classical optics using Fourier transforms
δ(t − t′), applied at time t'. This is where the convolution equation above comes from. The convolution equation is useful because it is often much easier
Fourier_optics
AI that generates content
(GPT) series developed by OpenAI, replacing traditional recurrent and convolutional models. The self-attention mechanism enables the model to determine
Generative_AI
Type of code in quantum computing
lower complexity. Quantum convolutional coding theory offers a different paradigm for coding quantum information. The convolutional structure is useful for
Quantum_convolutional_code
Signal representation used in automatic speech recognition
Hence, y ( n ) = x ( n ) ∗ h ( n ) {\displaystyle y(n)=x(n)*h(n)} (convolution) As speech is not stationary signal, it is divided into overlapped frames
Mel-frequency_cepstrum
Mathematical concept
singular integral operators of convolution type are the singular integral operators that arise on Rn and Tn through convolution by distributions; equivalently
Singular integral operators of convolution type
Singular_integral_operators_of_convolution_type
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
Type of database that uses vectors to represent other data
Wiggers, Kyle (2023-08-29). "Google's AlloyDB AI transforms databases to power generative AI apps". TechCrunch. Retrieved 2026-01-01. "5 Hard Problems
Vector_database
Elementwise product of two matrices
can also be used in artificial neural network models, specifically convolutional layers. Frobenius inner product Pointwise product Kronecker product
Hadamard_product_(matrices)
Interdisciplinary research area
multi-dimensional vectors that uses circuits as convolution filters is QCNN. It was inspired by the advantages of CNNs and the power of QML. It is made using a combination
Quantum_machine_learning
Robert Alexander Rankin and Atle Selberg independently constructed their convolution L-functions, now thought of as the Langlands L-function associated to
Rankin–Selberg_method
Involutive change of basis in linear algebra
Dyadic convolution between two vectors is equivalent to element-wise multiplication of their Hadamard transform representations; thus convolutional layers
Hadamard_transform
Generalized function whose value is zero everywhere except at zero
operation of convolution of functions: f ∗ g ∈ L1(R) whenever f and g are in L1(R). However, there is no identity in L1(R) for the convolution product: no
Dirac_delta_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
functions.. These include algebraic transformations, integration and convolution methods, constructions from bell-shaped functions, solutions of ordinary
Sigmoid_function
Peak divided by the Root mean square (RMS) of the waveform
Haim H. (2020). Low PAPR Waveform Design for OFDM Systems Based on Convolutional Autoencoder. 2020 IEEE International Conference on Advanced Networks
Crest_factor
Type of knowledge base
Thomas (April 14–17, 2020). Knowledge graph entity alignment with graph convolutional networks: lessons learned. Advances in Information Retrieval: 42nd European
Knowledge_graph
Mathematical operation
Mellin transform may also be viewed as the Gelfand transform for the convolution algebra of the locally compact abelian group of positive real numbers
Mellin_transform
2020 text-generating language model
transformer model of deep neural network, which supersedes recurrence and convolution-based architectures with a technique known as "attention". This attention
GPT-3
Addition, multiplication, division, ...
of complementation. Operations on functions include composition and convolution. Operations may not be defined for every possible value of its domain
Operation_(mathematics)
Type of rotorcraft
roots helix (ἕλιξ, genitive helikos (ἕλῐκος), "helix, spiral, whirl, convolution"), and pteron (πτερόν, "wing"). The word is often (erroneously, from
Helicopter
Fundamental theorem in probability theory and statistics
a statement about the properties of density functions under convolution: the convolution of a number of density functions tends to the normal density
Central_limit_theorem
Amateur radio communications software
transmitter power in dBm. The WSPR protocol compresses the information in the message into 50 bits (binary digits). These are encoded using a convolutional code
WSPR_(amateur_radio_software)
CONVOLUTION POWER
CONVOLUTION POWER
Girl/Female
Italian Spanish
Consolation.
Girl/Female
Muslim
Consolation, Comfort
Boy/Male
Hindu
Patience, Consolation
Boy/Male
Indian, Tamil
Consolation
Girl/Female
Spanish American
Consolation.
Boy/Male
Tamil
Santvan | ஸாஂதà¯à®µà®¨
Consolation
Santvan | ஸாஂதà¯à®µà®¨
Boy/Male
African
Consolation.
Girl/Female
Spanish
Consolation.
Boy/Male
Hindu
Supplication, Consolation
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Telugu
Consolation
Boy/Male
Hindu, Indian
Consolation
Girl/Female
Latin Spanish
Consolation.
Boy/Male
Hindu
Consolation
Girl/Female
Spanish
Consolation.
Girl/Female
Indian, Malayalam
Consolation
Boy/Male
Tamil
Patience, Consolation
Boy/Male
Hindu
Patience, Consolation
Girl/Female
Hebrew
Consolation.
Girl/Female
Tamil
Santawana | ஸஂதவாநா
Consolation
Santawana | ஸஂதவாநா
Girl/Female
Hebrew
Consolation.
CONVOLUTION POWER
CONVOLUTION POWER
Boy/Male
Christian, Hawaiian, Hebrew, Indian
The Just; Judicious
Boy/Male
Hindu, Indian, Marathi, Sanskrit
Conquered
Girl/Female
Arabic, Muslim, Sindhi
Daughter of Alqamah
Girl/Female
Indian
Rock born, Hard and strong, I am
Boy/Male
Arabic, Muslim
The Biblical Elijah is the English Language Equivalent
Girl/Female
Tamil
Janaki Priya | ஜாநகீ பà¯à®°à®¿à®¯Â
Goddess Sita (Daughter of king Janak)
Girl/Female
American, Assamese, Celebrity, Danish, French, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Telugu, Traditional
Peaceful; Daughter of King Dasarath; Very Calm
Biblical
disquiet
Girl/Female
Gujarati, Indian
Happiness
Boy/Male
Hindu
Ornament of water means wind
CONVOLUTION POWER
CONVOLUTION POWER
CONVOLUTION POWER
CONVOLUTION POWER
CONVOLUTION POWER
n.
The state of being rolled upon itself, or rolled or doubled together; a tortuous or sinuous winding or fold, as of something rolled or folded upon itself.
n.
The presiding officer of a convocation.
a.
Having convolutions.
n.
The act of twisting; a contortion; a flexure; a convolution; a bending.
a.
Pertaining to a gyrus, or convolution.
n.
Involution in one's self; hence, abstraction of thought; reverie.
n.
Encouragement; solace; consolation in trouble; also, that which affords consolation.
a.
Consisting of many folds, coils, or convolutions.
a.
Below the margin; submarginal; as, an inframarginal convolution of the brain.
n.
An advocate or defender of convocation.
n.
A twist; a convolution.
n.
One who gives consolation.
n.
A twist; a convolution.
n.
The relation which exists between three or more sets of points, a.a', b.b', c.c', so related to a point O on the line, that the product Oa.Oa' = Ob.Ob' = Oc.Oc' is constant. Sets of lines or surfaces possessing corresponding properties may be in involution.
n.
An irregular, tortuous folding of an organ or part; as, the convolutions of the intestines; the cerebral convolutions. See Brain.
a.
Of or pertaining to a convocation.
a.
Capable of receiving consolation.
n.
The act of rolling anything upon itself, or one thing upon another; a winding motion.
n.
One who administers comfort or consolation.
n.
A representative of the clergy in convocation.