Efficient Quantization Research Articles

Integer‐Sheet‐Pump Quantization for Hexahedral Meshing

AbstractSeveral state‐of‐the‐art algorithms for semi‐structured hexahedral meshing involve a so called quantization step to decide on the integer DoFs of the meshing problem, corresponding to the number of hexahedral elements to embed into certain regions of the domain. Existing reliable methods for quantization are based on solving a sequence of integer quadratic programs (IQP). Solving these in a timely and predictable manner with general‐purpose solvers is a challenge, even more so in the open‐source field. We present here an alternative robust and efficient quantization scheme that is instead based on solving a series of continuous linear programs (LP), for which solver availability and efficiency are not an issue. In our formulation, such LPs are used to determine where inflation or deflation of virtual hexahedral sheets are favorable. We compare our method to two implementations of the former IQP formulation (using a commercial and an open‐source MIP solver, respectively), finding that (a) the solutions found by our method are near‐optimal or optimal in most cases, (b) these solutions are found within a much more predictable time frame, and (c) the state of the art run time is outperformed, in the case of using the open‐source solver by orders of magnitude.

AE-Qdrop: Towards Accurate and Efficient Low-Bit Post-Training Quantization for A Convolutional Neural Network

Blockwise reconstruction with adaptive rounding helps achieve acceptable 4-bit post-training quantization accuracy. However, adaptive rounding is time intensive, and the optimization space of weight elements is constrained to a binary set, thus limiting the performance of quantized models. The optimality of block-wise reconstruction requires that subsequent network blocks remain unquantized. To address this, we propose a two-stage post-training quantization scheme, AE-Qdrop, encompassing block-wise reconstruction and global fine-tuning. In the block-wise reconstruction stage, a progressive optimization strategy is introduced as a replacement for adaptive rounding, enhancing both quantization accuracy and efficiency. Additionally, the integration of randomly weighted quantized activation helps mitigate the risk of overfitting. In the global fine-tuning stage, the weights of each quantized network block are corrected simultaneously through logit matching and feature matching. Experiments in image classification and object detection tasks validate that AE-Qdrop achieves high precision and efficient quantization. For the 2-bit MobileNetV2, AE-Qdrop outperforms Qdrop in quantization accuracy by 6.26%, and its quantization efficiency is fivefold higher.

Quantized minimum error entropy with fiducial points for robust regression

Minimum error entropy with fiducial points (MEEF) has received a lot of attention, due to its outstanding performance to curb the negative influence caused by non-Gaussian noises in the fields of machine learning and signal processing. However, the estimate of the information potential of MEEF involves a double summation operator based on all available error samples, which can result in large computational burden in many practical scenarios. In this paper, an efficient quantization method is therefore adopted to represent the primary set of error samples with a smaller subset, generating a quantized MEEF (QMEEF). Some basic properties of QMEEF are presented and proved from theoretical perspectives. In addition, we have applied this new criterion to train a class of linear-in-parameters models, including the commonly used linear regression model, random vector functional link network, and broad learning system as special cases. Experimental results on various datasets are reported to demonstrate the desirable performance of the proposed methods to perform regression tasks with contaminated data.

Trainable quantization for Speedy Spiking Neural Networks.

Spiking neural networks are considered as the third generation of Artificial Neural Networks. SNNs perform computation using neurons and synapses that communicate using binary and asynchronous signals known as spikes. They have attracted significant research interest over the last years since their computing paradigm allows theoretically sparse and low-power operations. This hypothetical gain, used from the beginning of the neuromorphic research, was however limited by three main factors: the absence of an efficient learning rule competing with the one of classical deep learning, the lack of mature learning framework, and an important data processing latency finally generating energy overhead. While the first two limitations have recently been addressed in the literature, the major problem of latency is not solved yet. Indeed, information is not exchanged instantaneously between spiking neurons but gradually builds up over time as spikes are generated and propagated through the network. This paper focuses on quantization error, one of the main consequence of the SNN discrete representation of information. We argue that the quantization error is the main source of accuracy drop between ANN and SNN. In this article we propose an in-depth characterization of SNN quantization noise. We then propose a end-to-end direct learning approach based on a new trainable spiking neural model. This model allows adapting the threshold of neurons during training and implements efficient quantization strategies. This novel approach better explains the global behavior of SNNs and minimizes the quantization noise during training. The resulting SNN can be trained over a limited amount of timesteps, reducing latency, while beating state of the art accuracy and preserving high sparsity on the main datasets considered in the neuromorphic community.

Efficient quantization of painting images by relevant colors

Realistic images often contain complex variations in color, which can make economical descriptions difficult. Yet human observers can readily reduce the number of colors in paintings to a small proportion they judge as relevant. These relevant colors provide a way to simplify images by effectively quantizing them. The aim here was to estimate the information captured by this process and to compare it with algorithmic estimates of the maximum information possible by colorimetric and general optimization methods. The images tested were of 20 conventionally representational paintings. Information was quantified by Shannon’s mutual information. It was found that the estimated mutual information in observers’ choices reached about 90% of the algorithmic maxima. For comparison, JPEG compression delivered somewhat less. Observers seem to be efficient at effectively quantizing colored images, an ability that may have applications in the real world.

Quadratic variable step-size quantization for efficient raw-data acquisition of image sensors

This paper verifies, via simulations, that quadratic quantization is the most efficient quantization scheme for image-sensor raw-data acquisition. First, discrete-input quadratic quantizers for quantizing the number of photons that sensor pixels receive are developed. Using the discrete-input quadratic quantizers, it is shown that multi-bit QIS outputs can be quantized without loss of image information. Next, artificially generated extremely weak-signal regions are employed to show that quadratic quantizers can preserve all the image information using much lower bit-depth than linear and exponential quantizers. It is concluded that quadratic quantizers should be hardware implemented in image sensors and there is no need to keep linear raw data for the final output of image sensors.

Algorithm and hardware co-design co-optimization framework for LSTM accelerator using quantized fully decomposed tensor train

Nowadays, from companies to academics, researchers across the world are interested in developing Deep Neural Networks (DNNs) due to their incredible feats in various applications, such as image recognition, playing complex games, and large-scale information retrieval such as web search. However, when people enjoy the advantages of DNNs, the high computational and power demands on resource-constrained electronic devices of the DNN model have received more attention. Optimizing the DNN model, such as model compression, is crucial to ensure wide deployment of DNNs and promote DNNs to implement most resource-constrained scenarios. Among many techniques, tensor train (TT) decomposition is considered a very promising technology. Although our previous efforts achieve (1) expanding limits of the number of multiplications eliminating all redundant computations; and (2) decomposing into multistage processing to reduce memory traffic, the potential of this work is not fully explored.In this paper, we investigate and demystify the TT decomposition within a thoughtful hardware mind. This paper develops an efficient hardware optimization methodology within a novel hardware solution. Two key merits will be achieved in this project: (1) it enables a novel approach to apply TT-decomposition on the entire LSTM model; (2) a much more efficient quantization method has been proposed at the hardware optimization level; (3) an efficient hardware accelerator that unitizes the hardware and algorithm co-design method has been designated.Based on these novelties, the proposed work can achieve 1.69× power reduction and 2.28× power efficiency (GOPS/W) in different workloads. In addition, compared to the state-of-the-art C-LSTM, it achieves 2.09× higher throughput, 3.67% accuracy increase, 2.45× power efficiency, and a 1.18× power reduction. The results show that our proposed accelerator exhibits significant advantages over state-of-the-art solutions.

Limited Feedback Design Based on Kronecker Product Codebook for Massive MIMO Systems

To realize massive multiple-input multiple-output (MIMO) systems, the uniform planar array (UPA) structure has been adopted to deploy a large number of antennas in a limited area of a radio unit at a base station. Subsequently, the Kronecker product (KP) codebook, consisting of horizontal and vertical-domain codebooks, was introduced to enable efficient quantization and feedback for the channel state information (CSI) under the UPA structure. In this paper, we propose advanced limited feedback schemes based on the KP codebook for massive MIMO systems. First, we propose one feedback bit allocation scheme to maximize the beamforming gain. Eigenvalues of spatial correlation channels are used to determine the numbers of feedback bits for horizontal and vertical-domain CSI, and the numbers of feedback bits to maximize the beamforming gain are derived as a closed-form expression. Moreover, we propose a novel feedback and pilot transmission scheme to reduce both the feedback and pilot overhead. The proposed feedback and pilot transmission scheme utilizes the property that the small-scale fading information can be compressed only to the horizontal-domain CSI when the spatial correlation of the vertical-domain channel is high. Simulation results show that, with the use of the proposed feedback bit allocation, the beamforming gain increases by up to 65% compared with the fixed feedback bit allocation when the horizontal and vertical-domain spatial correlation coefficients are equal to 0.57, and the numbers of horizontal and vertical-domain antennas are 8 and 12, respectively. In addition, it is also shown that the proposed feedback and pilot transmission scheme improves the ergodic rate by up to 48% compared with conventional feedback schemes.

EPQuant: A Graph Neural Network compression approach based on product quantization

Graph Neural Networks (GNNs) have been widely used in graph analysis due to their strong performance on a wide variety of tasks. Unfortunately, as the size of graphs keeps growing, large graphs can easily consume Terabytes, and training on such graphs may take days. The high memory footprint limits the usage of GNNs on resource-constrained devices like smartphones and IoT devices. Hence, reducing the storage cost, training time, and inference latency is highly desirable. In this work, we apply Product Quantization (PQ) on GNNs for the first time to achieve superior memory capacity reduction. To alleviate the processing burden caused by PQ and improve compression performance, we propose Enhanced Product Quantization (EPQ). It reduces the input graph data, which tends to dominate memory consumption, and accelerates clustering in PQ. Moreover, an efficient quantization framework11Github repository:https://github.com/Lyun-Huang/EPQuant for GNNs is proposed, which combines EPQ with Scalar Quantization (SQ), to achieve improved compression performance and computation acceleration on off-the-shelf hardware, enabling the deployment of GNNs on resource-constrained devices. In addition, the proposed quantization framework can be applied to the existing GNNs without too much porting effort. Extensive experimental results show that the proposed quantization scheme can achieve 321.26× and 184.03× memory capacity compression for input graph data and overall storage, respectively. This impressive memory reduction can come with an accuracy loss of less than 1%.

Efficient Quantisation and Weak Covering of High Dimensional Cubes

Let {mathbb {Z}}_n = {Z_1, ldots , Z_n} be a design; that is, a collection of n points Z_j in [-1,1]^d. We study the quality of quantisation of [-1,1]^d by the points of {mathbb {Z}}_n and the problem of quality of coverage of [-1,1]^d by {{{mathcal {B}}}}_d({mathbb {Z}}_n,r), the union of balls centred at Z_j in {mathbb {Z}}_n. We concentrate on the cases where the dimension d is not small, dge 5, and n is not too large, nle 2^d. We define the design {{mathbb {D}}_{n,delta }} as a 2^{d-1} design defined on vertices of the cube [-delta ,delta ]^d, 0le delta le 1. For this design, we derive a closed-form expression for the quantisation error and very accurate approximations for the coverage area {text {vol}}{([-1,1]^d cap {{{mathcal {B}}}}_d({mathbb {Z}}_n,r))}. We provide results of a large-scale numerical investigation confirming the accuracy of the developed approximations and the efficiency of the designs {{mathbb {D}}_{n,delta }}.

High-Performance VLSI Architecture of DLMS Adaptive Filter for Fast-Convergence and Low-MSE

This brief presents a high-performance VLSI architecture of delayed least mean square (DLMS) adaptive filter for fast-convergence and low-mean square error (MSE) using distributed arithmetic (DA). The proposed design estimates response against the adaptation delays using a parallel predictive adder tree followed by a shift accumulate (SA) unit. An efficient quantization scheme with two bits of scaled error signal is also suggested. Single SA unit for multiple DA bases is used to reduce the number of adders and registers. Simulation and synthesis results show that the proposed design for 32 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order provides 19.72% lesser area, 25.51% lesser power, lesser 28.89% MSE and 59.91% lesser MSE/area over the best existing design.

Rate–distortion optimal evolutionary algorithm for JPEG quantization with multiple rates

The JPEG standard is used extensively in image-related applications. The optimization on a JPEG-standard compressor is of high importance for image storage and transmission. In this paper, we propose a versatile and efficient quantization optimization method for image compression. It is based on multi-objective optimization and is JPEG standard-compatible. Unlike the existing optimization methods, our method fully considers the rate–distortion optimal principle and provides several optimal solutions to address the multiple-rate requirement in applications. In the multi-objective evolutionary optimization framework, the fitness of each quantization table for JPEG compression is evaluated efficiently by the searching in a look-up table, which is constructed based on the statistics of each DCT band in a pre-defined manner. Then, the population update strategy based on the rate–distortion optimal principle is recommended to guide the evolution toward the best rate–distortion performance. Furthermore, to maintain the population’s diversity and uniformity, convex-hull based environmental selection is recommended to identify the solutions at the first Pareto front, and the identified solutions are enriched further with scaling operation to fill the blank rate range. The experimental results for several classic datasets demonstrate the superiority of our method in terms of solution distribution, coding efficiency, and computational complexity.

Performance-Optimized Quantization for SAR and InSAR Applications

For the design of present and next-generation spaceborne SAR missions, constantly increasing data rates are being demanded, which impose stringent requirements in terms of onboard memory and downlink capacity. In this scenario, the efficient quantization of SAR raw data is of primary importance, since the utilized compression rate is directly related to the volume of data to be stored and transmitted to the ground and, at the same time, it affects the resulting SAR imaging performance. In this paper, we introduce the performance-optimized block-adaptive quantization (PO-BAQ), a novel approach for SAR raw data compression which aims at optimizing the resource allocation and, at the same time, the quality of the resulting SAR and InSAR products. This goal is achieved by exploiting the a priori knowledge of the local SAR backscatter statistics, which allows for the generation of high-resolution bitrate maps that can be employed to fulfill a predefined performance requirement. Analyses on experimental TanDEM-X interferometric data are presented, which demonstrate the potentials of the proposed method as a helpful tool for performance budget definition and data rate optimization of present and future SAR missions.

Reliability‐based quantization for soft decoding of LDPC codes in short‐reach optical links

Efficient quantizer design is vital in high-speed optical receivers. In this paper, the authors propose a three-level (1.5-bit) reliability-based quantizer for low-complexity soft decoding of low-density parity-check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate-compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability-based quantizer, and it is shown that the resulting quantizer-aware LDPC codes significantly outperform other existing codes of similar rates.

RATQ: A Universal Fixed-Length Quantizer for Stochastic Optimization

We present Rotated Adaptive Tetra-iterated Quantizer (RATQ), a fixed-length quantizer for gradients in first order stochastic optimization. RATQ is easy to implement and involves only a Hadamard transform computation and adaptive uniform quantization with appropriately chosen dynamic ranges. For noisy gradients with almost surely bounded Euclidean norms, we establish an information theoretic lower bound for optimization accuracy using finite precision gradients and show that RATQ almost attains this lower bound. For mean square bounded noisy gradients, we use a gain-shape quantizer which separately quantizes the Euclidean norm and uses RATQ to quantize the normalized unit norm vector. We establish lower bounds for performance of any optimization procedure and shape quantizer, when used with a uniform gain quantizer. Finally, we propose an adaptive quantizer for gain which when used with RATQ for shape quantizer outperforms uniform gain quantization and is, in fact, close to optimal. As a by-product, we show that our fixed-length quantizer RATQ has almost the same performance as the optimal variable-length quantizers for distributed mean estimation. Also, we obtain an efficient quantizer for Gaussian vectors which attains a rate very close to the Gaussian rate-distortion function and is, in fact, universal for sub Gaussian input vectors.

Mel Scale-Based Linear Prediction Approach to Reduce the Prediction Filter Order in CELP Paradigm

This paper proposes a novel method to reduce the order of prediction filter from 10 to 7 in Code Excited Linear Prediction (CELP) coding framework by the inclusion of psychoacoustic Mel scale into Linear Predictive Coding (Mel-LPC). Efficient quantization methods using 2-split Vector Quantization (VQ) for Mel-LPC obtained a reduction of 4 bits/frame and resulted in a total bit gain of 200 bps. A weighting scheme for the Euclidean distance measure gave a reduction of 6 bits/frame that adds up to a total bit gain of 300 bps. A lower Mel-LPC order of 3 has been employed for unvoiced frames by using the perceptual quality as selection criteria and an efficient VQ method using 5 bits is developed which brought down the average bit requirement to 11.5 bits/frame. To incorporate this into Mel-LPC-based CELP encoding scheme, a neural network-based voiced-unvoiced classification algorithm using 5 derived features as input has been constructed and this selection of filter order based on signal statistics provides the benefit of bit reduction by 625 and 325 bps, respectively, for 10th order LPC and 7th order Mel-LPC. In addition to all, the incorporation of Mel-LPC gives a better performance in the estimation of formants.

Phase-frequency jointly quantizing method for cost-effective all-optical analog-to-digital conversion

We propose for the first time a two-dimensional phase-frequency jointly quantizing method for cost-effective all-optical analog-to-digital conversion (ADC), both on power consumption and structure complexity. By fully harnessing the power-dependent phase and frequency shift of the probe and pump light, respectively, that simultaneously occurs during the cross-phase modulation process, the method is studied with an on-chip interferometer structure based on nonlinear silicon-organic hybrid slot waveguide. Simulation results show the 4-bit quantization resolution is achieved by using only one interferometer, where N interferometers should be used in the conventional methods with resolution of N-bit. The proposed method provides an efficient optical quantization technique for all-optical ADC, also opens a new mind for exploring advanced all-optical ADC techniques using multi-dimensional degrees of freedom of light.

High-Throughput and Improved-Convergent Design of Pipelined Adaptive DFE for 5G Communication

This brief presents a high-throughput and improved convergent design of pipelined adaptive decision feedback equalizer (ADFE) for 5G communication system. The proposed ADFE design achieves 3.3 Gbps for 4-quadrature amplitude modulation (4-QAM) and 8th order feedback filter (FBF). A novel look-up table update scheme for M-ary QAM ADFE is proposed. Further, we present an efficient quantization scheme for the proposed design. Theoretical derivations and simulation results confirm that the convergence performance of the proposed ADFE is superior. For instance, the proposed design for 16-QAM and 16th order FBF takes 167 less iterations and improves 4.03 dB error performance, while it provides nearly 8.96 times higher throughput as compared to the best existing design.

Efficient CTDSM based on GM‐C quantiser and improved dynamic element matching

In this study, a continuous-time delta-sigma modulator (CTDSM) is developed using a Gm-C based noise-shaping quantiser (Gm-C-NSQ) with an improved dynamic element matching (i-DEM) algorithm. Here, a Gm-C integrator is used to develop NSQ, since it increases the effectiveness of the proposed modulator in terms of power consumption and die area. This Gm-C-NSQ uses only three dynamic latches to provide efficient quantisation level and to increase the order of noise shaping. Moreover, an i-DEM algorithm is utilised to reduce the non-linearities of the quantiser and mismatching error of the digital-to-analogue converters presented in the feedback structure of the modulator. Here, an 180 nm CMOS technology is used to design the proposed modulator and it functions at 2.6 MHz sampling frequency. Simulation results show that the proposed modulator can achieve a peak spurious-free dynamic range (SFDR) of 93.67 dB and a peak signal-to-noise ratio of 87.38 dB for 20 kHz signal bandwidth. Furthermore, the proposed modulator consumes 0.0863 mW power when 1.2 V supply voltage is applied.

An Efficient Deep Learning Framework for Low Rate Massive MIMO CSI Reporting

Channel state information (CSI) reporting is important for multiple-input multiple-output (MIMO) wireless transceivers to achieve high capacity and energy efficiency in frequency division duplex (FDD) mode. CSI reporting for massive MIMO systems could consume large bandwidth and degrade spectrum efficiency. Deep learning (DL)-based CSI reporting integrated with channel characteristics has demonstrated success in improving CSI compression and recovery. To further improve the encoding efficiency of CSI feedback, we develop an efficient DL-based compression framework CQNet to jointly tackle CSI compression, codeword quantization, and recovery under the bandwidth constraint. CQNet is directly compatible with other DL-based CSI feedback works for further enhancement. We propose a more efficient quantization scheme in the radial coordinate by introducing a novel magnitude-adaptive phase quantization framework. Compared with traditional CSI reporting, CQNet demonstrates superior CSI feedback efficiency and better CSI reconstruction accuracy.