Effective Training of Convolutional Neural Networks with Low-bitwidth Weights and Activations

This paper tackles the problem of training a deep convolutional neural network of both low-bitwidth weights and activations. Optimizing a low-precision network is very challenging due to the non-differentiability of the quantizer, which may result in substantial accuracy loss. To address this, we propose three practical approaches, including (i) progressive quantization; (ii) stochastic precision; and (iii) joint knowledge distillation to improve the network training. First, for progressive quantization, we propose two schemes to progressively find good local minima. Specifically, we propose to first optimize a net with quantized weights and subsequently quantize activations. This is in contrast to the traditional methods which optimize them simultaneously. Furthermore, we propose a second progressive quantization scheme which gradually decreases the bit-width from high-precision to low-precision during training. Second, to alleviate the excessive training burden due to the multi-round training stages, we further propose a one-stage stochastic precision strategy to randomly sample and quantize sub-networks while keeping other parts in full-precision. Finally, we adopt a novel learning scheme to jointly train a full-precision model alongside the low-precision one. By doing so, the full-precision model provides hints to guide the low-precision model training and significantly improves the performance of the low-precision network. Extensive experiments on various datasets (e.g., CIFAR-100, ImageNet) show the effectiveness of the proposed methods.Comment: Accepted to IEEE T. Pattern Analysis and Machine Intelligence (TPAMI). Extended version of arXiv:1711.00205 (CVPR 2018

Forward and Backward Information Retention for Accurate Binary Neural Networks

Weight and activation binarization is an effective approach to deep neural network compression and can accelerate the inference by leveraging bitwise operations. Although many binarization methods have improved the accuracy of the model by minimizing the quantization error in forward propagation, there remains a noticeable performance gap between the binarized model and the full-precision one. Our empirical study indicates that the quantization brings information loss in both forward and backward propagation, which is the bottleneck of training accurate binary neural networks. To address these issues, we propose an Information Retention Network (IR-Net) to retain the information that consists in the forward activations and backward gradients. IR-Net mainly relies on two technical contributions: (1) Libra Parameter Binarization (Libra-PB): simultaneously minimizing both quantization error and information loss of parameters by balanced and standardized weights in forward propagation; (2) Error Decay Estimator (EDE): minimizing the information loss of gradients by gradually approximating the sign function in backward propagation, jointly considering the updating ability and accurate gradients. We are the first to investigate both forward and backward processes of binary networks from the unified information perspective, which provides new insight into the mechanism of network binarization. Comprehensive experiments with various network structures on CIFAR-10 and ImageNet datasets manifest that the proposed IR-Net can consistently outperform state-of-the-art quantization methods

효율적인 심층 신경망을 위한 양자화 알고리즘 및 방법론

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 유승주.Deep neural networks (DNN) are becoming increasingly popular and widely adopted for various applications. Energy efficiency of neural networks is critically important for both edge devices and servers. It is imperative to optimize neural networks in terms of both speed and energy consumption while maintaining the accuracy of the network. Quantization is one of the most effective optimization techniques. By reducing the bit-width of activations and weights, both the speed and energy can be improved by executing more computations using the same amount of memory access and computational resources (e.g. silicon chip area and battery). It is expected that computations with 4-bit and lower precision will contribute to the energy efficient and real-time characteristics of future deep learning applications. One major drawback of quantization is the drop in accuracy, resulting from the reduction in the degree of freedom of data representation. Recently, there have been several studies that demonstrated that the inference of DNNs can be accurately done by using 8-bit precision. However, many studies show that the network quantized into 4-bit or less precision suffers from significant quality degradation. Especially, the state-of-the art networks cannot be quantized easily due to their optimized structure. In this dissertation, several methods are proposed that use different approaches to minimize the reduction in the accuracy of the quantized DNNs. Weighted- entropy-based quantization is designed to fully utilize the limited number of quantization levels by maximizing the weighted information of the quantized data. This work shows the potential of multi-bit quantization for both activation and weight. Value-aware quantization, or outlier-aware quantization is designed to support sub-4-bit quantization, while allowing a small amount (1 ~ 3 %) of large values in high precision. This helps the quantized data to maintain the statistics, e.g. mean and variance corresponding to the full-precision, thus minimizing the accuracy drop after quantization. The dedicated hardware accelerator, called OLAccel, is also proposed to maximize the performance of the network quantized by the outlier-aware quantization. The hardware takes advantage of the benefit of reduced precision, i.e. 4-bit, with minimal accuracy drop by the proposed quantization algorithm. Precision-highway is the structural concept that forms an end-to-end high-precision information flow while performing ultra-low-precision computations. This minimizes the accumulated quantization error, which helps to improve the accuracy of the network even with extremely low precision. BLast, the training methodology, and differentiable and unified quantization (DuQ), a novel quantization algorithm, are designed to support sub-4-bit quantization for the optimized mobile networks, i.e. MobileNet-v3. These methods allow the MobileNet-v3 network to be quantized into 4-bit for both activation and weight with negligible accuracy loss.딥 뉴럴 네트워크 (DNN)는 활용 범위를 점차 넓혀가며 다양한 분야에 적용되고 있다. 뉴럴 네트워크는 서버 뿐만 아니라 임베디드 기기에서도 널리 활용되고 있으며 이로인해 뉴럴 네트워크의 효율성을 높이는 것은 점점 더 중요해지는 중이다. 이제 정확도를 유지하면서 속도를 빠르게 하고 에너지 소모를 줄이는 뉴럴 네트워크의 최적화는 필수적 요소로 자리잡았다. 양자화는 가장 효과적인 최적화 기법 중 하나이다. 뉴런의 활성도 (activation) 및 학습 가중치 (weight)를 저장하는데 필요한 비트 수를 줄임으로써 동일한 양의 데이터 접근과 연산 비용 (칩 면적 및 에너지 소모 등)으로 더 많은 연산이 가능해지며 이로인해 속도와 에너지 소모를 동시에 최적화할 수 있다. 추후 딥 러닝을 활용하기 위하여 필요할 것으로 예측되는 에너지 효율 및 연산 속도를 만족시키기 위해서 4 비트 혹은 더 적은 정밀도 기반의 양자화 연산이 지대한 공헌을 할 것으로 기대된다. 그러나 양자화의 가장 중요한 단점 중 하나는 데이터의 표현형을 제한하여 자유도가 떨어지게 됨으로서 발생하는 정확도의 손실이다. 이러한 단점을 해결하기 위하여 다양한 연구들이 진행중이다. 최근 일부 연구들은 8 비트의 정밀도에서 뉴럴 네트워크를 활용해 결과를 추론 (inference)하는데 정확도 손실이 거의 없음을 보고하고 있다. 반면 그 외의 다양한 연구들을 통해 4 비트 혹은 더 낮은 정밀도에서 양자화를 적용했을 때 많은 네트워크들의 정확도가 크게 손상되는 현상도 함께 보고되고 있다. 특히 최근 제안된 네트워크들의 경우 성능 향상을 위해 도입한 최적화된 구조가 양자화 하기 어려운 특성을 가져 이러한 현상이 심화된다. 본 논문에서는 양자화된 DNN의 정확도 손실을 최소화하기위한 다양한 방법들을 제안하였다. 가중 엔트로피 기반 양자화 (Weighted-entropy-based quantization)은 제한된 개수의 양자화 레벨을 최대한 활용하기 위하여 양자화된 데이터의 정보량을 최대화하는 방향으로 양자화를 진행하도록 설계되었다. 이 연구를 통해 아주 깊은 네트워크에서도 뉴런의 활성도와 학습 가중치 모두의 양자화가 적용 가능함을 보였다. 값-의식 양자화 (value-aware quantization), 혹은 예외-의식 양자화 (outlier-aware quantization)는 빈도는 낮지만 큰 값을 가지는 데이터를 큰 정밀도로 저장하는 대신 나머지 데이터에 4 비트 이하의 양자화를 적용하도록 설계된 알고리즘이다. 이는 원본 데이터의 평균과 분산 같은 특성이 양자화된 후에도 유지하도록 도와주어 양자화된 네트워크의 정확도를 유지하는데 기여한다. 이에 더하여 OLAccel이라 명명된 특화 가속기를 제안하였다. 이 가속기는 값-의식 양자화 알고리즘을 통해 양자화된 네트워크를 가속함으로써 정확도 감소는 최소화 하면서 낮은 정밀도의 성능 이득을 최대화한다. 고정밀도-통로 구조 (precision-highway)는 네트워크의 구조를 개선하여 초저정밀도 연산을 수행하면서도 고정밀도 정보 통로를 생성한다. 이는 양자화로 인하여 에러가 누적되는 현상을 완화하여 매우 낮은 정밀도에서 정확도를 개선하는데 기여한다. 학습 기법인 BLast와 미분 가능하고 통합된 양자화 알고리즘 (DuQ)는 MobileNet-v3과 같은 최적화된 모바일향 네트워크를 최적화하기 위하여 제안되었다. 이 방법들을 통해 미미한 정확도 손실만으로 MobileNet-v3의 활성도 및 학습 가중치 모두를 4 비트 정밀도로 양자화하는데 성공하였다.Chapter 1. Introduction 1 Chapter 2. Background and RelatedWork 4 Chapter 3. Weighted-entropy-based Quantization 15 3.1 Introduction 15 3.2 Motivation 17 3.3 Quantization based on Weighted Entropy 20 3.3.1 Weight Quantization 20 3.3.2 Activation Quantization 24 3.3.3 IntegratingWeight/Activation Quantization into the Training Algorithm 27 3.4 Experiment 28 3.4.1 Image Classification: AlexNet, GoogLeNet and ResNet-50/101 28 3.4.2 Object Detection: R-FCN with ResNet-50 35 3.4.3 Language Modeling: An LSTM 37 3.5 Conclusion 38 Chapter 4. Value-aware Quantization for Training and Inference of Neural Networks 40 4.1 Introduction 40 4.2 Motivation 41 4.3 Proposed Method 43 4.3.1 Quantized Back-Propagation 44 4.3.2 Back-Propagation of Full-Precision Loss 46 4.3.3 Potential of Further Reduction in Computation Cost 47 4.3.4 Local Sorting in Data Parallel Training 48 4.3.5 ReLU and Value-aware Quantization (RV-Quant) 49 4.3.6 Activation Annealing 50 4.3.7 Quantized Inference 50 4.4 Experiments 51 4.4.1 Training Results 52 4.4.2 Inference Results 59 4.4.3 LSTM Language Model 61 4.5 Conclusions 62 Chapter 5. Energy-efficient Neural Network Accelerator Based on Outlier-aware Low-precision Computation 63 5.1 Introduction 63 5.2 Proposed Architecture 65 5.2.1 Overall Structure 65 5.2.2 Dataflow 68 5.2.3 PE Cluster 72 5.2.4 Normal PE Group 72 5.2.5 Outlier PE Group and Cluster Output Tri-buffer 75 5.3 Evaluation Methodology 78 5.4 Experimental Results 80 5.5 Conclusion 90 Chapter 6. Precision Highway for Ultra Low-Precision Quantization 92 6.1 Introduction 92 6.2 Proposed Method 93 6.2.1 Precision Highway on Residual Network 94 6.2.2 Precision Highway on Recurrent Neural Network 96 6.2.3 Practical Issues with Precision Highway 98 6.3 Training 99 6.3.1 LinearWeight Quantization based on Laplace Distribution Model 99 6.3.2 Fine-tuning for Weight/Activation Quantization 100 6.4 Experiments 101 6.4.1 Experimental Setup 101 6.4.2 Analysis of Accumulated Quantization Error 101 6.4.3 Loss Surface Analysis of Quantized Model Training 103 6.4.4 Evaluating the Accuracy of Quantized Model 103 6.4.5 Hardware Cost Evaluation of Quantized Model 108 6.5 Conclusion 109 Chapter 7. Towards Sub-4-bit Quantization of Optimized Mobile Netowrks 114 7.1 Introduction 114 7.2 BLast Training 117 7.2.1 Notation 118 7.2.2 Observation 118 7.2.3 Activation Instability Metric 120 7.2.4 BLast Training 122 7.3 Differentiable and Unified Quantization 124 7.3.1 Rounding and Truncation Errors 124 7.3.2 Limitations of State-of-the-Art Methods 124 7.3.3 Proposed Method: DuQ 126 7.3.4 Handling Negative Values 128 7.4 Experiments 131 7.4.1 Accuracy on ImageNet Dataset 131 7.4.2 Discussion on Fused-BatchNorm 133 7.4.3 Ablation Study 134 7.5 Conclusion 137 Chapter 8 Conclusion 138 Bibliography 141 국문초록 154 Acknowledgements 157Docto

Distribution-sensitive Information Retention for Accurate Binary Neural Network

Model binarization is an effective method of compressing neural networks and accelerating their inference process. However, a significant performance gap still exists between the 1-bit model and the 32-bit one. The empirical study shows that binarization causes a great loss of information in the forward and backward propagation. We present a novel Distribution-sensitive Information Retention Network (DIR-Net) that retains the information in the forward and backward propagation by improving internal propagation and introducing external representations. The DIR-Net mainly relies on three technical contributions: (1) Information Maximized Binarization (IMB): minimizing the information loss and the binarization error of weights/activations simultaneously by weight balance and standardization; (2) Distribution-sensitive Two-stage Estimator (DTE): retaining the information of gradients by distribution-sensitive soft approximation by jointly considering the updating capability and accurate gradient; (3) Representation-align Binarization-aware Distillation (RBD): retaining the representation information by distilling the representations between full-precision and binarized networks. The DIR-Net investigates both forward and backward processes of BNNs from the unified information perspective, thereby providing new insight into the mechanism of network binarization. The three techniques in our DIR-Net are versatile and effective and can be applied in various structures to improve BNNs. Comprehensive experiments on the image classification and objective detection tasks show that our DIR-Net consistently outperforms the state-of-the-art binarization approaches under mainstream and compact architectures, such as ResNet, VGG, EfficientNet, DARTS, and MobileNet. Additionally, we conduct our DIR-Net on real-world resource-limited devices which achieves 11.1x storage saving and 5.4x speedup

Efficient Deep Neural Networks

The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous driving, augmented reality, and internet-of-things. Training DNNs requires a large amount of data, which is difficult to obtain. Edge devices such as mobile phones have limited compute capacity, and therefore, require specialized and efficient DNNs. However, due to the enormous design space and prohibitive training costs, designing efficient DNNs for different target devices is challenging. So the question is, with limited data, compute capacity, and model complexity, can we still successfully apply deep neural networks?This dissertation focuses on the above problems and improving the efficiency of deep neural networks at four levels. Model efficiency: we designed neural networks for various computer vision tasks and achieved more than 10x faster speed and lower energy. Data efficiency: we developed an advanced tool that enables 6.2x faster annotation of a LiDAR point cloud. We also leveraged domain adaptation to utilize simulated data, bypassing the need for real data. Hardware efficiency: we co-designed neural networks and hardware accelerators and achieved 11.6x faster inference. Design efficiency: the process of finding the optimal neural networks is time-consuming. Our automated neural architecture search algorithms discovered, using 421x lower computational cost than previous search methods, models with state-of-the-art accuracy and efficiency