Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks

The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization.

Reinforcement Learning Based Quantization Strategy Optimal Assignment Algorithm for Mixed Precision

The quantization algorithm compresses the original network by reducing the numerical bit width of the model,which improves the computation speed. Because different layers have different redundancy and sensitivity to databit width. Reducing the data bit width will result in a loss of accuracy. Therefore, it is difficult to determinethe optimal bit width for different parts of the network with guaranteed accuracy. Mixed precision quantizationcan effectively reduce the amount of computation while keeping the model accuracy basically unchanged. In thispaper, a hardware-aware mixed precision quantization strategy optimal assignment algorithm adapted to low bitwidth is proposed, and reinforcement learning is used to automatically predict the mixed precision that meets theconstraints of hardware resources. In the state-space design, the standard deviation of weights is used to measurethe distribution difference of data, the execution speed feedback of simulated neural network accelerator inferenceis used as the environment to limit the action space of the agent, and the accuracy of the quantization model afterretraining is used as the reward function to guide the agent to carry out deep reinforcement learning training. Theexperimental results show that the proposed method obtains a suitable model layer-by-layer quantization strategyunder the condition that the computational resources are satisfied, and themodel accuracy is effectively improved.The proposed method has strong intelligence and certain universality and has strong application potential in thefield of mixed precision quantization and embedded neural network model deployment.

In situ calibrated angle between the quantization axis and the propagating direction of the light field for trapping neutral atoms

The recently developed magic-intensity trapping technique of neutral atoms efficiently mitigates the detrimental effect of light shifts on atomic qubits and substantially enhances the coherence time. This technique relies on applying a bias magnetic field precisely parallel to the wave vector of a circularly polarized trapping laser field. However, due to the presence of the vector light shift experienced by the trapped atoms, it is challenging to precisely define a parallel magnetic field, especially at a low bias magnetic field strength, for the magic-intensity trapping of85Rb qubits. In this work, we present a method to calibrate the angle between the bias magnetic field and the trapping laser field with the compensating magnetic fields in the other two directions orthogonal to the bias magnetic field direction. Experimentally, with a constantdepth trap and a fixed bias magnetic field, we measure the respective resonant frequencies of the atomic qubits in a linearly polarized trap and a circularly polarized one via the conventional microwave Rabi spectra with different compensating magnetic fields and obtain the corresponding total magnetic fields via the respective resonant frequencies using the Breit–Rabi formula. With known total magnetic fields, the angle is a function of the other two compensating magnetic fields.Finally, the projection value of the angle on either of the directions orthogonal to the bias magnetic field direction can be reduced to 0(4)° by applying specific compensating magnetic fields. The measurement error is mainly attributed to the fluctuation of atomic temperature. Moreover, it also demonstrates that, even for a small angle, the effect is strong enough to cause large decoherence of Rabi oscillation in a magic-intensity trap. Although the compensation method demonstrated here is explored for the magic-intensity trapping technique, it can be applied to a variety of similar precision measurements with trapped neutral atoms.

Network-Assisted Full-Duplex Cell-Free mmWave Massive MIMO Systems with DAC Quantization and Fronthaul Compression

In this paper,we investigate networkassisted full-duplex(NAFD)cell-free millimeter-wave(mmWave)massive multiple-input multiple-output(MIMO)systems with digital-to-analog converter(DAC)quantization and fronthaul compression.We propose to maximize the weighted uplink and downlink sum rate by jointly optimizing the power allocation of both the transmitting remote antenna units(T-RAUs)and uplink users and the variances of the downlink and uplink fronthaul compression noises.To deal with this challenging problem,we further apply a successive convex approximation(SCA)method to handle the non-convex bidirectional limited-capacity fronthaul constraints.The simulation results verify the convergence of the proposed SCA-based algorithm and analyze the impact of fronthaul capacity and DAC quantization on the spectral efficiency of the NAFD cell-free mmWave massive MIMO systems.Moreover,some insightful conclusions are obtained through the comparisons of spectral efficiency,which shows that NAFD achieves better performance gains than cotime co-frequency full-duplex cloud radio access network(CCFD C-RAN)in the cases of practical limited-resolution DACs.Specifically,their performance gaps with 8-bit DAC quantization are larger than that with1-bit DAC quantization,which attains a 5.5-fold improvement.

A Novel Quantization and Model Compression Approach for Hardware Accelerators in Edge Computing

Massive computational complexity and memory requirement of artificial intelligence models impede their deploy-ability on edge computing devices of the Internet of Things(IoT).While Power-of-Two(PoT)quantization is pro-posed to improve the efficiency for edge inference of Deep Neural Networks(DNNs),existing PoT schemes require a huge amount of bit-wise manipulation and have large memory overhead,and their efficiency is bounded by the bottleneck of computation latency and memory footprint.To tackle this challenge,we present an efficient inference approach on the basis of PoT quantization and model compression.An integer-only scalar PoT quantization(IOS-PoT)is designed jointly with a distribution loss regularizer,wherein the regularizer minimizes quantization errors and training disturbances.Additionally,two-stage model compression is developed to effectively reduce memory requirement,and alleviate bandwidth usage in communications of networked heterogenous learning systems.The product look-up table(P-LUT)inference scheme is leveraged to replace bit-shifting with only indexing and addition operations for achieving low-latency computation and implementing efficient edge accelerators.Finally,comprehensive experiments on Residual Networks(ResNets)and efficient architectures with Canadian Institute for Advanced Research(CIFAR),ImageNet,and Real-world Affective Faces Database(RAF-DB)datasets,indicate that our approach achieves 2×∼10×improvement in the reduction of both weight size and computation cost in comparison to state-of-the-art methods.A P-LUT accelerator prototype is implemented on the Xilinx KV260 Field Programmable Gate Array(FPGA)platform for accelerating convolution operations,with performance results showing that P-LUT reduces memory footprint by 1.45×,achieves more than 3×power efficiency and 2×resource efficiency,compared to the conventional bit-shifting scheme.

Image Steganography by Pixel-Value Differencing Using General Quantization Ranges

A new steganographic method by pixel-value differencing(PVD)using general quantization ranges of pixel pairs’difference values is proposed.The objective of this method is to provide a data embedding technique with a range table with range widths not limited to powers of 2,extending PVD-based methods to enhance their flexibility and data-embedding rates without changing their capabilities to resist security attacks.Specifically,the conventional PVD technique partitions a grayscale image into 1×2 non-overlapping blocks.The entire range[0,255]of all possible absolute values of the pixel pairs’grayscale differences in the blocks is divided into multiple quantization ranges.The width of each quantization range is a power of two to facilitate the direct embedding of the bit information with high embedding rates.Without using power-of-two range widths,the embedding rates can drop using conventional embedding techniques.In contrast,the proposed method uses general quantization range widths,and a multiple-based number conversion mechanism is employed skillfully to implement the use of nonpower-of-two range widths,with each pixel pair being employed to embed a digit in the multiple-based number.All the message bits are converted into a big multiple-based number whose digits can be embedded into the pixel pairs with a higher embedding rate.Good experimental results showed the feasibility of the proposed method and its resistance to security attacks.In addition,implementation examples are provided,where the proposed method adopts non-power-of-two range widths and employsmultiple-based number conversion to expand the data-hiding and steganalysis-resisting capabilities of other PVD methods.

Learning Vector Quantization-Based Fuzzy Rules Oversampling Method

Imbalanced datasets are common in practical applications,and oversampling methods using fuzzy rules have been shown to enhance the classification performance of imbalanced data by taking into account the relationship between data attributes.However,the creation of fuzzy rules typically depends on expert knowledge,which may not fully leverage the label information in training data and may be subjective.To address this issue,a novel fuzzy rule oversampling approach is developed based on the learning vector quantization(LVQ)algorithm.In this method,the label information of the training data is utilized to determine the antecedent part of If-Then fuzzy rules by dynamically dividing attribute intervals using LVQ.Subsequently,fuzzy rules are generated and adjusted to calculate rule weights.The number of new samples to be synthesized for each rule is then computed,and samples from the minority class are synthesized based on the newly generated fuzzy rules.This results in the establishment of a fuzzy rule oversampling method based on LVQ.To evaluate the effectiveness of this method,comparative experiments are conducted on 12 publicly available imbalance datasets with five other sampling techniques in combination with the support function machine.The experimental results demonstrate that the proposed method can significantly enhance the classification algorithm across seven performance indicators,including a boost of 2.15%to 12.34%in Accuracy,6.11%to 27.06%in G-mean,and 4.69%to 18.78%in AUC.These show that the proposed method is capable of more efficiently improving the classification performance of imbalanced data.

Hierarchical Controller Synthesis Under Linear Temporal Logic Specifications Using Dynamic Quantization

Linear temporal logic(LTL)is an intuitive and expressive language to specify complex control tasks,and how to design an efficient control strategy for LTL specification is still a challenge.In this paper,we implement the dynamic quantization technique to propose a novel hierarchical control strategy for nonlinear control systems under LTL specifications.Based on the regions of interest involved in the LTL formula,an accepting path is derived first to provide a high-level solution for the controller synthesis problem.Second,we develop a dynamic quantization based approach to verify the realization of the accepting path.The realization verification results in the necessity of the controller design and a sequence of quantization regions for the controller design.Third,the techniques of dynamic quantization and abstraction-based control are combined together to establish the local-to-global control strategy.Both abstraction construction and controller design are local and dynamic,thereby resulting in the potential reduction of the computational complexity.Since each quantization region can be considered locally and individually,the proposed hierarchical mechanism is more efficient and can solve much larger problems than many existing methods.Finally,the proposed control strategy is illustrated via two examples from the path planning and tracking problems of mobile robots.

Does There Exist the Applicability Limit of PDE to Describe Physical Phenomena?—A Personal Survey of Quantization, QED, Turbulence

What does it mean to study PDE (Partial Differential Equation)? How and what to do “to claim proudly that I’m studying a certain PDE”? Newton mechanic uses mainly ODE (Ordinary Differential Equation) and describes nicely movements of Sun, Moon and Earth etc. Now, so-called quantum phenomenum is described by, say Schrödinger equation, PDE which explains both wave and particle characters after quantization of ODE. The coupled Maxwell-Dirac equation is also “quantized” and QED (Quantum Electro-Dynamics) theory is invented by physicists. Though it is said this QED gives very good coincidence between theoretical1 and experimental observed quantities, but what is the equation corresponding to QED? Or, is it possible to describe QED by “equation” in naive sense?

Quantization of Action for Elementary Particles and the Principle of Least Action

The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. Even after approximate treatment, the results obtained are not completely consistent with those obtained by solving Schrödinger’s equation. This indicates that further research on the uncertainty principle is necessary. Therefore, using the de Broglie matter wave hypothesis, we quantize the action of an elementary particle in natural coordinates and obtain the quantization condition and a new deterministic relation. Using this quantization condition, we obtain the energy level formulas of an elementary particle in different conditions in a classical way that is completely consistent with the results obtained by solving Schrödinger’s equation. A new physical interpretation is given for the particle eigenfunction independence of probability for an elementary particle: an elementary particle is in a particle state at the space-time point where the action is quantized, and in a wave state in the rest of the space-time region. The space-time points of particle nature and the wave regions of particle motion constitute the continuous trajectory of particle motion. When an elementary particle is in a particle state, it is localized, whereas in the wave state region, it is nonlocalized.

A hybrid quantum encoding algorithm of vector quantization for image compression

Many classical encoding algorithms of vector quantization （VQ） of image compression that can obtain global optimal solution have computational complexity O（N）. A pure quantum VQ encoding algorithm with probability of success near 100% has been proposed, that performs operations 45√N times approximately. In this paper, a hybrid quantum VQ encoding algorithm between the classical method and the quantum algorithm is presented. The number of its operations is less than √N for most images, and it is more efficient than the pure quantum algorithm.

The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization?

The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.

Stabilization of Uncertain Systems With Markovian Modes of Time Delay and Quantization Density

This work studies the stabilization of a class of control systems that use communication networks as signal transmission medium. The lateral motion of independently actuated four-wheel vehicle is modeled as an uncertain-linear system. Time delay and quantization density are modeled as Markov chains.The networked control systems(NCSs) with plants being lateral motion are first transformed to switched linear systems with uncertain parameters. Sufficient and necessary conditions for the stochastic stability of closed-loop networked control systems are then established. By solving the matrix inequalities, this work presents an output-feedback controller that depends on the modes of time delay and quantization density. The controller performance is illustrated via a vehicular lateral motion system.

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

The Benefits of Affine Quantization

Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as p and q, and numerous classical Hamiltonians H(p,q), as well as field theories, such as π(x) and φ(x), and many classical Hamiltonians H(π,φ. However, in all such systems, there are situations for which canonical quantization fails. This includes certain particle and field theory problems. Affine quantization involves a simple recombination of classical variables that lead to a new chapter in the process of quantization, and which is able to solve a vast variety of normally insoluble systems, such as quartic interactions in scalar field theory in spacetime dimensions 4 and higher, as well as the quantization of Einstein’s gravity in 4 spacetime dimensions.

Quantization of light energy directly from classical electromagnetic theory in vacuum

It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles.

Establishing formal state space models via quantization forquantum control systems

Formal state space models of quantum control systems are deduced and a scheme to establish formal state space models via quantization could been obtained for quantum control systems is proposed. State evolution of quantum control systems must accord with Schrdinger equations, so it is foremost to obtain Hamiltonian operators of systems. There are corresponding relations between operators of quantum systems and corresponding physical quantities of classical systems, such as momentum, energy and Hamiltonian, so Schrdinger equation models of corresponding quantum control systems via quantization could been obtained from classical control systems, and then establish formal state space models through the suitable transformation from Schrdinger equations for these quantum control systems. This method provides a new kind of path for modeling in quantum control.

Using Affine Quantization to Analyze Non-Renormalizable Scalar Fields and the Quantization of Einstein’s Gravity

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any quantization, such as Schroedinger’s representation and Schroedinger’s equation. Careful attention is paid toward seeking favored classical variables, which are those that should be promoted to the principal quantum operators. This effort leads toward classical variables that have a constant positive, zero, or negative curvature, which typically characterize such favored variables. This focus leans heavily toward affine variables with a constant negative curvature, which leads to a surprisingly accommodating analysis of non-renormalizable scalar models as well as Einstein’s general relativity.

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.

An Efficient Information Hiding Scheme Based on Closest Paired Tree Structure Vector Quantization

Information hiding schemes based on vector quantization （VQ） usually require lengthy VQ encoding and decoding processes. In this paper, we propose an efficient information hiding method based on closest paired tree structure vector quantization （CPTSVQ）. The simulation result shows that the execution time of the proposed scheme is much shorter than that attained by previous approaches.