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Search problem in quantum mechanics
The hidden linear function problem, is a search problem that generalizes the Bernstein–Vazirani problem. In the Bernstein–Vazirani problem, the hidden function
Hidden linear function problem
Hidden_linear_function_problem
systems of linear equations Hidden linear function problem: oracle problem involving a hidden linear function Hidden shift problem: problem of finding
List_of_algorithms
Seven mathematical problems with a US$1 million prize for each solution
is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X. The official statement of the problem was given
Millennium_Prize_Problems
Very general problem in computer science
H. Hidden subgroup problem: Let G {\displaystyle G} be a group, X {\displaystyle X} a finite set, and f : G → X {\displaystyle f:G\to X} a function that
Hidden_subgroup_problem
System where changes of output are not proportional to changes of input
(or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest
Nonlinear_system
nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant
Describing_function
Type of activation function
(rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU (
Rectified_linear_unit
Quantum algorithm
quantum computing software development framework by IBM. Hidden Linear Function problem Simon's problem Ethan Bernstein and Umesh Vazirani (1997). "Quantum
Bernstein–Vazirani_algorithm
Statistical modeling method
than a single dependent variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are
Linear_regression
Algorithm for supervised learning of binary classifiers
is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier
Perceptron
Aizerman problem states that a linear system in feedback with a sector nonlinearity would be stable if the linear system is stable for any linear gain of
Aizerman's_conjecture
Problem in computer science
In quantum computing, the hidden shift problem is a type of oracle-based problem. Various versions of this problem have quantum algorithms which can run
Hidden_shift_problem
Artificial neural network node function
likely to suffer from the vanishing gradient problem. Ridge functions are multivariate functions acting on a linear combination of the input variables. Often
Activation_function
Type of artificial neural network
function. Circa 1800, Legendre (1805) and Gauss (1795) created the simplest feedforward network which consists of a single weight layer with linear activation
Feedforward_neural_network
Estimate of time taken for running an algorithm
the type of function appearing in the big O notation. For example, an algorithm with time complexity O ( n ) {\displaystyle O(n)} is a linear time algorithm
Time_complexity
Generalized function whose value is zero everywhere except at zero
developed the theory of distributions, where it is defined as a linear form acting on functions. The graph of the Dirac delta is usually thought of as following
Dirac_delta_function
Classical problem in combinatorics
1} . This linear program belongs to the more general class of LPs for covering problems, as all the coefficients in the objective function and both sides
Set_cover_problem
Theoretical problem in quantum physics
definite result. The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different
Measurement_problem
Type of feedforward neural network
with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks
Multilayer_perceptron
Statistical Markov model
maximum likelihood estimation. For linear chain HMMs, the Baum–Welch algorithm can be used to estimate parameters. Hidden Markov models are known for their
Hidden_Markov_model
Overview of and topical guide to machine learning
Layered hidden Markov model Learnable function class Least squares support vector machine Leslie P. Kaelbling Linear genetic programming Linear predictor
Outline_of_machine_learning
Control theory for nonlinear or time-variant systems
treated as linear for purposes of control design: Feedback linearization And Lyapunov based methods: Lyapunov redesign Control-Lyapunov function Nonlinear
Nonlinear_control
Type of artificial neural network
basis function (RBF) networks typically have three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output
Radial_basis_function_network
Neural networks
introducing stronger non-linearities (either in the energy function or neurons’ activation functions) leading to super-linear (even an exponential) memory
Modern_Hopfield_network
Set of methods for supervised statistical learning
called the dual problem. Since the dual maximization problem is a quadratic function of the c i {\displaystyle c_{i}} subject to linear constraints, it
Support_vector_machine
Method of improving artificial neural network
^{2}}}} . Since the parameters of each hidden unit converge linearly, the whole optimization problem has a linear rate of convergence. Ioffe, Sergey; Szegedy
Batch_normalization
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Algorithm to be run on quantum computers
S2CID 2337707. Boneh, D.; Lipton, R. J. (1995). "Quantum cryptoanalysis of hidden linear functions". In Coppersmith, D. (ed.). Proceedings of the 15th Annual International
Quantum_algorithm
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More
P_versus_NP_problem
Smooth approximation of one-hot arg max
linear discriminant analysis, the input to the function is the result of K distinct linear functions, and the predicted probability for the jth class
Softmax_function
Family of machine learning approaches
{\displaystyle h_{0}^{d}} , the 0th hidden vector of decoder. Then, the intermediate vector is transformed by a linear map W Q {\displaystyle W^{Q}} into
Seq2seq
Hypersurface used by a classification algorithm
the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then it
Decision_boundary
Sequence of data points over time
the autocorrelation function Hjorth parameters FFT parameters Autoregressive model parameters Mann–Kendall test Univariate non-linear measures Measures
Time_series
Of a function, an additional effect besides returning a value
Unspecified behaviour Frame problem Spuler, David A.; Sajeev, A. Sayed Muhammed (January 1994). Compiler Detection of Function Call Side Effects. James Cook
Side effect (computer science)
Side_effect_(computer_science)
Overview of and topical guide to algorithms
tree search Automated planning and scheduling Constraint satisfaction problem Linear regression Logistic regression Decision tree learning Random forest
Outline_of_algorithms
Property of artificial neural networks
a network with a single hidden layer), using sigmoid activation functions in the hidden layer and linear activation functions in the input and output
Universal approximation theorem
Universal_approximation_theorem
Task of computing complete subgraphs
significantly less than linear. The clique decision problem is NP-complete. It was one of Richard Karp's original 21 problems shown NP-complete in his
Clique_problem
Conflict of interest when one person acts on another's behalf
typically either examine moral hazard (hidden actions) or adverse selection (hidden information). The principal–agent problem typically arises where the two parties
Principal–agent_problem
Problem in computer science
algorithm uses a linear number of queries and any classical probabilistic algorithm must use an exponential number of queries. This problem yields an oracle
Simon's_problem
Book by Marvin Minsky and Seymour Papert
any classification problem. (Existence theorem.) Minsky and Papert used perceptrons with restricted numbers of inputs of the hidden layer A-elements and
Perceptrons_(book)
Process by which a quantum system takes on a definitive state
( s z {\displaystyle s_{z}} ), and so on. The observable acts as a linear function on the states of the system; its eigenvectors correspond to the quantum
Wave_function_collapse
Projection of data onto lower-dimensional manifolds
potentially existing across non-linear manifolds (non-affine subspaces) which cannot be adequately captured by linear decomposition methods, onto lower-dimensional
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Subset of artificial intelligence
and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons
Machine_learning
Computation complexity problem
In quantum information, the hidden matching problem is a computational complexity problem that can be solved using quantum protocols: Let n {\displaystyle
Hidden_matching_problem
Mathematical description of quantum state
advantages to understanding wave functions as representing elements of an abstract vector space: All the powerful tools of linear algebra can be used to manipulate
Wave_function
Type of differential equation
PDE is called linear if it is linear in the unknown and its derivatives. For example, for a function u of x and y, a second order linear PDE is of the
Partial_differential_equation
linear stochastic partial differential equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear
Zakai_equation
Public key cryptosystem
Hidden Fields Equations (HFE), also known as HFE trapdoor function, is a public key cryptosystem which was introduced at Eurocrypt in 1996 and proposed
Hidden_Field_Equations
Methods for numerical approximations
objective function and the constraint. For instance, linear programming deals with the case that both the objective function and the constraints are linear. A
Numerical_analysis
On topology of algebraic curves and surfaces
regions of attraction, which are hidden attractors, and semi-stable limit cycles. In his speech, Hilbert presented the problems as: The upper bound of closed
Hilbert's_sixteenth_problem
algebra Stochastic satisfiability Linear temporal logic satisfiability and model checking Type inhabitation problem for simply typed lambda calculus Integer
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Machine learning technique
{\displaystyle \mu _{i}} is a learnable parameter. The weighting function is a linear-softmax function: w ( x ) i = e k i T x + b i ∑ j e k j T x + b j {\displaystyle
Mixture_of_experts
Evolutionary algorithm
the square root function. This kind of expression tree consists of the phenotypic expression of GEP genes, whereas the genes are linear strings encoding
Gene_expression_programming
Machine learning model training problem
x_{t}} is a function of h t {\displaystyle h_{t}} , as some x t = G ( h t ) {\displaystyle x_{t}=G(h_{t})} . The vanishing gradient problem already presents
Vanishing_gradient_problem
Function related to statistics and probability theory
reduces computational burden of the original maximization problem. For instance, in a linear regression with normally distributed errors, y = X β + u {\textstyle
Likelihood_function
Class of algorithms for pattern analysis
support-vector machine (SVM). These methods involve using linear classifiers to solve nonlinear problems. The general task of pattern analysis is to find and
Kernel_method
correction Best linear unbiased prediction Beta (finance) Beta-binomial distribution Beta-binomial model Beta distribution Beta function – for incomplete
List_of_statistics_articles
unknown probability density function recursively over time using incremental incoming measurements. It is one of the main problems defined by Norbert Wiener
Smoothing problem (stochastic processes)
Smoothing_problem_(stochastic_processes)
Form of artificial neural network
introducing stronger non-linearities (either in the energy function or neurons' activation functions) leading to super-linear (even an exponential) memory
Hopfield_network
Classification of Artificial Neural Networks (ANNs)
statistics. In classification problems the output layer is typically a sigmoid function of a linear combination of hidden layer values, representing a
Types of artificial neural networks
Types_of_artificial_neural_networks
numerical method for linear problems Nikolay Krylov, author of the edge-of-the-wedge theorem, Krylov–Bogolyubov theorem and describing function Aleksandr Kurosh
List of Russian mathematicians
List_of_Russian_mathematicians
1932 book by John von Neumann
mathematical argument against the idea of hidden variables. Von Neumann's claim rested on the assumption that any linear combination of Hermitian operators represents
Mathematical Foundations of Quantum Mechanics
Mathematical_Foundations_of_Quantum_Mechanics
List of quantum computing algorithms
including algorithms, algorithmic techniques, computational models, and problem frameworks used in quantum computing. A quantum algorithm is an algorithm
List_of_quantum_algorithms
Quantum search algorithm
Umesh Vazirani proved that any quantum solution to the problem needs to evaluate the function Ω ( N ) {\displaystyle \Omega ({\sqrt {N}})} times, so Grover's
Grover's_algorithm
Approach to finding numerical solutions of ordinary differential equations
of linear multistep methods. There are other modifications which uses techniques from compressive sensing to minimize memory usage In the film Hidden Figures
Euler_method
Interpretation of quantum mechanics
quantitative problem, Everett proposed a derivation of the Born rule based on the properties that a measure on the branches of the wave function should have
Many-worlds_interpretation
Neural network that learns efficient data encoding in an unsupervised manner
with one hidden layer with identity activation function. In the language of autoencoding, the input-to-hidden module is the encoder, and the hidden-to-output
Autoencoder
Hyperbolic analogues of trigonometric functions
x=\cosh x\,.} All functions with this property are linear combinations of sinh and cosh, in particular the exponential functions e x {\displaystyle e^{x}}
Hyperbolic_functions
Supervised machine learning techniques
structure; n {\displaystyle n} is problem-dependent, but must be fixed for each model). Let G E N {\displaystyle GEN} be a function that generates candidate predictions
Structured_prediction
Optimization algorithm for artificial neural networks
multi-class classification, while for the hidden layers this was traditionally a sigmoid function (logistic function or others) on each node (coordinate),
Backpropagation
Optimization algorithm
a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method
Gradient_descent
Class of second-order linear partial differential equations
matrix-valued function a ( x ) {\displaystyle a(x)} has a kernel of dimension 1. Under broad assumptions, an initial/boundary-value problem for a linear parabolic
Parabolic partial differential equation
Parabolic_partial_differential_equation
Set of statistical processes for estimating the relationships among variables
Function approximation Generalized linear model Kriging (a linear least squares estimation algorithm) Local regression Modifiable areal unit problem Multivariate
Regression_analysis
Flaw in mathematical modelling
slopes). Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent
Overfitting
Optimization algorithm
statistical estimation and machine learning consider the problem of minimizing an objective function that has the form of a sum: Q ( w ) = 1 n ∑ i = 1 n Q
Stochastic_gradient_descent
Class of artificial neural network
weights in a neural network can be modeled as a non-linear global optimization problem. A target function can be formed to evaluate the fitness or error of
Recurrent_neural_network
Technique to solve partial differential equations
function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem
Physics-informed neural networks
Physics-informed_neural_networks
Difficulties arising when analyzing data with many aspects ("dimensions")
of the combinatorics problems above and the distance function problems explained below. When solving dynamic optimization problems by numerical backward
Curse_of_dimensionality
Branch of mathematics
2x is its derivative. If a function is linear (that is if the graph of the function is a straight line), then the function can be written as y = mx +
Calculus
Frequency swept signal
rotational acceleration. Linear chirp Sound example for linear chirp (five repetitions) Problems playing this file? See media help. In a linear-frequency chirp
Chirp
Iterative method for finding maximum likelihood estimates in statistical models
to estimate a mixture of gaussians, or to solve the multiple linear regression problem. The EM algorithm was explained and given its name in a classic
Expectation–maximization algorithm
Expectation–maximization_algorithm
Type of stochastic recurrent neural network
for practical problems. They are named after the Boltzmann distribution in statistical mechanics, which is used in their sampling function. They were heavily
Boltzmann_machine
Cryptography based on quantum mechanical phenomena
so-called "key-management problem"). Moreover, this distribution alone does not address many other cryptographic tasks and functions, which are of vital importance
Quantum_cryptography
Problem in physics and quantum mechanics
scales linearly with the number of particles, n {\displaystyle n} . In quantum mechanics, however, the dimension of the many-body wave function scales
Many-body_problem
Research field that lies at the intersection of machine learning and computer security
can be simplified in linear regression and classification problems. Moreover, adversarial training is convex in this case. Linear models allow for analytical
Adversarial_machine_learning
Set of learning techniques in machine learning
on the input data. In particular, a minimization problem is formulated, where the objective function consists of the classification error, the representation
Feature_learning
Framework for machine learning
Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful
Statistical_learning_theory
Process of reducing the number of random variables under consideration
and bioinformatics. Methods are commonly divided into linear and nonlinear approaches. Linear approaches can be further divided into feature selection
Dimensionality_reduction
Type of artificial neural network
cases, the output weights of hidden nodes are usually learned in a single step, which essentially amounts to learning a linear model. The name "extreme learning
Extreme_learning_machine
Property of a model
method. E.g., when approximating a non-linear function f ( x ) {\displaystyle f(x)} using a learning method for linear models, there will be error in the
Bias–variance_tradeoff
Mechanism of spontaneous symmetry breaking
distortion in linear chains. In linear molecules with three or more atoms there may be PJTE distortions that do not violate the linearity but change the
Pseudo_Jahn–Teller_effect
Set of machine learning methods
parameter to the minimization problem of the learning algorithm. As an example, consider the case of supervised learning of a linear combination of a set of
Multiple_kernel_learning
Python package
Benchmark Problem #71 used to test the performance of nonlinear programming solvers. This particular optimization problem has an objective function min x
Gekko_(optimization_software)
Software programming optimization technique
programs. It works by storing the results of expensive calls to pure functions, so that these results can be returned quickly should the same inputs
Memoization
Interpretation of quantum mechanics
arbitrary quantum state ρ ^ {\displaystyle {\hat {\rho }}} may be written as a linear combination of the SIC projectors ρ ^ = ∑ i = 1 d 2 [ ( d + 1 ) P ( H i
QBism
Branch of statistics mathematics
classical functional linear regression models (FLMs) still involve a linear predictor, but combine it with a nonlinear link function, analogous to the idea
Functional_data_analysis
Description of a quantum-mechanical system
this case the total wave function is dependent on time as explained in the section on linearity below. In the language of linear algebra, this equation
Schrödinger_equation
Machine learning framework
formulated as a sequence of alternating linear integral operators on function spaces and point-wise non-linearities. Using an analogous architecture to finite-dimensional
Neural_operators
Interdisciplinary research area
possible. The number of storable patterns is typically limited by a linear function of the number of neurons, p ≤ O ( n ) {\displaystyle p\leq O(n)} .
Quantum_machine_learning
Machine learning technique
x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and
Random_feature
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
Girl/Female
American, Australian, British, Christian, English
Lives by the Linden Tree Hill
Girl/Female
English
The linden tree.
Boy/Male
British, English
From the Island of Linden Trees
Surname or Lastname
English
English : habitational name from various places such as Headon, Nottinghamshire, Hedon in East Yorkshire, and Heddon on the Wall and Black Heddon. Northumberland. The first is probably named from Old English hēah ‘high’ + dūn ‘hill’; the others have the same second element, combined with Old English hǣþ ‘heath’, ‘heather’.North German (Frisian) : variant of Hadden.
Male
English
Variant spelling of English Aidan, AIDEN means "little fire."
Boy/Male
Indian
Friction
Male
German
Middle High German byname HEIDEN means "heathen." The composer Josef Haydn's surname was a respelling of this name.
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Surname or Lastname
English
English : habitational name from Hidden in Berkshire or Clayhidon in Devon, recorded in Domesday Book as Hidone, from Old English hī(e)g ‘hay’ + dūn ‘hill’.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from Hebden in North Yorkshire or Hebden Bridge in West Yorkshire, both named from Old English hēope ‘rose-hip’ + denu ‘valley’.
Female
English
Anglicized form of Irish Gaelic ÉtaÃn, AIDEEN means "face."
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
English
Variant spelling of English Lyndon, LINDEN means "lime tree hill." Or from the vocabulary word, linden, meaning "lime tree."
Surname or Lastname
Scottish
Scottish : habitational name from a place so called near Kelso on the border with England. Early forms include Hadden, Hauden, and Halden; the place name is probably from Old English halh ‘nook’, ‘recess’ + denu ‘valley’.English : habitational name from a place in East Yorkshire, so named from Old Norse hǫfuð ‘head’ (replacing Old English hēafod) + Old English denu ‘valley’; the first element may have been used in the sense ‘principal’, ‘top’, or ‘end’.Americanized form of Norwegian Hovden.
Surname or Lastname
Scottish
Scottish : variant of Howden 1.English : variant of Haddon.Irish (Ulster and County Louth) : though mainly Scottish, this surname is sometimes used as an Anglicized form of Gaelic Ó hÉidÃn ‘descendant of ÉidÃn’ (see Hayden).North German (Frisian) : from the personal name Hadder, a derivative of any of the Germanic compound names formed with had ‘battle’, ‘strife’ as the first element.
Boy/Male
American, Australian, British, English
From the Linden Tree Hill
Boy/Male
Hindu
Lingam
Girl/Female
American, Australian, Chinese, Danish, German, Norse, Scandinavian, Swedish
Lime; Linden Tree
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
Male
English
Variant spelling of English Derek, DERYCK means "first of the people; king of nations."
Girl/Female
Tamil
Smile
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Exempted from Grief
Male
Welsh
Welsh form of Old Breton Arthmael, ARTHFAEL means "bear chief" or "warrior prince."
Female
Finnish
Finnish form of Greek Margarites, MARGAREETA means "pearl."
Boy/Male
Indian, Telugu
Avatar of Sai; Good
Girl/Female
Hindu, Indian
Reddish Brown Cow
Male
English
Variant spelling of English Ackley, ACKLEA means "oak meadow."
Girl/Female
Latin
Honor.
Male
Norwegian
Norwegian variant form of Scandinavian Balder, BALDOR means "lord, prince."
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
v. t.
The act of uniting, or the state of being united; junction.
n.
One who lines, as, a liner of shoes.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
adv.
In a hidden manner.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
n.
The things sold by auction or put up to auction.
v. t.
To sell by auction.
a.
Composed of lines; delineated; as, lineal designs.
a.
Pertaining to, or connected with, a function or duty; official.
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
a.
Pertaining to the function of an organ or part, or to the functions in general.
n.
The place or point of union, meeting, or junction; specifically, the place where two or more lines of railway meet or cross.
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
n.
A coarse kind of linen; -- called also harden.
p. p.
of Hide
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
adv.
In a linear manner; with lines.
a.
Linear.