Two examples of approximate arithmetic to reduce hardware complexity and power consumption

© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.As the end of Moore's Law approaches, electronic system designers must find ways to keep up with the ever increasing computational demands of the modern era. Some computationally intensive applications, such as multimedia processing, computer vision and artificial intelligence, present a unique feature that makes them especially suitable for hardware-level optimizations: their inherent robustness to noise and errors. This allows circuit designers to relax the constraint that arithmetic operations, such as multiplications and additions, must be completely accurate. Instead, approximations can be used in the arithmetic units, enabling system-level reductions in hardware area and power consumption, as well as improvements in performance, while hardly affecting the output of the final application. In this work, we explore two approximate arithmetic techniques. First, we consider approximations at the circuit design level by implementing several approximate multiplier units and evaluating their accuracy when used in executing YOLOv3, a state-of-the-art camera-based object detection deep neural network. Second, we apply the technique of overscaling to induce approximations in adder circuits by aggressively undervoltaging and overclocking them, and we compare the behavior of exact and approximate adders under these conditions. We find that, on one hand, some approximate multipliers are able to execute the YOLO network with almost no effect on the results, and on the other, approximate adder circuits are much more resilient to overscaling techniques than exact adders.This work was partially supported by Spanish MCIN/AEI/10.13039/501100011033, Project PID2019-103869RB-C33.Peer ReviewedPostprint (author's final draft

Evaluating critical bits in arithmetic operations due to timing violations

Various error models are being used in simulation of voltage-scaled arithmetic units to examine application-level tolerance of timing violations. The selection of an error model needs further consideration, as differences in error models drastically affect the performance of the application. Specifically, floating point arithmetic units (FPUs) have architectural characteristics that characterize its behavior. We examine the architecture of FPUs and design a new error model, which we call Critical Bit. We run selected benchmark applications with Critical Bit and other widely used error injection models to demonstrate the differences

Configurable Low Power Analog Multilayer Perceptron

A configurable, low power analog implementation of a multilayer perceptron (MLP) is presented in this work. It features a highly programmable system that allows the user to create a MLP neural network design of their choosing. In addition to the configurability, this neural network provides the ability of low power operation via analog circuitry in its neurons. The main MLP system is made up of 12 neurons that can be configurable to any number of layers and neurons per layer until all available resources are utilized. The MLP network is fabricated in a standard 0.13 μm CMOS process occupying approximately 1 mm2 of on-chip area. The MLP system is analyzed at several different configurations with all achieving a greater than 1 Tera-operations per second per Watt figure of merit. This work offers a high speed, low power, and scalable alternative to digital configurable neural networks

근사 컴퓨팅을 이용한 회로 노화 보상과 에너지 효율적인 신경망 구현

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 전기·정보공학부, 2020. 8. 이혁재.Approximate computing reduces the cost (energy and/or latency) of computations by relaxing the correctness (i.e., precision) of computations up to the level, which is dependent on types of applications. Moreover, it can be realized in various hierarchies of computing system design from circuit level to application level. This dissertation presents the methodologies applying approximate computing across such hierarchies; compensating aging-induced delay in logic circuit by dynamic computation approximation (Chapter 1), designing energy-efficient neural network by combining low-power and low-latency approximate neuron models (Chapter 2), and co-designing in-memory gradient descent module with neural processing unit so as to address a memory bottleneck incurred by memory I/O for high-precision data (Chapter 3). The first chapter of this dissertation presents a novel design methodology to turn the timing violation caused by aging into computation approximation error without the reliability guardband or increasing the supply voltage. It can be realized by accurately monitoring the critical path delay at run-time. The proposal is evaluated at two levels: RTL component level and system level. The experimental results at the RTL component level show a significant improvement in terms of (normalized) mean squared error caused by the timing violation and, at the system level, show that the proposed approach successfully transforms the aging-induced timing violation errors into much less harmful computation approximation errors, therefore it recovers image quality up to perceptually acceptable levels. It reduces the dynamic and static power consumption by 21.45% and 10.78%, respectively, with 0.8% area overhead compared to the conventional approach. The second chapter of this dissertation presents an energy-efficient neural network consisting of alternative neuron models; Stochastic-Computing (SC) and Spiking (SP) neuron models. SC has been adopted in various fields to improve the power efficiency of systems by performing arithmetic computations stochastically, which approximates binary computation in conventional computing systems. Moreover, a recent work showed that deep neural network (DNN) can be implemented in the manner of stochastic computing and it greatly reduces power consumption. However, Stochastic DNN (SC-DNN) suffers from problem of high latency as it processes only a bit per cycle. To address such problem, it is proposed to adopt Spiking DNN (SP-DNN) as an input interface for SC-DNN since SP effectively processes more bits per cycle than SC-DNN. Moreover, this chapter resolves the encoding mismatch problem, between two different neuron models, without hardware cost by compensating the encoding mismatch with synapse weight calibration. A resultant hybrid DNN (SPSC-DNN) consists of SP-DNN as bottom layers and SC-DNN as top layers. Exploiting the reduced latency from SP-DNN and low-power consumption from SC-DNN, the proposed SPSC-DNN achieves improved energy-efficiency with lower error-rate compared to SC-DNN and SP-DNN in same network configuration. The third chapter of this dissertation proposes GradPim architecture, which accelerates the parameter updates by in-memory processing which is codesigned with 8-bit floating-point training in Neural Processing Unit (NPU) for deep neural networks. By keeping the high precision processing algorithms in memory, such as the parameter update incorporating high-precision weights in its computation, the GradPim architecture can achieve high computational efficiency using 8-bit floating point in NPU and also gain power efficiency by eliminating massive high-precision data transfers between NPU and off-chip memory. A simple extension of DDR4 SDRAM utilizing bank-group parallelism makes the operation designs in processing-in-memory (PIM) module efficient in terms of hardware cost and performance. The experimental results show that the proposed architecture can improve the performance of the parameter update phase in the training by up to 40% and greatly reduce the memory bandwidth requirement while posing only a minimal amount of overhead to the protocol and the DRAM area.근사 컴퓨팅은 연산의 정확도의 손실을 어플리케이션 별 적절한 수준까지 허용함으로써 연산에 필요한 비용 (에너지나 지연시간)을 줄인다. 게다가, 근사 컴퓨팅은 컴퓨팅 시스템 설계의 회로 계층부터 어플리케이션 계층까지 다양한 계층에 적용될 수 있다. 본 논문에서는 근사 컴퓨팅 방법론을 다양한 시스템 설계의 계층에 적용하여 전력과 에너지 측면에서 이득을 얻을 수 있는 방법들을 제안하였다. 이는, 연산 근사화 (computation Approximation)를 통해 회로의 노화로 인해 증가된 지연시간을 추가적인 전력소모 없이 보상하는 방법과 (챕터 1), 근사 뉴런모델 (approximate neuron model)을 이용해 에너지 효율이 높은 신경망을 구성하는 방법 (챕터 2), 그리고 메모리 대역폭으로 인한 병목현상 문제를 높은 정확도 데이터를 활용한 연산을 메모리 내에서 수행함으로써 완화시키는 방법을 (챕터3) 제안하였다. 첫 번째 챕터는 회로의 노화로 인한 지연시간위반을 (timing violation) 설계마진이나 (reliability guardband) 공급전력의 증가 없이 연산오차 (computation approximation error)를 통해 보상하는 설계방법론 (design methodology)를 제안하였다. 이를 위해 주요경로의 (critical path) 지연시간을 동작시간에 정확하게 측정할 필요가 있다. 여기서 제안하는 방법론은 RTL component와 system 단계에서 평가되었다. RTL component 단계의 실험결과를 통해 제안한 방식이 표준화된 평균제곱오차를 (normalized mean squared error) 상당히 줄였음을 볼 수 있다. 그리고 system 단계에서는 이미지처리 시스템에서 이미지의 품질이 인지적으로 충분히 회복되는 것을 보임으로써 회로노화로 인해 발생한 지연시간위반 오차가 에러의 크기가 작은 연산오차로 변경되는 것을 확인 할 수 있었다. 결론적으로, 제안된 방법론을 따랐을 때 0.8%의 공간을 (area) 더 사용하는 비용을 지불하고 21.45%의 동적전력소모와 (dynamic power consumption) 10.78%의 정적전력소모의 (static power consumption) 감소를 달성할 수 있었다. 두 번째 챕터는 근사 뉴런모델을 활용하는 고-에너지효율의 신경망을 (neural network) 제안하였다. 본 논문에서 사용한 두 가지의 근사 뉴런모델은 확률컴퓨팅과 (stochastic computing) 스파이킹뉴런 (spiking neuron) 이론들을 기반으로 모델링되었다. 확률컴퓨팅은 산술연산들을 확률적으로 수행함으로써 이진연산을 낮은 전력소모로 수행한다. 최근에 확률컴퓨팅 뉴런모델을 이용하여 심층 신경망 (deep neural network)를 구현할 수 있다는 연구가 진행되었다. 그러나, 확률컴퓨팅을 뉴런모델링에 활용할 경우 심층신경망이 매 클락사이클마다 (clock cycle) 하나의 비트만을 (bit) 처리하므로, 지연시간 측면에서 매우 나쁠 수 밖에 없는 문제가 있다. 따라서 본 논문에서는 이러한 문제를 해결하기 위하여 스파이킹 뉴런모델로 구성된 스파이킹 심층신경망을 확률컴퓨팅을 활용한 심층신경망 구조와 결합하였다. 스파이킹 뉴런모델의 경우 매 클락사이클마다 여러 비트를 처리할 수 있으므로 심층신경망의 입력 인터페이스로 사용될 경우 지연시간을 줄일 수 있다. 하지만, 확률컴퓨팅 뉴런모델과 스파이킹 뉴런모델의 경우 부호화 (encoding) 방식이 다른 문제가 있다. 따라서 본 논문에서는 해당 부호화 불일치 문제를 모델의 파라미터를 학습할 때 고려함으로써, 파라미터들의 값이 부호화 불일치를 고려하여 조절 (calibration) 될 수 있도록 하여 문제를 해결하였다. 이러한 분석의 결과로, 앞 쪽에는 스파이킹 심층신경망을 배치하고 뒷 쪽애는 확률컴퓨팅 심층신경망을 배치하는 혼성신경망을 제안하였다. 혼성신경망은 스파이킹 심층신경망을 통해 매 클락사이클마다 처리되는 비트 양의 증가로 인한 지연시간 감소 효과와 확률컴퓨팅 심층신경망의 저전력 소모 특성을 모두 활용함으로써 각 심층신경망을 따로 사용하는 경우 대비 우수한 에너지 효율성을 비슷하거나 더 나은 정확도 결과를 내면서 달성한다. 세 번째 챕터는 심층신경망을 8비트 부동소숫점 연산으로 학습하는 신경망처리유닛의 (neural processing unit) 파라미터 갱신을 (parameter update) 메모리-내-연산으로 (in-memory processing) 가속하는 GradPIM 아키텍쳐를 제안하였다. GradPIM은 8비트의 낮은 정확도 연산은 신경망처리유닛에 남기고, 높은 정확도를 가지는 데이터를 활용하는 연산은 (파라미터 갱신) 메모리 내부에 둠으로써 신경망처리유닛과 메모리간의 데이터통신의 양을 줄여, 높은 연산효율과 전력효율을 달성하였다. 또한, GradPIM은 bank-group 수준의 병렬화를 이루어 내 높은 내부 대역폭을 활용함으로써 메모리 대역폭을 크게 확장시킬 수 있게 되었다. 또한 이러한 메모리 구조의 변경이 최소화되었기 때문에 추가적인 하드웨어 비용도 최소화되었다. 실험 결과를 통해 GradPIM이 최소한의 DRAM 프로토콜 변화와 DRAM칩 내의 공간사용을 통해 심층신경망 학습과정 중 파라미터 갱신에 필요한 시간을 40%만큼 향상시켰음을 보였다.Chapter I: Dynamic Computation Approximation for Aging Compensation 1 1.1 Introduction 1 1.1.1 Chip Reliability 1 1.1.2 Reliability Guardband 2 1.1.3 Approximate Computing in Logic Circuits 2 1.1.4 Computation approximation for Aging Compensation 3 1.1.5 Motivational Case Study 4 1.2 Previous Work 5 1.2.1 Aging-induced Delay 5 1.2.2 Delay-Configurable Circuits 6 1.3 Proposed System 8 1.3.1 Overview of the Proposed System 8 1.3.2 Proposed Adder 9 1.3.3 Proposed Multiplier 11 1.3.4 Proposed Monitoring Circuit 16 1.3.5 Aging Compensation Scheme 19 1.4 Design Methodology 20 1.5 Evaluation 24 1.5.1 Experimental setup 24 1.5.2 RTL component level Adder/Multiplier 27 1.5.3 RTL component level Monitoring circuit 30 1.5.4 System level 31 1.6 Summary 38 Chapter II: Energy-Efficient Neural Network by Combining Approximate Neuron Models 40 2.1 Introduction 40 2.1.1 Deep Neural Network (DNN) 40 2.1.2 Low-power designs for DNN 41 2.1.3 Stochastic-Computing Deep Neural Network 41 2.1.4 Spiking Deep Neural Network 43 2.2 Hybrid of Stochastic and Spiking DNNs 44 2.2.1 Stochastic-Computing vs Spiking Deep Neural Network 44 2.2.2 Combining Spiking Layers and Stochastic Layers 46 2.2.3 Encoding Mismatch 47 2.3 Evaluation 49 2.3.1 Latency and Test Error 49 2.3.2 Energy Efficiency 51 2.4 Summary 54 Chapter III: GradPIM: In-memory Gradient Descent in Mixed-Precision DNN Training 55 3.1 Introduction 55 3.1.1 Neural Processing Unit 55 3.1.2 Mixed-precision Training 56 3.1.3 Mixed-precision Training with In-memory Gradient Descent 57 3.1.4 DNN Parameter Update Algorithms 59 3.1.5 Modern DRAM Architecture 61 3.1.6 Motivation 63 3.2 Previous Work 65 3.2.1 Processing-In-Memory 65 3.2.2 Co-design Neural Processing Unit and Processing-In-Memory 66 3.2.3 Low-precision Computation in NPU 67 3.3 GradPIM 68 3.3.1 GradPIM Architecture 68 3.3.2 GradPIM Operations 69 3.3.3 Timing Considerations 70 3.3.4 Update Phase Procedure 73 3.3.5 Commanding GradPIM 75 3.4 NPU Co-design with GradPIM 76 3.4.1 NPU Architecture 76 3.4.2 Data Placement 79 3.5 Evaluation 82 3.5.1 Evaluation Methodology 82 3.5.2 Experimental Results 83 3.5.3 Sensitivity Analysis 88 3.5.4 Layer Characterizations 90 3.5.5 Distributed Data Parallelism 90 3.6 Summary 92 3.6.1 Discussion 92 Bibliography 113 요약 114Docto

Approximate Computing Survey, Part I: Terminology and Software & Hardware Approximation Techniques

The rapid growth of demanding applications in domains applying multimedia processing and machine learning has marked a new era for edge and cloud computing. These applications involve massive data and compute-intensive tasks, and thus, typical computing paradigms in embedded systems and data centers are stressed to meet the worldwide demand for high performance. Concurrently, the landscape of the semiconductor field in the last 15 years has constituted power as a first-class design concern. As a result, the community of computing systems is forced to find alternative design approaches to facilitate high-performance and/or power-efficient computing. Among the examined solutions, Approximate Computing has attracted an ever-increasing interest, with research works applying approximations across the entire traditional computing stack, i.e., at software, hardware, and architectural levels. Over the last decade, there is a plethora of approximation techniques in software (programs, frameworks, compilers, runtimes, languages), hardware (circuits, accelerators), and architectures (processors, memories). The current article is Part I of our comprehensive survey on Approximate Computing, and it reviews its motivation, terminology and principles, as well it classifies and presents the technical details of the state-of-the-art software and hardware approximation techniques.Comment: Under Review at ACM Computing Survey

Customisable arithmetic hardware designs

Imperial Users onl

Floating-Point Matrix Product on FPGA

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