Approximate Computing Technique Research Articles

Runtime accuracy alterable approximate floatingpoint multipliers

Modern systems demand high computational power within limited resources. Approximate computing is a promising approach to design arithmetic units with tight resources for error-tolerant applications such as image and signal processing and computer vision. A floating-point multiplier is one of the arithmetic units with the highest complexity in such applications. Designing a floating-point multiplier based on the approximate computing technique can reduce its complexity as well as increase performance and energy efficiency. However, an unknown error rate for upcoming input data is problematic to design appropriate approximate multipliers. The existing solution is to utilize an error estimator relying on statistical analysis. In this paper, we propose new approximate floating-point multipliers based on an accumulator and reconfigurable adders with an error estimator. Unlike previous designs, our proposed designs are able to change the levels of accuracy at runtime. Thus, we can make errors distributed more evenly. In contrast to other designs, our proposed design can maximize the performance gain since reconfigurable multipliers are able to operate two multiplications in parallel once the low accuracy mode is selected. Furthermore, we apply a simple rounding technique to approximate floating-point multipliers for additional improvement. Our simulation results reveal that our new method can reduce area by 70.98% when error tolerance margin of our target application is 5%, and when its error tolerance margin is 3%, our rounding enhanced simple adders-based approximate multiplier can save area by 65.9%, and our reconfigurable adder-based approximate multiplier with rounding can save the average delay and energy by 54.95% and 46.67% respectively compared to an exact multiplier.

An approximate-computing empowered green 6G downlink

Approximate computing (AC) is an emerging embedded computing paradigm whereby accurate arithmetic units (i.e., adders and multipliers) of a computing platform (e.g., CPU, FPGA, ASIC etc.) are replaced by their inexact counterparts. For the applications (e.g., voice, images etc.) where the error induced by inaccurate arithmetic units remains within tolerable limits, AC is a promising technique because it leads to the design of energy-efficient computing hardware that occupies less circuit area, and has lower latency as well. This work is the first to investigate the feasibility of the AC for single-antenna and dual-antenna 6G downlink. Specifically, we consider the AC-empowered transceiver design of a 6G downlink whereby the state-of-the-art approximate/inexact arithmetic units are leverage to implement the pulse shaping filters (at the base station (BS) side) and decoders/equalizers (at the user equipment (UE) side). For simulation purpose, images and randomly generated bits are transmitted using M-ary phase shift keying scheme. To quantify the loss in arithmetic accuracy due to the AC, bit error rate (BER), structural similarity index (SSIM) and correlation coefficient (CC) are utilized as performance metrics; while to quantify the energy-efficiency benefit of the proposed AC techniques, dynamic power and on-chip power are utilized as performance metrics. Monte-Carlo results indicate up to 87% savings in dynamic power and very reasonable arithmetic accuracy (with SSIM above 93% and a CC of 99%), due to the proposed AC techniques.

Back to the brink: Phylogeography and demographic history of the endangered Torreya jackii

AbstractBoth paleoclimatic change and anthropogenic habitat destruction can have adverse effects on species demography and, in turn, could lead a species towards being endangered and rare. Understanding the relative importance of these natural and anthropogenic factors driving species endangerment and rarity is thus crucial for effective conservation planning but remains elusive. Here, we examine the phylogeography and demographic history of an endangered conifer species in China, Torreya jackii Chun, and assess the relative importance of natural and anthropogenic factors that might have put the species in its endangered state. We collected tissue samples from all the 13 extant wild populations, and analyzed the genetic variation using eight nuclear microsatellites and four chloroplast and one mitochondrial DNA fragments. We found low genetic and nucleotide diversities, which could explain the absence of spatial and phylogeographic structure. Using a hierarchical approximate Bayesian computation technique, we identified the demographic scenario that best fits the genetic data and found that effective population size was low at least 200 000 years ago but expanded after the last glacial maximum (LGM). The paleoclimatic niche model revealed a profound effect of precipitation on the distribution of T. jackii and predicted that the current distribution areas were suitable during the LGM. Despite the post‐LGM expansion, the best‐supported scenario showed a dramatic population collapse during the past 300 years, when anthropogenic disturbances also increased dramatically. Overall, our study sheds light on how historical factors and human impacts jointly threaten the persistence of a species, and these aspects should be duly considered in species conservation planning.

Low-Power Ternary Multiplication Using Approximate Computing

We propose a novel approximate computing technique for low-power ternary multiplication. A carry-truncated ternary multiplier, error compensation circuits, and 2 ×2 ternary multipliers with various accuracies are proposed using the low-power design methodology with carbon nanotube FETs. An accuracy-configurable design method is proposed to design energy-efficient 6 ×6 approximate ternary multipliers. The energy benefit of the proposed 6 ×6 approximate ternary multipliers have been verified using HSPICE simulation. The proposed approximate design shows 82.8% power-delay product with 41.8% mean absolute percentage error improvement over the previous approximate multiplier-based design. Image processing applications are conducted using the proposed approximate designs to confirm that the accuracy of ternary multiplication is satisfied the user's requirement.

Probing Uncertainties in Diagnostics of a Synthetic Chromosphere

Abstract Effective spectroscopic diagnostics rely on the ability to convert a particular flux measurement into a physical interpretation. Knowledge of uncertainty is a central component of diagnostics. We present data from a simulated solar-like chromosphere, where we have addressed the question of whether degeneracy is a problem in mapping from a non-LTE chromospheric line profile to a particular vertical stratification of atmospheric properties along the line of sight. Our results indicate that stratification degeneracies do exist, at least in our simulated atmosphere. We quantify this effect through the creation of posterior densities for atmospheric properties based on the Mg ii h line profile using the approximate Bayesian computation (ABC) technique. We find that the predictive power of the ABC temperature posterior systematically varies as a function of atmospheric column mass and ground-truth temperature. The ABC posteriors more effectively reproduce the spectral intensity in the Ca ii 8542 Å line than they do temperature stratification, although residual error in the Ca ii line core is common. Our results illustrate that some degeneracies should be alleviated through simultaneous analysis of multiple chromospheric lines.

Security Threat Analyses and Attack Models for Approximate Computing Systems

Approximate computing (AC) represents a paradigm shift from conventional precise processing to inexact computation but still satisfying the system requirement on accuracy. The rapid progress on the development of diverse AC techniques allows us to apply approximate computing to many computation-intensive applications. However, the utilization of AC techniques could bring in new unique security threats to computing systems. This work does a survey on existing circuit-, architecture-, and compiler-level approximate mechanisms/algorithms, with special emphasis on potential security vulnerabilities. Qualitative and quantitative analyses are performed to assess the impact of the new security threats on AC systems. Moreover, this work proposes four unique visionary attack models, which systematically cover the attacks that build covert channels, compensate approximation errors, terminate normal error resilience mechanisms, and propagate additional errors. To thwart those attacks, this work further offers the guideline of countermeasure designs. Several case studies are provided to illustrate the implementation of the suggested countermeasures.

Phylogenetic Curved Optimal Regression for Adaptive Trait Evolution.

Regression analysis using line equations has been broadly applied in studying the evolutionary relationship between the response trait and its covariates. However, the characteristics among closely related species in nature present abundant diversities where the nonlinear relationship between traits have been frequently observed. By treating the evolution of quantitative traits along a phylogenetic tree as a set of continuous stochastic variables, statistical models for describing the dynamics of the optimum of the response trait and its covariates are built herein. Analytical representations for the response trait variables, as well as their optima among a group of related species, are derived. Due to the models’ lack of tractable likelihood, a procedure that implements the Approximate Bayesian Computation (ABC) technique is applied for statistical inference. Simulation results show that the new models perform well where the posterior means of the parameters are close to the true parameters. Empirical analysis supports the new models when analyzing the trait relationship among kangaroo species.

Algorithmic-Level Approximate Tensorial SVM Using High-Level Synthesis on FPGA

Approximate Computing Techniques (ACT) are promising solutions towards the achievement of reduced energy, time latency and hardware size for embedded implementations of machine learning algorithms. In this paper, we present the first FPGA implementation of an approximate tensorial Support Vector Machine (SVM) classifier with algorithmic level ACTs using High-Level Synthesis (HLS). A touch modality classification framework was adopted to validate the effectiveness of the proposed implementation. When compared to exact implementation presented in the state-of-the-art, the proposed implementation achieves a reduction in power consumption by up to 49% with a speedup of 3.2×. Moreover, the hardware resources are reduced by 40% while consuming 82% less energy in classifying an input touch with an accuracy loss less than 5%.

Multi-Objective Application-Driven Approximate Design Method

Approximate Computing (AxC) paradigm aims at designing computing systems that can satisfy the rising performance demands and improve the energy efficiency. AxC exploits the gap between the level of accuracy required by the users, and the actual precision provided by the computing system, for achieving diverse optimizations. Various AxC techniques have been proposed so far in the literature at different abstraction levels from hardware to software. These techniques have been successfully utilized and combined to realize approximate implementations of applications in various domains (e.g. data analytic, scientific computing, multimedia and signal processing, and machine learning). Unfortunately, state-of-the-art approximation methodologies focus on a single abstraction level, such as combining elementary components (e.g., arithmetic operations) which are firstly approximated using component-level metrics and then combined to provide a good trade-off between efficiency and accuracy at the application level. This hinders the possibility for designers to explore different approximation opportunities, optimized for different applications and implementation targets. Therefore, we designed and implemented E- \mathbb IDEA, an automatic framework that provides an application-driven approximation approach to find the best approximate versions of a given application targeting different implementations (i.e., hardware and software). E- \mathbb IDEA compounds 1) a source-to-source manipulation tool and 2) an evolutionary search engine to automatically realize approximate application variants and perform a Design-Space Exploration (DSE). The latter results in a set of non-dominate approximate solutions in terms of trade-off between accuracy and efficiency. Experimental results validate the effectiveness and the flexibility of the approach in generating optimized approximate implementations of different applications, by using different approximation techniques and different accuracy/error metrics and for different implementation targets.

An Efficient Selection-Based kNN Architecture for Smart Embedded Hardware Accelerators

K-Nearest Neighbor (kNN) is an efficient algorithm used in many applications, e.g., text categorization, data mining, and predictive analysis. Despite having a high computational complexity, kNN is a candidate for hardware acceleration since it is a parallelizable algorithm. This paper presents an efficient novel architecture and implementation for a kNN hardware accelerator targeting modern System-on-Chips (SoCs). The architecture adopts a selection-based sorter dedicated for kNN that outperforms traditional sorters in terms of hardware resources, time latency, and energy efficiency. The kNN architecture has been designed using High-Level Synthesis (HLS) and implemented on the Xilinx Zynqberry platform. Compared to similar state-of-the-art implementations, the proposed kNN provides speedups between $1.4\times $ and $875\times $ with 41% to 94% reductions in energy consumption. To further enhance the proposed architecture, algorithmic-level Approximate Computing Techniques (ACTs) have been applied. The proposed approximate kNN implementation accelerates the classification process by $2.3\times $ with an average reduced area size of 56% for a real-time tactile data processing case study. The approximate kNN consumes 69% less energy with an accuracy loss of less than 3% when compared to the proposed Exact kNN.

Data Reuse for Accelerated Approximate Warps

Many data-driven applications, including computer vision, machine learning, speech recognition, and medical diagnostics show tolerance to computation error. These applications are often accelerated on GPUs, but the performance improvements require high energy usage. In this article, we present DRAAW, an approximate computing technique capable of accelerating GPGPU applications at a warp level. In GPUs, warps are groups of threads which issued together across multiple cores. The slowest thread dictates the pace of the warp, so DRAAW identifies these bottlenecks and avoids them during approximation. We alleviate computation costs by using an approximate lookup table which tracks recent operations and reuses them to exploit temporal locality within applications. To improve neural network performance, we propose neuron aware approximation, a technique which profiles operations within network layers and automatically configures DRAAW to ensure computations with more impact on the output accuracy are subject to less approximation. We evaluate our design by placing DRAAW within each core of an Nvidia Kepler Architecture Titan. DRAAW improves throughput by up to $2.8\times $ and improves energy-delay product (EDP) by $5.6\times $ for six GPGPU applications while maintaining less than 5% output error. We show neuron aware approximation accelerates the inference of six neutral networks by $2.9\times $ and improves EDP by $6.2\times $ with less than 1% impact on prediction accuracy.

Efficient AI System Design With Cross-Layer Approximate Computing

Advances in deep neural networks (DNNs) and the availability of massive real-world data have enabled superhuman levels of accuracy on many AI tasks and ushered the explosive growth of AI workloads across the spectrum of computing devices. However, their superior accuracy comes at a high computational cost, which necessitates approaches beyond traditional computing paradigms to improve their operational efficiency. Leveraging the application-level insight of error resilience, we demonstrate how approximate computing (AxC) can significantly boost the efficiency of AI platforms and play a pivotal role in the broader adoption of AI-based applications and services. To this end, we present RaPiD, a multi-tera operations per second (TOPS) AI hardware accelerator core (fabricated at 14-nm technology) that we built from the ground-up using AxC techniques across the stack including algorithms, architecture, programmability, and hardware. We highlight the workload-guided systematic explorations of AxC techniques for AI, including custom number representations, quantization/pruning methodologies, mixed-precision architecture design, instruction sets, and compiler technologies with quality programmability, employed in the RaPiD accelerator.

FixM: Code generation of fixed point mathematical functions

Approximate computing has seen significant interest as a design philosophy oriented to performance and energy efficiency [1]. Precision tuning is an approximate computing technique that trades off the accuracy of operations for performance and energy by employing less precise data types, such as fixed point instead of floating point. However, the current state-of-the-art does not consider the possibility of optimizing mathematical functions whose computation is usually off-loaded to a library.In this work we extend a precision-tuning framework to perform tuning of trigonometric functions as well. We developed a new mathematical function library, which is parameterizable at compile-time depending on the data type and works natively in the fixed point numeric representation. Through modification of a compiler pass, the parameterized implementations of these trigonometric functions are inserted into the program seamlessly during the precision tuning process.Our approach, which we test on two microcontrollers with different architectures, achieves a speedup of up to 180%, and energy savings up to 60%, with a negligible cost in terms of error in the results.

Occurrence rates of planets orbiting M Stars: applying ABC to Kepler DR25, Gaia DR2, and 2MASS data

ABSTRACT We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii Rp = 0.5–4 R⊕ and orbital periods P = 0.5–256 d using the approximate Bayesian computation technique. This work incorporates the final Kepler DR25 planet candidate catalogue and data products and augments them with updated stellar properties using Gaia DR2 and 2MASS point source catalogue. We apply a set of selection criteria to select a sample of 1746 Kepler M dwarf targets that host 89 associated planet candidates. These early-type M dwarfs and late K dwarfs were selected from cross-referenced targets using several photometric quality flags from Gaia DR2 and colour–magnitude cuts using 2MASS magnitudes. We estimate a habitable zone occurrence rate of $f_{\textrm {M,HZ}} = 0.33^{+0.10}_{-0.12}$ for planets with 0.75–1.5 R⊕ size. We caution that occurrence rate estimates for Kepler M stars are sensitive to the choice of prior due to the small sample of target stars and planet candidates. For example, we find an occurrence rate of $4.2^{+0.6}_{-0.6}$ or $8.4^{+1.2}_{-1.1}$ planets per M dwarf (integrating over Rp = 0.5–4 R⊕ and P = 0.5–256 d) for our two choices of prior. These occurrence rates are greater than those for FGK dwarf target when compared at the same range of orbital periods, but similar to occurrence rates when computed as a function of equivalent stellar insolation. Combining our result with recent studies of exoplanet architectures indicates that most, and potentially all, early-type M dwarfs harbour planetary systems.

Approximate Adder: Lower-Part or Adder

High-performance VLSI systems are essential in real-time applications, in order to increase the performance of the VLSI systems, an approximate computing technique is followed where the performance of the circuit is enhanced by trading off it with a slight loss in the accuracy. These approximate circuits are used in error-tolerant applications, where output need not be accurate. This paper concentrates mainly on approximate adders, as they are major building blocks of DSP systems. The analysis of the Lower-part OR Adder for 4-bit addition and comparison of it with the precise adder i.e., Ripple Carry Adder using the mentor graphics tool in 90 nm CMOS technology are presented in this paper. Our experimental results show that there is 17%-70% savings in power dissipation, 4%-32% saving in the area, and 19%-84% savings in time due to approximate adder. As the LOA-2 and LOA-3 are performing optimally these two adders can be used for error-tolerant applications and based on the requirement LOA-2 or LOA-3 can be selected.

Approximate Bayesian computation (ABC) method for estimating parameters of the gamma process using noisy data

The stochastic gamma process (GP) has emerged as a versatile model of degradation processes affecting the performance of engineering structures and components. The GP model captures the temporal uncertainty in the degradation process, whereas the Bayesian approach is used to account for uncertainty in the model parameters. Although the conceptual approach to GP parameter estimation is straightforward, its practical implementation is quite challenging. The reason is that degradation data required for parameter estimation are invariably contaminated by measurement noise, which turns the likelihood function into a high-dimensional multivariate integral. To circumvent this difficulty, the paper presents a novel and practical approach based on the approximate Bayesian computation (ABC) technique. The ABC method is a simulation-based approach that does not require an explicit formulation of the likelihood function. Instead, ABC uses an “accept-reject” mechanism to perform the posterior computation. To reduce the rejection rate, the Markov chain Monte Carlo (MCMC) approach is used within the ABC algorithm. The proposed ABC-MCMC algorithm is shown to be computationally more efficient than the traditional likelihood-based method without compromising the numerical accuracy. A case study involving the modelling of corrosion in nuclear piping systems is presented, which confirms the practical usefulness of the proposed method.

Design Space Exploration of Stochastic Computing Architectures Implemented Using Integrated Optics

Approximate computing allows to trade-off design energy efficiency with computing accuracy. Stochastic computing is an approximate computing technique, where numbers are represented as bit streams corresponding to probabilities. The serial computation of the bit streams leads to reduced hardware complexity but involves high latency, which is the main limitation of the technique. Integrated optics technology relies on high propagation speed of signals, which has the potential to reduce the processing latency in stochastic computing. However, the design of stochastic computing architectures implemented using integrated optics involves the exploration of numerous parameters at system and technological levels. In this work, we propose a design space exploration framework that allows to optimize energy efficiency, computing accuracy, and latency of such architectures. The efficiency of the framework is evaluated using a Gamma correction image processing application. Results show that, for processing 160x160 pixels images, an acceptable ×4.5 increase in the errors leads to ×47 energy efficiency and ×16 processing speed. We also show that the same computing accuracy can be obtained for different energy efficiency and computing latency, thus, validating the ability of the framework to explore the design space.

Using Approximate Computing and Selective Hardening for the Reduction of Overheads in the Design of Radiation-Induced Fault-Tolerant Systems

Fault mitigation techniques based on pure software, known as software-implemented hardware fault tolerance (SIHFT), are very attractive for use in COTS (commercial off-the-shelf) microprocessors because they do not require physical modification of the system. However, these techniques cause software overheads that may affect the efficiency and costs of the overall system. This paper presents a design method of radiation-induced fault-tolerant microprocessor-based systems with lower execution time overheads. For this purpose, approximate computing and selective fault mitigation software-based techniques are used; thus it can be used in COTS devices. The proposal is validated through a case study for the TI MSP430 microcontroller. Results show that the designer can choose among a wide spectrum of design configurations, exploring different trade-offs between reliability, performance, and accuracy of results.

Adjustment for exploratory cut-off selection in randomized clinical trials with survival endpoint.

Defining the target population based on predictive biomarkers plays an important role during clinical development. After establishing a relationship between a biomarker candidate and response to treatment in exploratory phases, a subsequent confirmatory trial ideally involves only subjects with high potential of benefiting from the new compound. In order to identify those subjects in case of a continuous biomarker, a cut-off is needed. Usually, a cut-off is chosen that resulted in a subgroup with a large observed treatment effect in an exploratory trial. However, such a data-driven selection may lead to overoptimistic expectations for the subsequent confirmatory trial. Treatment effect estimates, probability of success, and posterior probabilities are useful measures for deciding whether or not to conduct a confirmatory trial enrolling the biomarker-defined population. These measures need to be adjusted for selection bias. We extend previously introduced Approximate Bayesian Computation techniques for adjustment of subgroup selection bias to a time-to-event setting with cut-off selection. Challenges in this setting are that treatment effects become time-dependent and that subsets are defined by the biomarker distribution. Simulation studies show that the proposed method provides adjusted statistical measures which are superior to naïve Maximum Likelihood estimators as well as simple shrinkage estimators.

Approximate Bayesian Computation for infectious disease modelling

Approximate Bayesian Computation (ABC) techniques are a suite of model fitting methods which can be implemented without a using likelihood function. In order to use ABC in a time-efficient manner users must make several design decisions including how to code the ABC algorithm and the type of ABC algorithm to use. Furthermore, ABC relies on a number of user defined choices which can greatly effect the accuracy of estimation. Having a clear understanding of these factors in reducing computation time and improving accuracy allows users to make more informed decisions when planning analyses. In this paper, we present an introduction to ABC with a focus of application to infectious disease models. We present a tutorial on coding practice for ABC in R and three case studies to illustrate the application of ABC to infectious disease models.