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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
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
systems of linear equations Hidden linear function problem: oracle problem involving a hidden linear function Hidden shift problem: problem of finding
List_of_algorithms
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Problem in computer science
Simon's problem, usually called Simon's algorithm, served as the inspiration for Shor's algorithm. Both problems are special cases of the abelian hidden subgroup
Simon's_problem
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
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
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
Disproved conjecture
belongs to the sector of linear stability, and a unique stable equilibrium coexists with a stable periodic solution (hidden oscillation). In discrete-time
Kalman's_conjecture
Of a function, an additional effect besides returning a value
functions without effects correspond to pure functions. Assembly language programmers must be aware of hidden side effects—instructions that modify parts
Side effect (computer science)
Side_effect_(computer_science)
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
power of a linear polynomial? Connes embedding problem in Von Neumann algebra theory Crouzeix's conjecture: the matrix norm of a complex function f {\displaystyle
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Interpretation of quantum mechanics
interpretation, and hidden variable theories such as Bohmian mechanics. In the many-worlds interpretation, the universal wave function evolves unitarily
Many-worlds_interpretation
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
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
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
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
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
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
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
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
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
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
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
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)
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
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)
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
Theorem in quantum mechanics
well-motivated. Specifically, von Neumann assumed that the probability function must be linear on all observables, commuting or non-commuting. His proof was derided
Gleason's_theorem
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
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
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
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
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
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
correction Best linear unbiased prediction Beta (finance) Beta-binomial distribution Beta-binomial model Beta distribution Beta function – for incomplete
List_of_statistics_articles
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
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
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
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
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
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
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
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
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
Representation of linear dynamical systems
dynamical structure function (DSF) is a representation of a linear time-invariant system that preserves the system's transfer function while also describing
Dynamical_structure_function
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
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
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
Algorithm for measuring similarity between temporal sequences
where the fluctuations in the time axis are modeled using a non-linear time-warping function. Considering any two speech patterns, we can get rid of their
Dynamic_time_warping
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
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
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
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
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
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
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
Class of artificial neural network
the hidden units are Bernoulli.[clarification needed] In this case, the logistic function for visible units is replaced by the softmax function P ( v
Restricted_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
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
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
Method of machine learning
with other convex loss functions. Consider the setting of supervised learning with f {\displaystyle f} being a linear function to be learned: f ( x j
Online_machine_learning
Number of arguments required by a function
programming, a function without arguments can be meaningful and not necessarily constant (due to side effects). Such functions may have some hidden input, such
Arity
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
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
Statistical regression where the dependent variable can take only two values
it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit
Probit_model
Study of resources used by an algorithm
resources needed to execute them. Usually, this involves determining a function that relates the size of an algorithm's input to the number of steps it
Analysis_of_algorithms
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
Boy/Male
Hindu
Lingam
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
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’.
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.
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Girl/Female
American, Australian, Chinese, Danish, German, Norse, Scandinavian, Swedish
Lime; Linden Tree
Female
English
Anglicized form of Irish Gaelic ÉtaÃn, AIDEEN means "face."
Girl/Female
American, Australian, British, Christian, English
Lives by the Linden Tree Hill
Male
English
Variant spelling of English Lyndon, LINDEN means "lime tree hill." Or from the vocabulary word, linden, meaning "lime tree."
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.
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Girl/Female
English
The linden tree.
Male
German
Middle High German byname HEIDEN means "heathen." The composer Josef Haydn's surname was a respelling of this name.
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’.
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Boy/Male
Indian
Friction
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.
Male
English
Variant spelling of English Aidan, AIDEN means "little fire."
Boy/Male
American, Australian, British, English
From the Linden Tree Hill
Boy/Male
British, English
From the Island of Linden Trees
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
Boy/Male
Dutch
Silent.
Girl/Female
Biblical
Bramble, enemy.
Girl/Female
Indian
Return of Love
Girl/Female
Gujarati, Hindu, Indian, Kannada, Marathi, Telugu
Wanderer; Traveller
Boy/Male
Australian, German, Greek
Vigilant
Biblical
a governor
Boy/Male
Hindu, Indian
Ten Scars of Agni
Girl/Female
English
God is gracious.
Surname or Lastname
English
English : nickname for a man with some fancied resemblance to a he-goat (Old English bucc(a)) or a male deer (Old English bucc). Old English Bucc(a) is found as a personal name, as is Old Norse Bukkr. Names such as Walter le Buk (Somerset 1243) are clearly nicknames.English : topographic name for someone who lived near a prominent beech tree, such as Peter atte Buk (Suffolk 1327), from Middle English buk ‘beech’ (from Old English bÅc).German : from a personal name, a short form of Burckhard (see Burkhart).North German and Danish : nickname for a fat man, from Middle Low German bÅ«k ‘belly’. Compare Bauch.German : variant of Bock.German : variant of Puck in the sense ‘defiant’, ‘spiteful’, or ‘stubborn’.German : topographic name from a field name, Buck ‘hill’.Emanuel Buck came from England to Plymouth Colony in the 1640s and in 1647 settled in Wethersfield, CT.
Girl/Female
Muslim
Rising star
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
HIDDEN LINEAR-FUNCTION-PROBLEM
n.
The things sold by auction or put up to auction.
n.
A coarse kind of linen; -- called also harden.
v. t.
The act of uniting, or the state of being united; junction.
v. t.
To sell by auction.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
p. p.
of Hide
adv.
In a linear manner; with lines.
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.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
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.
One who lines, as, a liner of shoes.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
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 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.
a.
Pertaining to, or connected with, a function or duty; official.
adv.
In a hidden manner.
a.
Composed of lines; delineated; as, lineal designs.
a.
Linear.
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.
a.
Pertaining to the function of an organ or part, or to the functions in general.