Convolutional neural networks require significant memory bandwidth and storage for intermediate computations, apart from substantial computing resources. Neural network quantization has significant benefits in reducing the amount of intermediate results, but it often requires the full datasets and time-consuming fine tuning to recover the accuracy lost after quantization. This paper introduces the first practical 4-bit post training quantization approach: it does not involve training the quantized model (fine-tuning), nor it requires the availability of the full dataset. We target the quantization of both activations and weights and suggest three complementary methods for minimizing quantization error at the tensor level, two of whom obtain a closed-form analytical solution. Combining these methods, our approach achieves accuracy that is just a few percents less the state-of-the-art baseline across a wide range of convolutional models. The source code to replicate all experiments is available on GitHub: \url{https://github.com/submission2019/cnn-quantization}.
As an effective technique to achieve the implementation of deep neural networks in edge devices, model quantization has been successfully applied in many practical applications. No matter the methods of quantization aware training (QAT) or post-training quantization (PTQ), they all depend on the target bit-widths. When the precision of quantization is adjusted, it is necessary to fine-tune the quantized model or minimize the quantization noise, which brings inconvenience in practical applications. In this work, we propose a method to train a model for all quantization that supports diverse bit…
Tsinghua University（清华大学）；University of Virginia（弗吉尼亚大学）；Intel Labs China（英特尔中国研究院）
Low-bit deep neural networks (DNNs) become critical for embedded applications due to their low storage requirement and computing efficiency. However, they suffer much from the non-negligible accuracy drop. This paper proposes the stochastic quantization (SQ) algorithm for learning accurate low-bit DNNs. The motivation is due to the following observation. Existing training algorithms approximate the real-valued elements/filters with low-bit representation all together in each iteration. The quantization errors may be small for some elements/filters, while are remarkable for others, which lead t…
This paper discusses three basic blocks for the inference of convolutional neural networks (CNNs). Pyramid Vector Quantization (PVQ) is discussed as an effective quantizer for CNNs weights resulting in highly sparse and compressible networks. Properties of PVQ are exploited for the elimination of multipliers during inference while maintaining high performance. The result is then extended to any other quantized weights. The Tiny Yolo v3 CNN is used to compare such basic blocks.
Conventional model quantization methods use a fixed quantization scheme to different data samples, which ignores the inherent "recognition difficulty" differences between various samples. We propose to feed different data samples with varying quantization schemes to achieve a data-dependent dynamic inference, at a fine-grained layer level. However, enabling this adaptive inference with changeable layer-wise quantization schemes is challenging because the combination of bit-widths and layers is growing exponentially, making it extremely difficult to train a single model in such a vast searching…
Powers-of-two (PoT) quantization reduces the number of bit operations of deep neural networks on resource-constrained hardware. However, PoT quantization triggers a severe accuracy drop because of its limited representation ability. Since DNN models have been applied for relatively complex tasks (e.g., classification for large datasets and object detection), improvement in accuracy for the PoT quantization method is required. Although some previous works attempt to improve the accuracy of PoT quantization, there is no work that balances accuracy and computation costs in a memory-efficient way.…
Recent researches on information bottleneck shed new light on the continuous attempts to open the black box of neural signal encoding. Inspired by the problem of lossy signal compression for wireless communication, this paper presents a Bitwise Information Bottleneck approach for quantizing and encoding neural network activations. Based on the rate-distortion theory, the Bitwise Information Bottleneck attempts to determine the most significant bits in activation representation by assigning and approximating the sparse coefficient associated with each bit. Given the constraint of a limited aver…
Singapore University of Technology and Design（新加坡科技设计大学）；University of Liverpool（利物浦大学）；University of Dayton（戴顿大学）
This paper proposes two novel techniques to train deep convolutional neural networks with low bit-width weights and activations. First, to obtain low bit-width weights, most existing methods obtain the quantized weights by performing quantization on the full-precision network weights. However, this approach would result in some mismatch: the gradient descent updates full-precision weights, but it does not update the quantized weights. To address this issue, we propose a novel method that enables {direct} updating of quantized weights {with learnable quantization levels} to minimize the cost fu…
Neural network quantization has an inherent problem called accumulated quantization error, which is the key obstacle towards ultra-low precision, e.g., 2- or 3-bit precision. To resolve this problem, we propose precision highway, which forms an end-to-end high-precision information flow while performing the ultra low-precision computation. First, we describe how the precision highway reduce the accumulated quantization error in both convolutional and recurrent neural networks. We also provide the quantitative analysis of the benefit of precision highway and evaluate the overhead on the state-o…
Deep neural network quantization with adaptive bitwidths has gained increasing attention due to the ease of model deployment on various platforms with different resource budgets. In this paper, we propose a meta-learning approach to achieve this goal. Specifically, we propose MEBQAT, a simple yet effective way of bitwidth-adaptive quantization aware training (QAT) where meta-learning is effectively combined with QAT by redefining meta-learning tasks to incorporate bitwidths. After being deployed on a platform, MEBQAT allows the (meta-)trained model to be quantized to any candidate bitwidth the…
Mixed-precision quantization can potentially achieve the optimal tradeoff between performance and compression rate of deep neural networks, and thus, have been widely investigated. However, it lacks a systematic method to determine the exact quantization scheme. Previous methods either examine only a small manually-designed search space or utilize a cumbersome neural architecture search to explore the vast search space. These approaches cannot lead to an optimal quantization scheme efficiently. This work proposes bit-level sparsity quantization (BSQ) to tackle the mixed-precision quantization …
ETH Zurich（苏黎世联邦理工学院）；Singapore Management University（新加坡管理大学）
We investigate the compression of deep neural networks by quantizing their weights and activations into multiple binary bases, known as multi-bit networks (MBNs), which accelerate the inference and reduce the storage for the deployment on low-resource mobile and embedded platforms. We propose Adaptive Loss-aware Quantization (ALQ), a new MBN quantization pipeline that is able to achieve an average bitwidth below one-bit without notable loss in inference accuracy. Unlike previous MBN quantization solutions that train a quantizer by minimizing the error to reconstruct full precision weights, ALQ…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）；AITRICS
Network quantization, which aims to reduce the bit-lengths of the network weights and activations, has emerged for their deployments to resource-limited devices. Although recent studies have successfully discretized a full-precision network, they still incur large quantization errors after training, thus giving rise to a significant performance gap between a full-precision network and its quantized counterpart. In this work, we propose a novel quantization method for neural networks, Cluster-Promoting Quantization (CPQ) that finds the optimal quantization grids while naturally encouraging the …
MILA（MILA（蒙特利尔学习算法研究所））；IMT Atlantique（IMT大西洋大学）；Sony Europe B.V.（索尼欧洲有限公司）
Low-bit quantization of network weights and activations can drastically reduce the memory footprint, complexity, energy consumption and latency of Deep Neural Networks (DNNs). However, low-bit quantization can also cause a considerable drop in accuracy, in particular when we apply it to complex learning tasks or lightweight DNN architectures. In this paper, we propose a training procedure that relaxes the low-bit quantization. We call this procedure \textit{DNN Quantization with Attention} (DQA). The relaxation is achieved by using a learnable linear combination of high, medium and low-bit qua…
Shanghai Jiao Tong University（上海交通大学）；Qualcomm AI Research（高通人工智能研究院）
Network quantization is an effective method for the deployment of neural networks on memory and energy constrained mobile devices. In this paper, we propose a Dynamic Network Quantization (DNQ) framework which is composed of two modules: a bit-width controller and a quantizer. Unlike most existing quantization methods that use a universal quantization bit-width for the whole network, we utilize policy gradient to train an agent to learn the bit-width of each layer by the bit-width controller. This controller can make a trade-off between accuracy and compression ratio. Given the quantization bi…
US AI Lab, ByteDance Inc.（美国人工智能实验室，字节跳动公司）；Northeastern University（东北大学）
Model quantization helps to reduce model size and latency of deep neural networks. Mixed precision quantization is favorable with customized hardwares supporting arithmetic operations at multiple bit-widths to achieve maximum efficiency. We propose a novel learning-based algorithm to derive mixed precision models end-to-end under target computation constraints and model sizes. During the optimization, the bit-width of each layer / kernel in the model is at a fractional status of two consecutive bit-widths which can be adjusted gradually. With a differentiable regularization term, the resource …
Sensetime Research（商汤科技研究院）；University of Oxford（牛津大学）；The University of Sydney（悉尼大学）
Quantization Neural Networks (QNN) have attracted a lot of attention due to their high efficiency. To enhance the quantization accuracy, prior works mainly focus on designing advanced quantization algorithms but still fail to achieve satisfactory results under the extremely low-bit case. In this work, we take an architecture perspective to investigate the potential of high-performance QNN. Therefore, we propose to combine Network Architecture Search methods with quantization to enjoy the merits of the two sides. However, a naive combination inevitably faces unacceptable time consumption or uns…
We introduce Bayesian Bits, a practical method for joint mixed precision quantization and pruning through gradient based optimization. Bayesian Bits employs a novel decomposition of the quantization operation, which sequentially considers doubling the bit width. At each new bit width, the residual error between the full precision value and the previously rounded value is quantized. We then decide whether or not to add this quantized residual error for a higher effective bit width and lower quantization noise. By starting with a power-of-two bit width, this decomposition will always produce har…
Quantization for deep neural networks have afforded models for edge devices that use less on-board memory and enable efficient low-power inference. In this paper, we present a comparison of model-parameter driven quantization approaches that can achieve as low as 3-bit precision without affecting accuracy. The post-training quantization approaches are data-free, and the resulting weight values are closely tied to the dataset distribution on which the model has converged to optimality. We show quantization results for a number of state-of-art deep neural networks (DNN) using large dataset like …
Beihang University（北京航空航天大学）；SenseTime Group Limited（商汤集团有限公司）；Beijing Institute of Technology（北京理工大学）
Hardware-friendly network quantization (e.g., binary/uniform quantization) can efficiently accelerate the inference and meanwhile reduce memory consumption of the deep neural networks, which is crucial for model deployment on resource-limited devices like mobile phones. However, due to the discreteness of low-bit quantization, existing quantization methods often face the unstable training process and severe performance degradation. To address this problem, in this paper we propose Differentiable Soft Quantization (DSQ) to bridge the gap between the full-precision and low-bit networks. DSQ can …
Network quantization, which aims to reduce the bit-lengths of the network weights and activations, has emerged as one of the key ingredients to reduce the size of neural networks for their deployments to resource-limited devices. In order to overcome the nature of transforming continuous activations and weights to discrete ones, recent study called Relaxed Quantization (RQ) [Louizos et al. 2019] successfully employ the popular Gumbel-Softmax that allows this transformation with efficient gradient-based optimization. However, RQ with this Gumbel-Softmax relaxation still suffers from bias-varian…
Model quantization is a widely used technique to compress and accelerate deep neural network (DNN) inference, especially when deploying to edge or IoT devices with limited computation capacity and power consumption budget. The uniform bit width quantization across all the layers is usually sub-optimal and the exploration of hybrid quantization for different layers is vital for efficient deep compression. In this paper, we employ the meta learning method to automatically realize low-bit hybrid quantization of neural networks. A MetaQuantNet, together with a Quantization function, are trained to…
Dankook University（檀国大学）；Complutense University of Madrid（马德里康普顿斯大学）
This paper proposes a training method having multiple cyclic training for achieving enhanced performance in low-bit quantized convolutional neural networks (CNNs). Quantization is a popular method for obtaining lightweight CNNs, where the initialization with a pretrained model is widely used to overcome degraded performance in low-resolution quantization. However, large quantization errors between real values and their low-bit quantized ones cause difficulties in achieving acceptable performance for complex networks and large datasets. The proposed training method softly delivers the knowledge…
Technion — Israel Institute of Technology（以色列理工学院）；Ruppin Academic Center（鲁平学术中心）
Quantization is a technique used in deep neural networks (DNNs) to increase execution performance and hardware efficiency. Uniform post-training quantization (PTQ) methods are common, since they can be implemented efficiently in hardware and do not require extensive hardware resources or a training set. Mapping FP32 models to INT8 using uniform PTQ yields models with negligible accuracy degradation; however, reducing precision below 8 bits with PTQ is challenging, as accuracy degradation becomes noticeable, due to the increase in quantization noise. In this paper, we propose a sparsity-aware q…
Qualcomm AI Research, Qualcomm Technologies, Inc.（高通AI研究，高通技术公司）；Qualcomm AI Research, Qualcomm Technologies Netherlands B.V.（高通AI研究，高通技术荷兰有限公司）；Seoul National University（首尔大学）
Unlike ReLU, newer activation functions (like Swish, H-swish, Mish) that are frequently employed in popular efficient architectures can also result in negative activation values, with skewed positive and negative ranges. Typical learnable quantization schemes [PACT, LSQ] assume unsigned quantization for activations and quantize all negative activations to zero which leads to significant loss in performance. Naively using signed quantization to accommodate these negative values requires an extra sign bit which is expensive for low-bit (2-, 3-, 4-bit) quantization. To solve this problem, we prop…
Recent machine learning methods use increasingly large deep neural networks to achieve state of the art results in various tasks. The gains in performance come at the cost of a substantial increase in computation and storage requirements. This makes real-time implementations on limited resources hardware a challenging task. One popular approach to address this challenge is to perform low-bit precision computations via neural network quantization. However, aggressive quantization generally entails a severe penalty in terms of accuracy, and often requires retraining of the network, or resorting …
Stanford University（斯坦福大学）；University of New South Wales（新南威尔士大学）
In this paper, we compress convolutional neural network (CNN) weights post-training via transform quantization. Previous CNN quantization techniques tend to ignore the joint statistics of weights and activations, producing sub-optimal CNN performance at a given quantization bit-rate, or consider their joint statistics during training only and do not facilitate efficient compression of already trained CNN models. We optimally transform (decorrelate) and quantize the weights post-training using a rate-distortion framework to improve compression at any given quantization bit-rate. Transform quant…
SDQ-LLM: Sigma-Delta Quantization for 1-bit LLMs of any size
Dept of Electronic Engineering, Tsinghua University, Beijing, China（电子工程系，清华大学，北京，中国）；Beijing National Research Center for Information Science and Technology, Beijing, China（北京信息科学与技术国家研究中心，北京，中国）
SenseTime Research（商汤科技研究院）；Tsinghua University（清华大学）；The Chinese University of Hong Kong（香港中文大学）；Beihang Univerisity（北京航空航天大学）
Low-bit quantization is challenging to maintain high performance with limited model capacity (e.g., 4-bit for both weights and activations). Naturally, the distribution of both weights and activations in deep neural network are Gaussian-like. Nevertheless, due to the limited bitwidth of low-bit model, uniform-like distributed weights and activations have been proved to be more friendly to quantization while preserving accuracy~\cite{Han2015Learning}. Motivated by this, we propose Scale-Clip, a Distribution Reshaping technique that can reshape weights or activations into a uniform-like distribu…
MPQ-DM: Mixed Precision Quantization for Extremely Low Bit Diffusion Models
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；ETH Zurich（苏黎世联邦理工学院）；Beijing Jiaotong University（北京交通大学）
Post-Training Quantization via Residual Truncation and Zero Suppression for Diffusion Models
Department of Artificial Intelligence（人工智能系）；Kyung Hee University（庆尚大学）；Department of Electrical Engineering（电气工程系）；Department of Computer Science（计算机科学系）
Recently, post-training quantization (PTQ) has driven much attention to produce efficient neural networks without long-time retraining. Despite its low cost, current PTQ works tend to fail under the extremely low-bit setting. In this study, we pioneeringly confirm that properly incorporating activation quantization into the PTQ reconstruction benefits the final accuracy. To deeply understand the inherent reason, a theoretical framework is established, indicating that the flatness of the optimized low-bit model on calibration and test data is crucial. Based on the conclusion, a simple yet effec…
Quantizing deep neural networks is an effective method for reducing memory consumption and improving inference speed, and is thus useful for implementation in resource-constrained devices. However, it is still hard for extremely low-bit models to achieve accuracy comparable with that of full-precision models. To address this issue, we propose learnable companding quantization (LCQ) as a novel non-uniform quantization method for 2-, 3-, and 4-bit models. LCQ jointly optimizes model weights and learnable companding functions that can flexibly and non-uniformly control the quantization levels of …
Qualcomm AI Research, Qualcomm Technologies, Inc.（高通技术公司高通人工智能研究院）；University of California Irvine（加州大学欧文分校）；Qualcomm AI Research, Qualcomm Technologies Netherlands B.V.（高通技术荷兰有限公司高通人工智能研究院）
We present PLONQ, a progressive neural image compression scheme which pushes the boundary of variable bitrate compression by allowing quality scalable coding with a single bitstream. In contrast to existing learned variable bitrate solutions which produce separate bitstreams for each quality, it enables easier rate-control and requires less storage. Leveraging the latent scaling based variable bitrate solution, we introduce nested quantization, a method that defines multiple quantization levels with nested quantization grids, and progressively refines all latents from the coarsest to the fines…
Hanyang University（汉阳大学）；NVIDIA（英伟达）；Seoul National University（首尔大学）
Despite breakthrough advances in image super-resolution (SR) with convolutional neural networks (CNNs), SR has yet to enjoy ubiquitous applications due to the high computational complexity of SR networks. Quantization is one of the promising approaches to solve this problem. However, existing methods fail to quantize SR models with a bit-width lower than 8 bits, suffering from severe accuracy loss due to fixed bit-width quantization applied everywhere. In this work, to achieve high average bit-reduction with less accuracy loss, we propose a novel Content-Aware Dynamic Quantization (CADyQ) meth…
