s-parameterized Weyl transformation and the corresponding quantization scheme

By extending the usual Weyl transformation to the s-parameterized Weyl transformation with s being a real parameter,we obtain the s-parameterized quantization scheme which includes P–Q quantization, Q–P quantization, and Weyl ordering as its three special cases. Some operator identities can be derived directly by virtue of the s-parameterized quantization scheme.

Number-Phase Quantization Scheme for L-C Circuit

For a mesoscopic L-C circuit,besides the Louisell's quantization scheme in which electric charge q andelectric current I are respectively quantized as the coordinate operator Q and momentum operator P,in this paperwe propose a new quantization scheme in the context of number-phase quantization through the standard Lagrangianformalism.The comparison between this number-phase quantization with the Josephson junction's Cooper pair number-phase-difference quantization scheme is made.

Unifying the theory of integration within normal-,Weyl- and antinormal-ordering of operators and the s-ordered operator expansion formula of density operators

By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.

Mutual transformations between the P–Q, Q–P, and generalized Weyl ordering of operators

Based on the generalized Weyl quantization scheme, which relies on the generalized Wigner operator Ok （p, q） with a real k parameter and can unify the P-Q, Q-P, and Weyl ordering of operators in k = 1, - 1,0, respectively, we find the mutual transformations between 6 （p - P） （q - Q）, （q - Q） 3 （p - P）, and （p, q）, which are, respectively, the integration kernels of the P-Q, Q-P, and generalized Weyl quantization schemes. The mutual transformations provide us with a new approach to deriving the Wigner function of quantum states. The - and - ordered forms of （p, q） are also derived, which helps us to put the operators into their - and - ordering, respectively.

Speech compression scheme based on wavelet transform and vector quantization

A coding method of speech compression, which is based on Wavlet Transform and Vector Quantization (VQ), is developed and studied. The Wavlet Thansform or Wavlet Packet Thansform is used to process the speech signal, then VQ is used to compress the coefficients of Wavlet Thansform, and the entropy coding is used to decrease the bit rate. The experimental results show that the speech signal, sampled by 8 kHz sampling rate and 8 bit quatisation,i.e., 64 kbit/s bit rate, can be compressed to 6 - 8 kbit/s, and still have high speech quality,and the low-delay, only 8 ms.

AutoQNN: An End-to-End Framework for Automatically Quantizing Neural Networks

Exploring the expected quantizing scheme with suitable mixed-precision policy is the key to compress deep neural networks(DNNs)in high efficiency and accuracy.This exploration implies heavy workloads for domain experts,and an automatic compression method is needed.However,the huge search space of the automatic method introduces plenty of computing budgets that make the automatic process challenging to be applied in real scenarios.In this paper,we propose an end-to-end framework named AutoQNN,for automatically quantizing different layers utilizing different schemes and bitwidths without any human labor.AutoQNN can seek desirable quantizing schemes and mixed-precision policies for mainstream DNN models efficiently by involving three techniques:quantizing scheme search(QSS),quantizing precision learning(QPL),and quantized architecture generation(QAG).QSS introduces five quantizing schemes and defines three new schemes as a candidate set for scheme search,and then uses the Differentiable Neural Architecture Search(DNAS)algorithm to seek the layer-or model-desired scheme from the set.QPL is the first method to learn mixed-precision policies by reparameterizing the bitwidths of quantizing schemes,to the best of our knowledge.QPL optimizes both classification loss and precision loss of DNNs efficiently and obtains the relatively optimal mixed-precision model within limited model size and memory footprint.QAG is designed to convert arbitrary architectures into corresponding quantized ones without manual intervention,to facilitate end-to-end neural network quantization.We have implemented AutoQNN and integrated it into Keras.Extensive experiments demonstrate that AutoQNN can consistently outperform state-of-the-art quantization.For 2-bit weight and activation of AlexNet and ResNet18,AutoQNN can achieve the accuracy results of 59.75%and 68.86%,respectively,and obtain accuracy improvements by up to 1.65%and 1.74%,respectively,compared with state-of-the-art methods.Especially,compared with the full-precision AlexNet and ResNet18,the 2-bit models only slightly incur accuracy degradation by 0.26%and 0.76%,respectively,which can fulfill practical application demands.

A modification of Faddeev–Popov approach free from Gribov ambiguity

We propose a modified version of the Faddeev–Popov(FP)quantization approach for nonAbelian gauge field theory to avoid Gribov ambiguity.We show that by means of introducing a new method of inserting the correct identity into the Yang–Mills generating functional and considering the identity generated by an integral through a subgroup of the gauge group,the problem of Gribov ambiguity can be removed naturally.Meanwhile by handling the absolute value of the FP determinant with the method introduced by Williams and collaborators,we lift the Jacobian determinant together with the absolute value and obtain a local Lagrangian.The new Lagrangian will have a nilpotent symmetry which can be viewed as an analog of the Becchi–Rouet–Stora–Tyutin symmetry.