Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.
The rising popularity of intelligent mobile devices and the daunting computational cost of deep learning-based models call for efficient and accurate on-device inference schemes. We propose a quantization scheme that allows inference to be carried out using integer-only arithmetic, which can be implemented more efficiently than floating point inference on commonly available integer-only hardware. We also co-design a training procedure to preserve end-to-end model accuracy post quantization. As a result, the proposed quantization scheme improves the tradeoff between accuracy and on-device laten…
Neural networks are very popular in many areas, but great computing complexity makes it hard to run neural networks on devices with limited resources. To address this problem, quantization methods are used to reduce model size and computation cost, making it possible to use neural networks on embedded platforms or mobile devices. In this paper, an integer-only-quantization scheme is introduced. This scheme uses one layer that combines shift-based batch normalization and uniform quantization to implement 4-bit integer-only inference. Without big integer multiplication(which is used in previous …
Habana Labs – An Intel company（Habana Labs——英特尔旗下公司）；Technion（以色列理工学院）
Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations' dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer separately by optimizing its p…
Integer quantization of neural networks can be defined as the approximation of the high precision computation of the canonical neural network formulation, using reduced integer precision. It plays a significant role in the efficient deployment and execution of machine learning (ML) systems, reducing memory consumption and leveraging typically faster computations. In this work, we present an integer-only quantization strategy for Long Short-Term Memory (LSTM) neural network topologies, which themselves are the foundation of many production ML systems. Our quantization strategy is accurate (e.g.…
Beijing Institute of Technology（北京理工大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）；Tsinghua University（清华大学）
Deep neural network (DNN) quantization converting floating-point (FP) data in the network to integers (INT) is an effective way to shrink the model size for memory saving and simplify the operations for compute acceleration. Recently, researches on DNN quantization develop from inference to training, laying a foundation for the online training on accelerators. However, existing schemes leaving batch normalization (BN) untouched during training are mostly incomplete quantization that still adopts high precision FP in some parts of the data paths. Currently, there is no solution that can use onl…
Universita’ di Bologna（博洛尼亚大学）；ETH Zurich（苏黎世联邦理工学院）
This paper presents a novel end-to-end methodology for enabling the deployment of low-error deep networks on microcontrollers. To fit the memory and computational limitations of resource-constrained edge-devices, we exploit mixed low-bitwidth compression, featuring 8, 4 or 2-bit uniform quantization, and we model the inference graph with integer-only operations. Our approach aims at determining the minimum bit precision of every activation and weight tensor given the memory constraints of a device. This is achieved through a rule-based iterative procedure, which cuts the number of bits of the …
Low bit-width integer weights and activations are very important for efficient inference, especially with respect to lower power consumption. We propose Monte Carlo methods to quantize the weights and activations of pre-trained neural networks without any re-training. By performing importance sampling we obtain quantized low bit-width integer values from full-precision weights and activations. The precision, sparsity, and complexity are easily configurable by the amount of sampling performed. Our approach, called Monte Carlo Quantization (MCQ), is linear in both time and space, with the result…
This technical report aims at defining a formal framework for Deep Neural Network (DNN) layer-wise quantization, focusing in particular on the problems related to the final deployment. It also acts as a documentation for the NEMO (NEural Minimization for pytOrch) framework. It describes the four DNN representations used in NEMO (FullPrecision, FakeQuantized, QuantizedDeployable and IntegerDeployable), focusing in particular on a formal definition of the latter two. An important feature of this model, and in particular the IntegerDeployable representation, is that it enables DNN inference using…
Pre-trained language models like Ernie or Bert are currently used in many applications. These models come with a set of pre-trained weights typically obtained in unsupervised/self-supervised modality on a huge amount of data. After that, they are fine-tuned on a specific task. Applications then use these models for inference, and often some additional constraints apply, like low power-budget or low latency between input and output. The main avenue to meet these additional requirements for the inference settings, is to use low precision computation (e.g. INT8 rather than FP32), but this comes w…
Qualcomm AI Research（高通人工智能研究院）；Qualcomm Canada ULC（高通加拿大无限责任公司）；University of Toronto（多伦多大学）
Tiny machine learning (tinyML) has emerged during the past few years aiming to deploy machine learning models to embedded AI processors with highly constrained memory and computation capacity. Low precision quantization is an important model compression technique that can greatly reduce both memory consumption and computation cost of model inference. In this study, we focus on post-training quantization (PTQ) algorithms that quantize a model to low-bit (less than 8-bit) precision with only a small set of calibration data and benchmark them on different tinyML use cases. To achieve a fair compa…
QFlash: Bridging Quantization and Memory Efficiency in Vision Transformer Attention
University of Science and Technology（科学技术大学）；Electronics and Telecommunications Research Institute（电信研究所）；Pusan National University（釜山国立大学）；Jeonbuk National University（全州国立大学）
Quantization enables efficient acceleration of deep neural networks by reducing model memory footprint and exploiting low-cost integer math hardware units. Quantization maps floating-point weights and activations in a trained model to low-bitwidth integer values using scale factors. Excessive quantization, reducing precision too aggressively, results in accuracy degradation. When scale factors are shared at a coarse granularity across many dimensions of each tensor, effective precision of individual elements within the tensor are limited. To reduce quantization-related accuracy loss, we propos…
Enhancing Vector Quantization with Distributional Matching: A Theoretical and Empirical Study
University of Toronto（多伦多大学）；The Hong Kong University of Science and Technology（香港科学与技术大学）；Boston College（波士顿学院）；Lehigh University（莱特大学）；Southern University of Science and Technology（南方科技大学）
An Empirical Study of openPangu Quantization on Ascend NPUs
State Key Laboratory of Complex & Critical Software Environment, Beihang University（北京航空航天大学复杂关键软件环境国家重点实验室）；School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；School of Artificial Intelligence, Beihang University（北京航空航天大学人工智能学院）
Doctoral School of Applied Informatics and Applied Mathematics, Obuda University（应用信息与应用数学博士学院，奥布达大学）；John von Neumann Faculty of Informatics, Obuda University（约翰·冯·诺伊曼信息学院，奥布达大学）
Efficient Mixed Precision Quantization in Graph Neural Networks
Faculty of Computer Science, University of Vienna（计算机科学系，维也纳大学）；UniVie Doctoral School Computer Science, University of Vienna（UniVie计算机科学博士学院，维也纳大学）；Research Network Data Science, University of Vienna（数据科学研究网络，维也纳大学）
NestQuant: Post-Training Integer-Nesting Quantization for On-Device DNN
Key Laboratory of Big Data & Artificial Intelligence in Transportation (Beijing Jiaotong University), Ministry of Education（大数据与人工智能在交通中的关键实验室（北京交通大学，教育部））；School of Computer Science and Technology, Beijing Jiaotong University（计算机科学与技术学院，北京交通大学）；School of Artificial Intelligence, Beijing Normal University（人工智能学院，北京师范大学）；Department of Computer Science, City University of Hong Kong（计算机科学系，香港城市大学）
In this paper we present a simple and computationally efficient quantization scheme that enables us to reduce the resolution of the parameters of a neural network from 32-bit floating point values to 8-bit integer values. The proposed quantization scheme leads to significant memory savings and enables the use of optimized hardware instructions for integer arithmetic, thus significantly reducing the cost of inference. Finally, we propose a "quantization aware" training process that applies the proposed scheme during network training and find that it allows us to recover most of the loss in accu…
The ever-increasing computational complexity of deep learning models makes their training and deployment difficult on various cloud and edge platforms. Replacing floating-point arithmetic with low-bit integer arithmetic is a promising approach to save energy, memory footprint, and latency of deep learning models. As such, quantization has attracted the attention of researchers in recent years. However, using integer numbers to form a fully functional integer training pipeline including forward pass, back-propagation, and stochastic gradient descent is not studied in detail. Our empirical and m…
Beijing University of Posts and Telecommunications（北京邮电大学）；Beijing Institute of Technology（北京理工大学）；Capital Medical University（首都医科大学）；Tsinghua University（清华大学）
Huge computational costs brought by convolution and batch normalization (BN) have caused great challenges for the online training and corresponding applications of deep neural networks (DNNs), especially in resource-limited devices. Existing works only focus on the convolution or BN acceleration and no solution can alleviate both problems with satisfactory performance. Online training has gradually become a trend in resource-limited devices like mobile phones while there is still no complete technical scheme with acceptable model performance, processing speed, and computational cost. In this r…
University of Science and Technology of China（中国科学技术大学）
Integer-arithmetic-only networks have been demonstrated effective to reduce computational cost and to ensure cross-platform consistency. However, previous works usually report a decline in the inference accuracy when converting well-trained floating-point-number (FPN) networks into integer networks. We analyze this phonomenon and find that the decline is due to activation quantization. Specifically, when we replace conventional ReLU with Bounded ReLU, how to set the bound for each neuron is a key problem. Considering the tradeoff between activation quantization error and network learning abili…
Recurrent neural networks (RNN) are the backbone of many text and speech applications. These architectures are typically made up of several computationally complex components such as; non-linear activation functions, normalization, bi-directional dependence and attention. In order to maintain good accuracy, these components are frequently run using full-precision floating-point computation, making them slow, inefficient and difficult to deploy on edge devices. In addition, the complex nature of these operations makes them challenging to quantize using standard quantization methods without a si…
Quantization plays an important role in the energy-efficient deployment of deep neural networks on resource-limited devices. Post-training quantization is highly desirable since it does not require retraining or access to the full training dataset. The well-established uniform scheme for post-training quantization achieves satisfactory results by converting neural networks from full-precision to 8-bit fixed-point integers. However, it suffers from significant performance degradation when quantizing to lower bit-widths. In this paper, we propose a piecewise linear quantization (PWLQ) scheme to …
Friedrich-Alexander University Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡大学）
For many applications, utilizing DNNs (Deep Neural Networks) requires their implementation on a target architecture in an optimized manner concerning energy consumption, memory requirement, throughput, etc. DNN compression is used to reduce the memory footprint and complexity of a DNN before its deployment on hardware. Recent efforts to understand and explain AI (Artificial Intelligence) methods have led to a new research area, termed as explainable AI. Explainable AI methods allow us to understand better the inner working of DNNs, such as the importance of different neurons and features. The …
DeepGlint（深瞳）；OPEN AI LAB（开放智能实验室）；Beijing Institute of Technology（北京理工大学）
The 8 bits quantization has been widely applied to accelerate network inference in various deep learning applications. There are two kinds of quantization methods, training-based quantization and post-training quantization. Training-based approach suffers from a cumbersome training process, while post-training quantization may lead to unacceptable accuracy drop. In this paper, we present an efficient and simple post-training method via scale optimization, named EasyQuant (EQ),that could obtain comparable accuracy with the training-based method.Specifically, we first alternately optimize scales…
