Design of Energy-Efficient Approximate Arithmetic Circuits

Energy consumption has become one of the most critical design challenges in integrated circuit design. Arithmetic computing circuits, in particular array-based arithmetic computing circuits such as adders, multipliers, squarers, have been widely used. In many cases, array-based arithmetic computing circuits consume a significant amount of energy in a chip design. Hence, reduction of energy consumption of array-based arithmetic computing circuits is an important design consideration. To this end, designing low-power arithmetic circuits by intelligently trading off processing precision for energy saving in error-resilient applications such as DSP, machine learning and neuromorphic circuits provides a promising solution to the energy dissipation challenge of such systems. To solve the chip’s energy problem, especially for those applications with inherent error resilience, array-based approximate arithmetic computing (AAAC) circuits that produce errors while having improved energy efficiency have been proposed. Specifically, a number of approximate adders, multipliers and squarers have been presented in the literature. However, the chief limitation of these designs is their un-optimized processing accuracy, which is largely due to the current lack of systemic guidance for array-based AAAC circuit design pertaining to optimal tradeoffs between error, energy and area overhead. Therefore, in this research, our first contribution is to propose a general model for approximate array-based approximate arithmetic computing to guide the minimization of processing error. As part of this model, the Error Compensation Unit (ECU) is identified as a key building block for a wide range of AAAC circuits. We develop theoretical analysis geared towards addressing two critical design problems of the ECU, namely, determination of optimal error compensation values and identification of the optimal error compensation scheme. We demonstrate how this general AAAC model can be leveraged to derive practical design insights that may lead to optimal tradeoffs between accuracy, energy dissipation and area overhead. To further minimize energy consumption, delay and area of AAAC circuits, we perform ECU logic simplification by introducing don't cares. By applying the proposed model, we propose an approximate 16x16 fixed-width Booth multiplier that consumes 44.85% and 28.33% less energy and area compared with theoretically the most accurate fixed-width Booth multiplier when implemented using a 90nm CMOS standard cell library. Furthermore, it reduces average error, max error and mean square error by 11.11%, 28.11% and 25.00%, respectively, when compared with the best reported approximate Booth multiplier and outperforms the best reported approximate design significantly by 19.10% in terms of the energy-delay-mean square error product (EDE_(ms)). Using the same approach, significant energy consumption, area and error reduction is achieved for a squarer unit, with more than 20.00% EDE_(ms) reduction over existing fixed-width squarer designs. To further reduce error and cost by utilizing extra signatures and don't cares, we demonstrate a 16-bit fixed-width squarer that improves the energy-delay-max error (EDE_(max)) by 15.81%

A Scalable Correlator Architecture Based on Modular FPGA Hardware, Reuseable Gateware, and Data Packetization

A new generation of radio telescopes is achieving unprecedented levels of sensitivity and resolution, as well as increased agility and field-of-view, by employing high-performance digital signal processing hardware to phase and correlate large numbers of antennas. The computational demands of these imaging systems scale in proportion to BMN^2, where B is the signal bandwidth, M is the number of independent beams, and N is the number of antennas. The specifications of many new arrays lead to demands in excess of tens of PetaOps per second. To meet this challenge, we have developed a general purpose correlator architecture using standard 10-Gbit Ethernet switches to pass data between flexible hardware modules containing Field Programmable Gate Array (FPGA) chips. These chips are programmed using open-source signal processing libraries we have developed to be flexible, scalable, and chip-independent. This work reduces the time and cost of implementing a wide range of signal processing systems, with correlators foremost among them,and facilitates upgrading to new generations of processing technology. We present several correlator deployments, including a 16-antenna, 200-MHz bandwidth, 4-bit, full Stokes parameter application deployed on the Precision Array for Probing the Epoch of Reionization.Comment: Accepted to Publications of the Astronomy Society of the Pacific. 31 pages. v2: corrected typo, v3: corrected Fig. 1

ACE16K: The Third Generation of Mixed-Signal SIMD-CNN ACE Chips Toward VSoCs

Today, with 0.18-μm technologies mature and stable enough for mixed-signal design with a large variety of CMOS compatible optical sensors available and with 0.09-μm technologies knocking at the door of designers, we can face the design of integrated systems, instead of just integrated circuits. In fact, significant progress has been made in the last few years toward the realization of vision systems on chips (VSoCs). Such VSoCs are eventually targeted to integrate within a semiconductor substrate the functions of optical sensing, image processing in space and time, high-level processing, and the control of actuators. The consecutive generations of ACE chips define a roadmap toward flexible VSoCs. These chips consist of arrays of mixed-signal processing elements (PEs) which operate in accordance with single instruction multiple data (SIMD) computing architectures and exhibit the functional features of CNN Universal Machines. They have been conceived to cover the early stages of the visual processing path in a fully-parallel manner, and hence more efficiently than DSP-based systems. Across the different generations, different improvements and modifications have been made looking to converge with the newest discoveries of neurobiologists regarding the behavior of natural retinas. This paper presents considerations pertaining to the design of a member of the third generation of ACE chips, namely to the so-called ACE16k chip. This chip, designed in a 0.35-μm standard CMOS technology, contains about 3.75 million transistors and exhibits peak computing figures of 330 GOPS, 3.6 GOPS/mm2 and 82.5 GOPS/W. Each PE in the array contains a reconfigurable computing kernel capable of calculating linear convolutions on 3×3 neighborhoods in less than 1.5 μs, imagewise Boolean combinations in less than 200 ns, imagewise arithmetic operations in about 5 μs, and CNN-like temporal evolutions with a time constant of about 0.5 μs. Unfortunately, the many ideas underlying the design of this chip cannot be covered in a single paper; hence, this paper is focused on, first, placing the ACE16k in the ACE chip roadmap and, then, discussing the most significant modifications of ACE16K versus its predecessors in the family.LOCUST IST2001—38 097VISTA TIC2003—09 817 - C02—01Office of Naval Research N000 140 210 88

Basic Filters for Convolutional Neural Networks Applied to Music: Training or Design?

When convolutional neural networks are used to tackle learning problems based on music or, more generally, time series data, raw one-dimensional data are commonly pre-processed to obtain spectrogram or mel-spectrogram coefficients, which are then used as input to the actual neural network. In this contribution, we investigate, both theoretically and experimentally, the influence of this pre-processing step on the network's performance and pose the question, whether replacing it by applying adaptive or learned filters directly to the raw data, can improve learning success. The theoretical results show that approximately reproducing mel-spectrogram coefficients by applying adaptive filters and subsequent time-averaging is in principle possible. We also conducted extensive experimental work on the task of singing voice detection in music. The results of these experiments show that for classification based on Convolutional Neural Networks the features obtained from adaptive filter banks followed by time-averaging perform better than the canonical Fourier-transform-based mel-spectrogram coefficients. Alternative adaptive approaches with center frequencies or time-averaging lengths learned from training data perform equally well.Comment: Completely revised version; 21 pages, 4 figure

YodaNN: An Architecture for Ultra-Low Power Binary-Weight CNN Acceleration

Convolutional neural networks (CNNs) have revolutionized the world of computer vision over the last few years, pushing image classification beyond human accuracy. The computational effort of today's CNNs requires power-hungry parallel processors or GP-GPUs. Recent developments in CNN accelerators for system-on-chip integration have reduced energy consumption significantly. Unfortunately, even these highly optimized devices are above the power envelope imposed by mobile and deeply embedded applications and face hard limitations caused by CNN weight I/O and storage. This prevents the adoption of CNNs in future ultra-low power Internet of Things end-nodes for near-sensor analytics. Recent algorithmic and theoretical advancements enable competitive classification accuracy even when limiting CNNs to binary (+1/-1) weights during training. These new findings bring major optimization opportunities in the arithmetic core by removing the need for expensive multiplications, as well as reducing I/O bandwidth and storage. In this work, we present an accelerator optimized for binary-weight CNNs that achieves 1510 GOp/s at 1.2 V on a core area of only 1.33 MGE (Million Gate Equivalent) or 0.19 mm$^2$ and with a power dissipation of 895 {\mu}W in UMC 65 nm technology at 0.6 V. Our accelerator significantly outperforms the state-of-the-art in terms of energy and area efficiency achieving 61.2 TOp/s/[email protected] V and 1135 GOp/s/[email protected] V, respectively