Vector Computers Research Articles

Design and Chip Implementation of a SMI/MVDR Dual-Mode Beamformer for Wireless MIMO Communication Systems

This paper presents a low complexity chip design supporting dual-mode beamforming, i.e. sampling matrix inversion (SMI) and the minimum variance distortionless response (MVDR), for wireless Multiple-Input Multiple-Output (MIMO) communication systems. The auto-correlation matrix inversion is the critical computing kernel shared by the two beamforming schemes. To alleviate the computing complexity, the auto-correlation matrix is approximated by a Toeplitz counterpart, which can be decomposed efficiently by applying the Cholesky decomposition and the Schur algorithm. This leads to an O (N 3 ) to O (N 2 ) complexity reduction, where N is the matrix size, while preserving computing parallelism for the hardware design. In addition, a diagonal loading technique is employed to mitigate the stability problem when the matrix is ill-conditioned. Simulation results indicate that no performance loss is observed due to the algorithm simplification measures. A systolic array based mapping procedure converts the two beamforming algorithms to a unified hardware accelerator design with 80% shared circuitry. Complex-valued divisions are achieved by adopting a hardware efficient coordinate rotation digital computer (CORDIC) scheme. In chip implementation, a TSMC 90nm UTM process technology is used and the design specs largely follow the requirements of IEEE 802.11ac standard. The core size of the chip design is 0.68mm2. The measurement results show that the chip can operate up to 200MHz with a power consumption of 49.03mW. It can complete the computation of a new beamforming vector (of size 8) every 0.64us and exhibits the highest throughput among the 6 compared designs.

A 2.9–33.0 TOPS/W Reconfigurable 1-D/2-D Compute-Near-Memory Inference Accelerator in 10-nm FinFET CMOS

A 10-nm compute-near-memory (CNM) accelerator augments SRAM with multiply accumulate (MAC) units to reduce interconnect energy and achieve 2.9 8b-TOPS/W for matrix–vector computation. The CNM provides high memory bandwidth by accessing SRAM subarrays to enable low-latency, real-time inference in fully connected and recurrent neural networks with small mini-batch sizes. For workloads with greater arithmetic intensity, such as large-batch convolutional neural networks, the CNM reconfigures into a 2-D systolic array to amortize memory access energy over a greater number of computations. Variable-precision 8b/4b/2b/1b MACs increase throughput by up to $8\times $ for binary operations at 33.0 1b-TOPS/W.

FPGAN: An FPGA Accelerator for Graph Attention Networks With Software and Hardware Co-Optimization

The Graph Attention Networks (GATs) exhibit outstanding performance in multiple authoritative node classification benchmark tests (including transductive and inductive). The purpose of this research is to implement an FPGA-based accelerator called FPGAN for graph attention networks that achieves significant improvement on performance and energy efficiency without losing accuracy compared with PyTorch baseline. It eliminates the dependence on digital signal processors (DSPs) and large amounts of on-chip memory and can even work well on low-end FPGA devices. We design FPGAN with software and hardware co-optimization across the full stack from algorithm through architecture. Specifically, we compress model to reduce the model size, quantify features to perform fixed-point calculation, replace multiplication addition cell (MAC) with shift addition units (SAUs) to eliminate the dependence on DSPs, and design an efficient algorithm to approximate SoftMax function. We also adjust the activation functions and fuse operations to further reduce the computation requirement. Moreover, all data is vectorized and aligned for scalable vector computation and efficient memory access. All the above optimizations are integrated into a universal hardware pipeline for various structures of GATs. We evaluate our design on an Inspur F10A board with an Intel Arria 10 GX1150 and 16 GB DDR3 memory. Experimental results show that FPGAN can achieve 7.34 times speedup over Nvidia Tesla V100 and 593 times over Xeon CPU Gold 5115 while maintaining accuracy, and 48 times and 2400 times on energy efficiency respectively.

8T SRAM Cell as a Multibit Dot-Product Engine for Beyond Von Neumann Computing

Large-scale digital computing almost exclusively relies on the von Neumann architecture, which comprises separate units for storage and computations. The energy-expensive transfer of data from the memory units to the computing cores results in the well-known von Neumann bottleneck. Various approaches aimed toward bypassing the von Neumann bottleneck are being extensively explored in the literature. These include in-memory computing based on CMOS and beyond CMOS technologies, wherein by making modifications to the memory array, vector computations can be carried out as close to the memory units as possible. Interestingly, in-memory techniques based on CMOS technology are of special importance due to the ubiquitous presence of field-effect transistors and the resultant ease of large-scale manufacturing and commercialization. On the other hand, perhaps the most important computation required for applications such as machine learning, etc., comprises the dot-product operation. Emerging nonvolatile memristive technologies have been shown to be very efficient in computing analog dot products in an in situ fashion. The memristive analog computation of the dot product results in much faster operation as opposed to digital vector in-memory bitwise Boolean computations. However, challenges with respect to large-scale manufacturing coupled with the limited endurance of memristors have hindered rapid commercialization of memristive-based computing solutions. In this paper, we show that the standard 8 transistor (8T) digital SRAM array can be configured as an analoglike in-memory multibit dot-product engine (DPE). By applying appropriate analog voltages to the read ports of the 8T SRAM array and sensing the output current, an approximate analog–digital DPE can be implemented. We present two different configurations for enabling multibit dot-product computations in the 8T SRAM cell array, without modifying the standard bit-cell structure. We also demonstrate the robustness of the present proposal in presence of nonidealities such as the effect of line resistances and transistor threshold voltage variations. Since our proposal preserves the standard 8T-SRAM array structure, it can be used as a storage element with standard read–write instructions and also as an on-demand analoglike dot-product accelerator.

Comparison of Implementation of Computation of Video Image Displacement Vectors in Built-in Systems

В работе рассмотрены алгоритмы вычисления векторов смещения видеоизображений, которые находят применение в смартфонах, цифровых фотокамерах, различных специализированных изделиях для стабилизации изображений, контроля дорожного движения, при аэрофотосъемках, при сопровождении объектов и в других приложениях. Для сравнительной оценки эффективности использования вычислительных ресурсов при реализации алгоритмов вычисления векторов смещения были выбраны: алгоритм на основе метода Лукаса – Кэнейда и алгоритм, основанный на согласованной фильтрации изображения. Определялось глобальное смещение изображения с использованием аппаратной платформы - системы на кристалле Xilinx семейства Ultrascale+. Матричные вычисления алгоритма Лукаса – Кэнейда были реализованы 4 одинаковыми аппаратными блоками, что позволило вычислять смещения между кадрами одновременно для 4 точек. В этом случае время вычисления оптического потока составило в среднем 7,5 мс. В реализации алгоритма согласованной фильтрации изображения на базе ДДПФ также использовалось 4 аппаратных блока, позволяющих распараллелить вычисления. В результате время работы алгоритма составило 2,9 мс, при этом процессорное время, необходимое для работы алгоритма, составило 0,2 мс. В процессе реализации определены слабые места алгоритмов, необходимое количество аппаратных ресурсов системы на кристалле. Показано, что при наличии достаточных аппаратных ресурсов определение смещения соседних кадров видеоряда гораздо эффективнее реализуется на базе согласованной фильтрации, чем алгоритмом Лукаса – Кэнейда.

Non-Stationary Acceleration Strategies for PageRank Computing

In this work, a non-stationary technique based on the Power method for accelerating the parallel computation of the PageRank vector is proposed and its theoretical convergence analyzed. This iterative non-stationary model, which uses the eigenvector formulation of the PageRank problem, reduces the needed computations for obtaining the PageRank vector by eliminating synchronization points among processes, in such a way that, at each iteration of the Power method, the block of iterate vector assigned to each process can be locally updated more than once, before performing a global synchronization. The parallel implementation of several strategies combining this novel non-stationary approach and the extrapolation methods has been developed using hybrid MPI/OpenMP programming. The experiments have been carried out on a cluster made up of 12 nodes, each one equipped with two Intel Xeon hexacore processors. The behaviour of the proposed parallel algorithms has been studied with realistic datasets, highlighting their performance compared with other parallel techniques for solving the PageRank problem. Concretely, the experimental results show a time reduction of up to 58.4 % in relation to the parallel Power method, when a small number of local updates is performed before each global synchronization, outperforming both the two-stage algorithms and the extrapolation algorithms, more sharply as the number of processes increases.

Dynamical systems: Approximate Lagrangians and Noether symmetries

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

Computation of State Vector of Networked Control System using Combination of Laplace Transform and Variational Iteration Method

Networked Control System (NCS) is a control system in which system components such as sensor, actuator and controller communicate over a network. Networked control system model is represented by , where the state vector and the control input . In this paper the state vector of the networked control system is computed by obtaining the solution of first order delay differential equation using the combination of Laplace and Variational Iteration method.

An adaptive local time-stepping scheme for multiresolution simulations of hyperbolic conservation laws

We present an adaptive local time-stepping (ALTS) scheme for a block-structured multiresolution scheme of hyperbolic conservation laws for fluid flow. The stability of standard local time-stepping (LTS) schemes with level-dependent time-step sizes is improved by local time-step size adaptation when progressing through the underlying multi-stage time integration scheme. The novelty of the approach is that it merges flux computation and time integration of the state vector with projection and prediction operations of the multiresolution scheme [15]. This enables consistent time integration of subdomains with different refinement levels without the need for intermediate time synchronization which can be prohibitively expensive in parallel computations. Consequently, coarser subdomains are advanced in time only once finer subdomains have advanced to the same time instant. Full spatial resolution adaptivity for integrated regions after each substep is maintained.The new scheme exhibits significantly improved numerical stability as compared to previous LTS schemes due to the local time-step size adaptation at each substep. The computational overhead of the incurred additional operations is small. In applications, the ALTS scheme demonstrates the same computational efficiency as standard LTS schemes.The new scheme can be applied to any explicit single-step time-integration scheme and is independent of the employed spatial discretization scheme. The improved stability is demonstrated with several one- and two-dimensional examples of flows with one and two phases, applying second- and third-order Runge-Kutta time integration schemes.

Speed and Biases of Fourier-Based Pricing Choices: Analysis of the Bastes and Asymmetric Variance Gamma Models

This paper compares the CPU effort and numerical biases of six Fourier-based implementations. Our analyses focus on two jump-related models that can consistently price options with different strikes and maturities: (i) the Bates jump-diffusion model, which combines jumps with stochastic volatility and (ii) the Asymmetric Variance Gamma (AVG) model, a pure-jump process where an infinite number of jumps can occur in any interval of time. We show that both truncation and discretization errors significantly increase as we move away from the diffusive Black-Scholes-Merton dynamics. While most pricing choices converge to the Bates reference values, Attari’s formula is the only Fourier-based method that does not completely blow up in any AVG problematic region. In terms of CPU speed, the strike vector computations proposed by Zhu (2010) significantly improve the computational burden, rendering the use of fast Fourier transforms and plain delta-probability decompositions inefficient.

Treatments of the singularity in the level set method for unstructured meshes

Straightforward computation of normal vectors and curvature of interface is a main advantage of the level set method. However, the level set method may have discontinuities (kinks) in its derivatives that may lead to erroneous estimation of the normal vector and curvature during topological changes. In this study, we extended two existing methods of singularity treatment for the level set method on structured mesh, i.e., the Salac and Lu method (SLM) and local level set extraction method (LOLEX), to those with unstructured mesh in the framework of finite element formulation. An iterative treatment for the dependent nodes that belong to two elements cut by different interfaces was newly proposed for the LOLEX approach on unstructured mesh. Three static simulations showed that the present SLM or LOLEX for unstructured mesh accurately computed the normal vector and the curvature in the regions with singularity. Two dynamic cases were further simulated to investigate the effect of singularity-treatment on the mass conservation as well as the merging mechanism of droplets. While SLM and LOLEX provided results consistent with existing experimental results, it was confirmed that LOLEX provided a better mass conservation and more accurate curvature fields than SLM after coalescence.

Radiation in bent asymmetric coupled waveguides.

A numerical study of the radiation in coupled bent waveguides is presented. Such arrangements of curved waveguides in reduced radiation-loss configurations can be used to enhance the quality factor of integrated microresonators. 3D full vector computations of the complex modal fields (and propagation constants) and the transient propagation effects have been performed. The results obtained agree qualitatively with former 2D finite-difference time-domain (FDTD) analyses. At the same time, the calculations presented meet the accuracy requirements for the design of practical implementations that are unattainable with 2D approaches.

A fast forward algorithm for three-dimensional magnetic anomaly on undulating terrain

This paper presents a fast and high-precision three-dimensional magnetic anomaly forward algorithm on undulating terrain. Firslty, The forward algorithm for three-dimensional magnetic anomalies on a horizontal observation surface is developed with the Block-Toeplitz-Toeplitz-Block (BTTB) matrix. In the proposed algorithm, the cuboid elements are used to divide the underground space. And the position of the observation point is set as the projection of the central point of the cuboid element onto the observation surface. With the symmetry of the BTTB matrix, the coefficient matrix is compressed and stored to reduces the memory requirements during the computation process. In order to deal with the coefficient matrix and parameter vector computations, the matrix cross-multiplication computation is transformed into a point-multiplication computation with the fast Fourier transform (FFT) method. Then, to solve the problem of undulating terrain, a hierarchical interpolation method is proposed in forward algorithm, in which the undulating terrain is divided into several horizontal observation surfaces. Subsequently, the magnetic field on the undulating terrain is interpolated. Some 3D models with horizontal observation surface and undulating terrain are tested to verify the proposed algorithm. The results show that the forward algorithm has the advantages of fast computation speed, high precision, and low memory requirement. It is suitable for large-scale (ten millions of nodes) three-dimensional magnetic forward modeling.

P-Tensor Product in Compressed Sensing

The dimension matching is a tough problem in the vector and matrix computations. In the traditional mode, there is only one way to calculate the angle between the 1-D plane and the 3-D vector, it is the projection. However, there are a number of lines on the plane, and taking only the projection to represent the plane is kind of a narrow choice. Furthermore, in the matrix multiplication, the dimension restriction is strict. In order to solve these problems, this paper defines a new model called ${P}$ -tensor product (PTP), which cannot only define the inner product of two vectors with unmatched dimensions but also give a new way to solve the problems in the matrix operations. Aiming at decreasing the large storage space of the random matrix in compressed sensing (CS), the PTP can reconstruct a high-dimensional matrix by using a matrix, which can be chosen as any kind of matrix. Similar with the traditional CS, we analyze some reconstruction conditions of PTP-CS such as, the spark, the coherence, and the restricted isometry property. The theorems proposed in this paper have a broad sense, and they possess a good universality for various tensor product CS methods. The experimental results demonstrate that our PTP-CS model can not only give more choices to the types of Kronecker matrix and decrease the storage space of the traditional CS but also maintain the considerable recovery performance. Besides, the proposed PTP-CS model can improve the signal transmission efficiency in the Internet of Things.

Computing Observability of Gates in Combinational Logic Circuits by Bit-Parallel Simulation

The article considers vector computation methods (bit-parallel simulation) for determining the observability of combinational logic gates. The computations produce an ODC (observability don’t care) set of all gates for a given set of circuit states. These results make it possible to evaluate the probability of logical masking of a random circuit fault. The methods are compared by accuracy and time costs using testing results for ISCAS ’85 benchmark circuits.

Speed Variation along an Imposed Linear Trajectory, for Robotic Arms Motion

The paper describes a method of speed (velocity) computation, named mixt profile, during a motion upon an imposed linear trajectory. The method assures an accurate positioning at the end of motion (movement), in a well determinate time lapse. The described method is linked with position vector computation, about a robotic arm.

A Multifunction Unit for Matrix, Vector and Elementary Functions Computation in Mobile GPU Shaders

This paper presents a delay and area optimized multifunction unit with a wide operation set of matrix, vector, and elementary functions for mobile and wearable GPU shaders. The proposed unit unifies 25 non-trivial arithmetic operations on its single four-way arithmetic hardware. It employs two programmable modules for the unification of its operations. Novel unification architectures for these programmable modules are presented to optimize delay and area of the unit. Based on these architectures, the multifunction unit shows 10% and 3.5% reductions in its delay and area, respectively, compared with the prior art.

Skeleton-Based Human Action Recognition through Third-Order Tensor Representation and Spatio-Temporal Analysis

Given the broad range of applications from video surveillance to human–computer interaction, human action learning and recognition analysis based on 3D skeleton data are currently a popular area of research. In this paper, we propose a method for action recognition using depth sensors and representing the skeleton time series sequences as higher-order sparse structure tensors to exploit the dependencies among skeleton joints and to overcome the limitations of methods that use joint coordinates as input signals. To this end, we estimate their decompositions based on randomized subspace iteration that enables the computation of singular values and vectors of large sparse matrices with high accuracy. Specifically, we attempt to extract different feature representations containing spatio-temporal complementary information and extracting the mode-n singular values with regards to the correlations of skeleton joints. Then, the extracted features are combined using discriminant correlation analysis, and a neural network is used to recognize the action patterns. The experimental results presented use three widely used action datasets and confirm the great potential of the proposed action learning and recognition method.

An Interpretable and Scalable Recommendation Method Based on Network Embedding

Matrix factorization is a widely used technique in recommender systems. However, its performance is often affected by the sparsity and the scalability. To address the above-mentioned problem, we propose an interpretable and scalable recommendation method based on network embedding (ISRM_NE) in this paper. First, a novel user-item co-occurrence network is presented, which reflects both the user's preferences and the co-occurrence relationship among items. Second, the conceptions of tightness and equivalence are given to describe the structural similarity in the network, which can explore four relationships in recommender system: user's preference, item co-occurrence relationship, user's potential preference, and similarity between users. Finally, two sampling strategies are combined to traverse the network so as to get the latent vector of items and users through network representation learning. Thus, the top-N recommendation can be achieved by vector computing. The proposed method called ISRM_NE improves the performance of the recommender system in terms of interpretability and scalability. Moreover, extensive experiments on two real-world datasets demonstrate that the ISRM_NE outperforms three popular methods.

Noise Robust Speaker Recognition Based on Adaptive Frame Weighting in GMM for i-Vector Extraction

Even though speaker recognition has gained significant progress in recent years, its performance is known to be deteriorated severely with the existence of strong background noises. Inspired by a recently proposed clean-frame selection approach, this work investigates a relatively elegant weighting method when computing the Baum-Welch statistics of Gaussian mixture models (GMMs) in i-vector extraction. By introducing weighting parameters to the frames of enrollment/testing utterances, the optimization problem is redefined and solved. New updating rules are derived by incorporating weights to the computation of posterior probabilities, mean vectors, and covariance matrices of the GMM. The experiments conducted on the Speakers in the Wild (SITW) database show that the proposed algorithm has significantly improved the performance of i-vector-based speaker recognition systems in noisy environments. Compared with the GMM i-vector baseline, the equal error rate is reduced from 5.75 to 4.72 and the minimum value of cost function (C det min ) is reduced from 0.4825 to 0.4505. Slight but significant superiority is also observed over the method with an additional feature enhancement frontend by using deep neural networks.