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New Perspective on Inner Product Quantization
Physical Review Letters, 1998Summary: We devise a new and highly accurate quantization procedure for the inner product representation, in both configuration and momentum space. Utilizing the representation \(\Psi(\xi)=\sum_ia_i[E]\xi^iR_\beta(\xi)\), for an appropriate reference function, \(R_\beta(\xi)\), we demonstrate that the (convergent) zeros of the coefficient functions ...
Tymczak, C. J. +3 more
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QUANTIZED SYMMETRIZATIONS AND ⋆-PRODUCTS
Quantum Theory and Symmetries, 2002Mathematics
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The pointwise product in Weyl quantization
Journal of Physics A: Mathematical and General, 2004The present paper is devoted to an analysis of the recently introduced Bracken product of operators (which is distributive, commutative and associative), whose symbol is the pointwise product of distributions, in the framework of Weyl's approach to quantization, consisting, roughly speaking, in associating functions on phase space (the simplest case \(\
Dubin, D. A., Hennings, M. A.
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Uniform Variance Product Quantization
Applied Mechanics and Materials, 2014Product quantization (PQ) is an efficient and effective vector quantization approach to fast approximate nearest neighbor (ANN) search especially for high-dimensional data. The basic idea of PQ is to decompose the original data space into the Cartesian product of some low-dimensional subspaces and then every subspace is quantized separately with the ...
Qin Zhen Guo, Zhi Zeng, Shu Wu Zhang
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Accelerating Product Quantization Query Execution Runtime
Proceedings of the 2021 International Conference on Management of Data, 2021Product Quantization is a method for approximate nearest neighbor search. I review and analyze two recent SIMD-based query acceleration techniques and propose an algorithmic solution agnostic to the underlying hardware. This new method is competitive in terms of runtime to the SIMD-based methods and alleviates their drawbacks: reduced accuracy and ...
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Structure Sensitive Hashing With Adaptive Product Quantization
IEEE Transactions on Cybernetics, 2016Hashing has been proved as an attractive solution to approximate nearest neighbor search, owing to its theoretical guarantee and computational efficiency. Though most of prior hashing algorithms can achieve low memory and computation consumption by pursuing compact hash codes, however, they are still far beyond the capability of learning discriminative
Xianglong Liu 0001 +4 more
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Quarter-Point Codeword Expansion for Product Quantization
2019 IEEE International Conference on Multimedia and Expo (ICME), 2019Due to its low storage cost and high query accuracy, Product Quantization (PQ) has been widely used for approximate nearest neighbor (ANN) search. However, almost all existing PQ-based methods use the nearest clustering center as the codeword, which might not fully utilize the information of distances from data points to clustering centers.
Shan An +5 more
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Differentiable Optimized Product Quantization and Beyond
Proceedings of the ACM Web Conference 2023, 2023Zepu Lu +6 more
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The *-product Quantization of the Heisenberg Group
Proceedings of the International School of Physics “Enrico Fermi”, 1996F. Bonechi +3 more
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Star Products and Deformation Quantization
2017Among the “flavors” of deformation quantization, there are two whose interplay informs much of Boutet de Monvel’s work on this subject. In the first, sometimes known as semiclassical, a commutative algebra to be deformed, with associativity retained, is augmented by an external parameter (Planck’s constant in the application to classical/quantum ...
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