For computer vision applications, prior works have shown the efficacy of reducing the numeric precision of model parameters (network weights) in deep neural networks but also that reducing the precision of activations hurts model accuracy much more than reducing the precision of model parameters. We study schemes to train networks from scratch using reduced-precision activations without hurting the model accuracy. We reduce the precision of activation maps (along with model parameters) using a novel quantization scheme and increase the number of filter maps in a layer, and find that this scheme compensates or surpasses the accuracy of the baseline full-precision network. As a result, one can significantly reduce the dynamic memory footprint, memory bandwidth, computational energy and speed up the training and inference process with appropriate hardware support. We call our scheme WRPN - wide reduced-precision networks. We report results using our proposed schemes and show that our results are better than previously reported accuracies on ILSVRC-12 dataset while being computationally less expensive compared to previously reported reduced-precision networks.
Convolution is one of the fundamental operations of deep neural networks with demanding matrix computation. In a graphic processing unit (GPU), Tensor Core is a specialized matrix processing hardware equipped with reduced-precision matrix-multiply-accumulate (MMA) instructions to increase throughput. However, it is challenging to achieve optimal performance since the best scheduling of MMA instructions varies for different convolution sizes. In particular, reduced-precision MMA requires many elements grouped as a matrix operand, seriously limiting data reuse and imposing packing and layout ove…
This paper presents the impact of using quantization on the efficiency of multi-class text classification in the training process of a support vector machine (SVM). This work is focused on comparing the efficiency of SVM model trained using reduced precision with its original form. The main advantage of using quantization is decrease in computation time and in memory footprint on the dedicated hardware platform which supports low precision computation like GPU (16-bit) or FPGA (any bit-width). The paper presents the impact of a precision reduction of the SVM training process on text classifica…
Chosun University（朝鲜大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We present a pipelined multiplier with reduced activities and minimized interconnect based on online digit-serial arithmetic. The working precision has been truncated such that $p<n$ bits are used to compute $n$ bits product, resulting in significant savings in area and power. The digit slices follow variable precision according to input, increasing upto $p$ and then decreases according to the error profile. Pipelining has been done to achieve high throughput and low latency which is desirable for compute intensive inner products. Synthesis results of the proposed designs have been presented a…
Concordia University（康考迪亚大学）；Child Mind Institute（儿童心理研究所）
Mondrian Forests are a powerful data stream classification method, but their large memory footprint makes them ill-suited for low-resource platforms such as connected objects. We explored using reduced-precision floating-point representations to lower memory consumption and evaluated its effect on classification performance. We applied the Mondrian Forest implementation provided by OrpailleCC, a C++ collection of data stream algorithms, to two canonical datasets in human activity recognition: Recofit and Banos \emph{et al}. Results show that the precision of floating-point values used by tree …
School of Computing, Newcastle University（纽卡斯尔大学计算机学院）；Department of Computer Science, Durham University（杜伦大学计算机科学系）
With the growing significance of graphs as an effective representation of data in numerous applications, efficient graph analysis using modern machine learning is receiving a growing level of attention. Deep learning approaches often operate over the entire adjacency matrix -- as the input and intermediate network layers are all designed in proportion to the size of the adjacency matrix -- leading to intensive computation and large memory requirements as the graph size increases. It is therefore desirable to identify efficient measures to reduce both run-time and memory requirements allowing f…
Mixed-signal artificial neural networks (ANNs) that employ analog matrix-multiplication accelerators can achieve higher speed and improved power efficiency. Though analog computing is known to be susceptible to noise and device imperfections, various analog computing paradigms have been considered as promising solutions to address the growing computing demand in machine learning applications, thanks to the robustness of ANNs. This robustness has been explored in low-precision, fixed-point ANN models, which have proven successful on compressing ANN model size on digital computers. However, thes…
Imperial College London（帝国理工学院）；Samsung AI Center（三星人工智能中心）
Large-scale convolutional neural networks (CNNs) suffer from very long training times, spanning from hours to weeks, limiting the productivity and experimentation of deep learning practitioners. As networks grow in size and complexity, training time can be reduced through low-precision data representations and computations. However, in doing so the final accuracy suffers due to the problem of vanishing gradients. Existing state-of-the-art methods combat this issue by means of a mixed-precision approach utilising two different precision levels, FP32 (32-bit floating-point) and FP16/FP8 (16-/8-b…
Center for Computational Quantum Physics, Flatiron Institute（计算量子物理中心，Flatiron研究所）；Department of Mathematical Sciences, Rutgers University（数学科学系，罗格斯大学）；Center for Computational Mathematics, Flatiron Institute（计算数学中心，Flatiron研究所）
Quantization Error as a Metric for Dynamic Precision Scaling in Neural Net Training
Department of Electrical and Computer Engineering（电气与计算机工程系）；University of Toronto（多伦多大学）；Toronto, ON, Canada（加拿大安大略省多伦多市）
最近的工作已经探索了在神经网络训练期间降低参数、激活和梯度的数值精度，作为降低训练计算成本的一种方式（Na & Mukhopadhyay，2016）（Courbariaux et al.，2014年）。我们提出了一种新的动态精度缩放（DPS）计划。通过使用随机定点舍入、基于量化误差的缩放方案以及训练过程中的动态位宽，我们在MNIST数据集上实现了98.8%的测试准确度，与深度学习框架中使用的标准32位浮点值相比，权重的平均位宽仅为16位，激活的平均位宽为14位。
Deep learning models typically use single-precision (FP32) floating point data types for representing activations and weights, but a slew of recent research work has shown that computations with reduced-precision data types (FP16, 16-bit integers, 8-bit integers or even 4- or 2-bit integers) are enough to achieve same accuracy as FP32 and are much more efficient. Therefore, we designed fbgemm, a high-performance kernel library, from ground up to perform high-performance quantized inference on current generation CPUs. fbgemm achieves efficiency by fusing common quantization operations with a hi…
Graz University of Technology（格拉茨技术大学）；Ruperts Karls University（海德堡大学）
While machine learning techniques are traditionally resource intensive, we are currently witnessing an increased interest in hardware and energy efficient approaches. This need for resource-efficient machine learning is primarily driven by the demand for embedded systems and their usage in ubiquitous computing and IoT applications. In this article, we provide a resource-efficient approach for multi-channel speech enhancement based on Deep Neural Networks (DNNs). In particular, we use reduced-precision DNNs for estimating a speech mask from noisy, multi-channel microphone observations. This spe…
Structure-Aware Numerical Stabilization for Half-Precision Proximal Policy Optimization
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
