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Process of mapping a continuous set to a countable set
referred to as quantization error, noise or distortion. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital
Quantization (signal processing)
Quantization_(signal_processing)
Topics referred to by the same term
Look up quantization in Wiktionary, the free dictionary. Quantization is the process of constraining an input from a continuous or otherwise large set
Quantization
Data compression improvement algorithm
have the lowest rate-distortion ratio. Trellis quantization effectively finds the optimal quantization for each block to maximize the PSNR relative to
Trellis_quantization
Systematic procedure of turning a classical theory into a quantum one
generalization involving infinite degrees of freedom is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field
Quantization_(physics)
Classical quantization technique from signal processing
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the
Vector_quantization
Type of machine learning model
preserving most of its performance. Quantization can be further classified as static quantization if the quantization parameters are determined beforehand
Large_language_model
Continuous progression from past to future
down in the figure depending on the acceleration of the observer. Time quantization is a hypothetical concept that time has a smallest possible unit. In
Time
Formulation of the quantum many-body problem
Canonical quantization First quantization Geometric quantization Quantization (physics) Schrödinger functional Scalar field theory Second quantization on Wikiversity
Second_quantization
Music studio-software process
of beats. The purpose of quantization in music processing is to provide a more beat-accurate timing of sounds. Quantization is frequently applied to a
Quantization_(music)
Minimum amount of a physical entity involved in an interaction
levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence
Quantum
Image processing technique
In computer graphics, color quantization or color image quantization is quantization applied to color spaces; it is a process that reduces the number of
Color_quantization
Lossy compression technique
Specific applications include DCT data quantization in JPEG and DWT data quantization in JPEG 2000. Color quantization reduces the number of colors used in
Quantization (image processing)
Quantization_(image_processing)
Converting classical mechanics to quantum mechanics
realization that is today understood as first quantization. To understand the term first quantization one must first understand what it means for something
First_quantization
Process in quantum mechanical theories
context, it is also called the second quantization of fields, in contrast to the semi-classical first quantization of single particles. When it was first
Canonical_quantization
streamlined by Giorgio Parisi and Yong-Shi Wu. Stochastic quantization serves to quantize Euclidean field theories, and is used for numerical applications
Stochastic_quantization
Transfer function for HDR displays
The perceptual quantizer (PQ), published by SMPTE as SMPTE ST 2084, is a transfer function that allows for HDR display by replacing the gamma curve used
Perceptual_quantizer
Predecessor to modern quantum mechanics (1900–1925)
orientations, so that the process of quantization does not pick out a preferred axis. For this reason, the name "space quantization" fell out of favor, and the
Old_quantum_theory
Pyramid vector quantization (PVQ) is a method used in audio and video codecs to quantize and transmit unit vectors, i.e. vectors whose magnitudes are
Pyramid_vector_quantization
Video encoding algorithm
Adaptive Quantization Not Suck". 2008-02-22. Archived from the original on 2020-08-07. Implementation of variance-based adaptive quantization in x264 The
Variance Adaptive Quantization
Variance_Adaptive_Quantization
Online vector quantization algorithm
searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction
TurboQuant
Formulation to quantize gauge field theories in physics
relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry. Quantization rules in earlier quantum field theory (QFT)
BRST_quantization
In data compression, twin vector quantization is related to vector quantization, but the speed of the quantization is doubled by the secondary vector
Twin_vector_quantization
Noise that reduces quantization error
process is called quantization. Each coded value is a discrete step... if a signal is quantized without using dither, there will be quantization distortion related
Dither
Recipe for constructing a quantum analog of a classical physical theory
quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization
Geometric_quantization
Measure for analyzing digitizing schemes
strength and the quantization error (also known as quantization noise) introduced in the analog-to-digital conversion. As SQNR applies to quantized signals, the
Signal-to-quantization-noise ratio
Signal-to-quantization-noise_ratio
Quantization of cyclotron orbits
quantization contributes towards magnetic susceptibility of metals, known as Landau diamagnetism. Under strong magnetic fields, Landau quantization leads
Landau_levels
System that converts an analog signal into a digital signal
signal. The conversion involves quantization of the input, so it necessarily introduces a small amount of quantization error. Furthermore, instead of continuously
Analog-to-digital_converter
Method for converting signals between digital and analog
feedback loop during quantization to the lower bit depth that continuously corrects quantization errors and moves quantization noise to higher frequencies
Delta-sigma_modulation
Ratio of the desired signal to the background noise
possible noise level is the error caused by the quantization of the signal, sometimes called quantization noise. This noise level is non-linear and signal-dependent;
Signal-to-noise_ratio
Atomic model introduced by Niels Bohr in 1913
the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson–Sommerfeld quantization condition
Bohr_model
Lossy compression method for reducing the size of digital images
domain, the process of reducing information is called quantization. In simpler terms, quantization is a method for optimally reducing a large number scale
JPEG
deformation quantization of the corresponding Poisson algebra. It is due to Maxim Kontsevich. Given a Poisson algebra (A, {⋅, ⋅}), a deformation quantization is
Kontsevich quantization formula
Kontsevich_quantization_formula
also be "water". Hence, the predicate "apple" is quantized, while "water" is not. Formally, a quantization predicate QUA can be defined as follows, where
Quantization_(linguistics)
Intrinsic quantum property of particles
momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer
Spin_(physics)
Mapping between functions in the quantum phase space
Weyl quantization. It is now understood that Weyl quantization does not satisfy all the properties one would require for consistent quantization and therefore
Wigner–Weyl_transform
geometric quantization, quantization commutes with reduction states that the space of global sections of a line bundle L satisfying the quantization condition
Quantization commutes with reduction
Quantization_commutes_with_reduction
Physical theory with fields invariant under the action of local "gauge" Lie groups
variety of means. Methods for quantization are covered in the article on quantization. The main point to quantization is to be able to compute quantum
Gauge_theory
Large language model with ternary weights
Zhisong; Mi, Haitao; Yu, Dong (2024). "Low-Bit Quantization Favors Undertrained LLMS: Scaling Laws for Quantized LLMS with 100T Training Tokens". arXiv:2411
1.58-bit_large_language_model
Quantized unit of magnetic flux
from Φ0. The flux quantization is a key idea behind a SQUID, which is one of the most sensitive magnetometers available. Flux quantization also plays an important
Magnetic_flux_quantum
Number of bits of information recorded for each digital audio sample
determined by quantization error. The bit depth has no impact on the frequency response, which is constrained by the sample rate. Quantization error introduced
Audio_bit_depth
Charge carried by one proton or electron
the electric constant, and ħ is the reduced Planck constant. Charge quantization is the principle that the charge of any object is an integer multiple
Elementary_charge
deformation quantization through a ★-product to implicitly address all convergence subtleties (usually not addressed in formal deformation quantization). Insofar
Deformation_quantization
Software library for similarity search
following families of vector quantization methods are supported: Binary Quantization Scalar Quantization (SQ) Product Quantization (PQ), including Polysemous
FAISS
Extension of the Bohr model
the quantized angular momentum condition of the Bohr model with a radial quantization (condition by William Wilson, the Wilson–Sommerfeld quantization condition):
Bohr–Sommerfeld_model
Physical hypothesis
Redshift quantization, also referred to as redshift periodicity, redshift discretization, preferred redshifts and redshift-magnitude bands, is the hypothesis
Redshift_quantization
Description of gravity using discrete values
Carlo Rovelli and Lee Smolin to derive naturally from a non-perturbative quantization of general relativity. Spin networks do not represent quantum states
Quantum_gravity
vector quantization (LVQ) is a prototype-based supervised classification algorithm. LVQ is the supervised counterpart of vector quantization systems
Learning_vector_quantization
Software library for LLM inference
inference on edge devices, such as: Ahead of time model quantization and on-the-fly kv-cache quantization. Speculative decoding. Partial offloading of model
Llama.cpp
Theory of quantum gravity merging quantum mechanics and general relativity
{E}}_{i}^{3}{\tilde {E}}^{3i}}}.} According to the rules of canonical quantization the triads E ~ i 3 {\displaystyle {\tilde {E}}_{i}^{3}} should be promoted
Loop_quantum_gravity
Signal encoder
the quantized signal. The incorporation of the decoder inside the encoder allows quantization of the differences, including nonlinear quantization, in
Differential pulse-code modulation
Differential_pulse-code_modulation
Distortion of media caused by lossy data compression
after reconstruction. Because this quantization process is applied individually in each block, neighboring blocks quantize coefficients differently. This
Compression_artifact
Quantum field that enables consistent quantization
rigorously quantize non-Abelian Yang–Mills theory, such as done with BRST quantization. A field with a negative ghost number (the number of ghosts excitations
Ghost_(physics)
Figure of merit for analog-to-digital conversion
The quantization error of a signal is the difference between the original continuous value and its discretization, and the mean square quantization error
Mean square quantization error
Mean_square_quantization_error
Hypothetical particle with one magnetic pole
charge quantization has appeared. (The concept of local gauge invariance—see Gauge theory—provides a natural explanation of charge quantization, without
Magnetic_monopole
Quantization giving rise to photons
is derived from a "first" quantized Hamiltonian, the quantization of the Schrödinger field is the second time quantization is performed, hence the name
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Technique in computational quantum field theory
The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to
Light-front computational methods
Light-front_computational_methods
Video encoding standard
absence of any quantization and rounding errors). In reality, there are some (sometimes large) rounding errors introduced both by quantization in the encoder
MPEG-1
Digital signal performance enhancement
the quantization error is measured and on the next cycle added with the next sample prior to quantization. The effect is that the quantization error
Noise_shaping
Quasiparticle of mechanical vibrations
mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves
Phonon
Data structure in computer science
"Color quantization using octrees.", 4 September 2008. Retrieved on 12 December 2014. Wikimedia Commons has media related to Octrees. Octree Quantization in
Octree
Continuous time-varying signal
bandwidth and dynamic range constraints on the representation and adds quantization noise. The term analog signal usually refers to electrical signals; however
Analog_signal
Technique used to encode voices in telephony
differential pulse-code modulation (DPCM) that varies the size of the quantization step, to allow further reduction of the required data bandwidth for a
Adaptive differential pulse-code modulation
Adaptive_differential_pulse-code_modulation
Telecommunications and signal processing technique
limited-range uniform quantizer, and a (continuous-domain) signal dynamic range expander that inverts the compressor function. This type of quantization is frequently
Companding
Vector quantization algorithm minimizing the sum of squared deviations
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which
K-means_clustering
Binary file format for storing machine-learning models
2-bit to 8-bit quantized integer types, common floating-point data formats such as float32, float16 and bfloat16, and 1.58-bit quantization. Several "K-quant"
GGUF
Digital representation of sampled analog signals
type of PCM in which the quantization levels are linearly uniform. This is in contrast to PCM encodings in which quantization levels vary as a function
Pulse-code_modulation
In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra g {\displaystyle {\mathfrak
Quantized_enveloping_algebra
Formulation of general relativity
canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac.[3] Dirac's approach allows the quantization of systems
Canonical_quantum_gravity
German-born theoretical physicist (1879–1955)
Development of our Views on the Composition and Essence of Radiation"), on the quantization of light, and in an earlier 1909 paper, Einstein showed that Max Planck's
Albert_Einstein
Russian mathematician and physicist (1934–2017)
three-body problem and for the development of path-integral methods in the quantization of non-abelian gauge field theories, including the introduction of the
Ludvig_Faddeev
The quantized state systems (QSS) methods are a family of numerical integration solvers based on the idea of state quantization, dual to the traditional
Quantized state systems method
Quantized_state_systems_method
(5 May 1997). "An Overview of Color Quantization Techniques". p. 4. Retrieved 24 April 2014. Image quantization Median cut + variations Image::Pngslimmer
Median_cut
Video codec library
pixel motion compensation, lumi masking, trellis quantization, and H.263, MPEG and custom quantization matrices. Xvid is a primary competitor of the DivX
Xvid
American information theorist and professor
best known for his contributions to quantization and compression, particularly the development of vector quantization. In 1980, Gray was elevated to the
Robert_M._Gray
Electromagnetic effect in physics
resistance was exactly quantized. For this finding, von Klitzing was awarded the 1985 Nobel Prize in Physics. A link between exact quantization and gauge invariance
Quantum_Hall_effect
Motion of charged particles
quantization contributes towards magnetic susceptibility of metals, known as Landau diamagnetism. Under strong magnetic fields, Landau quantization leads
Cyclotron_motion
Lowest possible energy of a quantum system or field
"particles" are actually created: spontaneous emission. Dirac described the quantization of the electromagnetic field as an ensemble of harmonic oscillators with
Zero-point_energy
Signal with discrete values in time and amplitude
the quantization used), provided that the signal has negligible power in frequencies above the Nyquist limit and does not saturate the quantizer. Common
Digital signal (signal processing)
Digital_signal_(signal_processing)
Form of modulation
successively influences every other quantization measurement and its error. This has the effect of averaging out the quantization error, while noise shaping it
Pulse-density_modulation
Image dithering algorithm by Bill Atkinson
top-to-bottom, left-to-right (i.e. in row-major order), quantizing pixel values one by one. Each time the quantization error is transferred to the neighboring pixels
Atkinson_dithering
Elementary particle or quantum of light
electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;
Photon
experiment: quantization should not have been observable. At least five years would elapse before this mystery was resolved: quantization was observed
History_of_quantum_mechanics
Gauge fixing procedure
In quantum field theory, the Gupta–Bleuler formalism is a way of quantizing the electromagnetic field. The formulation is due to theoretical physicists
Gupta–Bleuler_formalism
Open-source software for large language model inference
supports features such as continuous batching, distributed inference, quantization, and OpenAI-compatible APIs. vLLM was introduced in 2023 by researchers
VLLM
1922 physical experiment demonstrating that atomic spin is quantized
to their quantized spin. Historically, this experiment was decisive in convincing physicists of the reality of angular-momentum quantization in all atomic-scale
Stern–Gerlach_experiment
Audio performance differences between technologies
according to theory, always introduce quantization distortion. This distortion can be rendered as uncorrelated quantization noise through the use of dither
Comparison of analog and digital recording
Comparison_of_analog_and_digital_recording
Tabular arrangement of the chemical elements
number. The Danish physicist Niels Bohr applied Max Planck's idea of quantization to the atom. He concluded that the energy levels of electrons were quantised:
Periodic_table
Quantum mechanics posed in terms of category theory
Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably
Categorical_quantum_mechanics
Action of a massive abelian gauge field
gauge-fixed version of the Stueckelberg action via the Higgs mechanism. Quantizing the Proca action requires the use of second class constraints. If m
Proca_action
Operator in quantum field theory
charge Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory
Pauli–Lubanski_pseudovector
Audio companding algorithm
transmission; in the digital domain, it can reduce the quantization error (hence increasing the signal-to-quantization-noise ratio). These SNR increases can be traded
Mu-law_algorithm
Data pre-processing technique
median).[citation needed] It is related to quantization: data binning operates on the abscissa axis while quantization operates on the ordinate axis. Binning
Data_binning
Science textbook by Mark D. McDonnell
Resonance: From Suprathreshold Stochastic Resonance to Stochastic Signal Quantization is a science text, with a foreword by Sergey M. Bezrukov and Bart Kosko
Stochastic_Resonance_(book)
Effect in quantum mechanics where conductivity acquires quantized values
"anomalous"), the quantum anomalous Hall effect is its quantized version. The Hall conductivity acquires quantized values proportional to integer multiples of the
Quantum_anomalous_Hall_effect
Flaws caused by insufficient color depth
time stretching, which adds frames. Downsampling Quantization error Discretization error Color quantization Level-set method Chao, Cheng-Kang Ted (15 July
Posterization
Generalization of the Dirac equation
L. Parker, D. Toms (2009). Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity. Cambridge University Press. p. 227. ISBN 978-0-521-877-879
Dirac equation in curved spacetime
Dirac_equation_in_curved_spacetime
Quantized flux circulation of some physical quantity
Fritz London published a very closely related work on magnetic flux quantization in superconductors. London's fluxoid can also be viewed as a quantum
Quantum_vortex
Type of artificial intelligence model
can be reduced by quantization. Work on large language models mostly translate to small language models: pruning and quantization are also widely used
Small_language_model
File format
rounding (quantization) and so it does not introduce any quantization noise. After the wavelet transform, the coefficients are scalar-quantized to reduce
Progressive_Graphics_File
Computer color depth
8-bit image, the image must go through a process called color quantization. Color quantization is the process of creating a color map for a less color dense
8-bit_color
QUANTIZATION
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Boy/Male
Muslim
Considerate, Inseparable friend
Boy/Male
Arabic
Servant of the Charitable One
Girl/Female
Indian, Sikh
Tradition; Prestigious Customs
Boy/Male
Hindu, Indian
Lord Shiva
Girl/Female
German, Greek
Shining; Brightness; Variant of Helen
Boy/Male
Hebrew
Powerful.
Boy/Male
Hindu
From gods familiy
Girl/Female
Tamil
Vanisri | வாநீஷà¯à®°à¯€
Girl/Female
Arabic, Muslim
Heaven
Boy/Male
Indian, Punjabi, Sikh
Sun; Shy
QUANTIZATION
QUANTIZATION
QUANTIZATION
QUANTIZATION
QUANTIZATION