Deep neural networks (DNNs) have been widely and successfully applied to various applications, but they require large amounts of memory and computational power. This severely restricts their deployment on resource-limited devices. To address this issue, many efforts have been made on training low-bit weight DNNs. In this paper, we focus on training ternary weight \{-1, 0, +1\} networks which can avoid multiplications and dramatically reduce the memory and computation requirements. A ternary weight network can be considered as a sparser version of the binary weight counterpart by replacing some -1s or 1s in the binary weights with 0s, thus leading to more efficient inference but more memory cost. However, the existing approaches to training ternary weight networks cannot control the sparsity (i.e., percentage of 0s) of the ternary weights, which undermines the advantage of ternary weights. In this paper, we propose to our best knowledge the first sparsity-control approach (SCA) to training ternary weight networks, which is simply achieved by a weight discretization regularizer (WDR). SCA is different from all the existing regularizer-based approaches in that it can control the sparsity of the ternary weights through a controller $α$ and does not rely on gradient estimators. We theoretically and empirically show that the sparsity of the trained ternary weights is positively related to $α$. SCA is extremely simple, easy-to-implement, and is shown to consistently outperform the state-of-the-art approaches significantly over several benchmark datasets and even matches the performances of the full-precision weight counterparts.
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Quantization is spearheading the increase in performance and efficiency of neural network computing systems making headway into commodity hardware. We present SWIS - Shared Weight bIt Sparsity, a quantization framework for efficient neural network inference acceleration delivering improved performance and storage compression through an offline weight decomposition and scheduling algorithm. SWIS can achieve up to 54.3% (19.8%) point accuracy improvement compared to weight truncation when quantizing MobileNet-v2 to 4 (2) bits post-training (with retraining) showing the strength of leveraging sha…
MobileNets family of computer vision neural networks have fueled tremendous progress in the design and organization of resource-efficient architectures in recent years. New applications with stringent real-time requirements on highly constrained devices require further compression of MobileNets-like already compute-efficient networks. Model quantization is a widely used technique to compress and accelerate neural network inference and prior works have quantized MobileNets to 4-6 bits albeit with a modest to significant drop in accuracy. While quantization to sub-byte values (i.e. precision les…
Inference time, model size, and accuracy are critical for deploying deep neural network models. Numerous research efforts have been made to compress neural network models with faster inference and higher accuracy. Pruning and quantization are mainstream methods to this end. During model quantization, converting individual float values of layer weights to low-precision ones can substantially reduce the computational overhead and improve the inference speed. Many quantization methods have been studied, for example, vector quantization, low-bit quantization, and binary/ternary quantization. This …
William & Mary（威廉与玛丽学院）；Northeastern University（东北大学）；University of Southern California（南加州大学）
It is appealing but challenging to achieve real-time deep neural network (DNN) inference on mobile devices because even the powerful modern mobile devices are considered as ``resource-constrained'' when executing large-scale DNNs. It necessitates the sparse model inference via weight pruning, i.e., DNN weight sparsity, and it is desirable to design a new DNN weight sparsity scheme that can facilitate real-time inference on mobile devices while preserving a high sparse model accuracy. This paper designs a novel mobile inference acceleration framework GRIM that is General to both convolutional n…
Pruning neural networks has regained interest in recent years as a means to compress state-of-the-art deep neural networks and enable their deployment on resource-constrained devices. In this paper, we propose a robust compressive learning framework that efficiently prunes network parameters during training with minimal computational overhead. We incorporate fast mechanisms to prune individual layers and build upon these to automatically prune the entire network under a user-defined budget constraint. Key to our end-to-end network pruning approach is the formulation of an intuitive and easy-to…
Transformer-based pre-training models like BERT have achieved remarkable performance in many natural language processing tasks.However, these models are both computation and memory expensive, hindering their deployment to resource-constrained devices. In this work, we propose TernaryBERT, which ternarizes the weights in a fine-tuned BERT model. Specifically, we use both approximation-based and loss-aware ternarization methods and empirically investigate the ternarization granularity of different parts of BERT. Moreover, to reduce the accuracy degradation caused by the lower capacity of low bit…
Deep neural networks are widely used in machine learning applications. However, the deployment of large neural networks models can be difficult to deploy on mobile devices with limited power budgets. To solve this problem, we propose Trained Ternary Quantization (TTQ), a method that can reduce the precision of weights in neural networks to ternary values. This method has very little accuracy degradation and can even improve the accuracy of some models (32, 44, 56-layer ResNet) on CIFAR-10 and AlexNet on ImageNet. And our AlexNet model is trained from scratch, which means it's as easy as to tra…
One important classifier ensemble for multiclass classification problems is Error-Correcting Output Codes (ECOCs). It bridges multiclass problems and binary-class classifiers by decomposing multiclass problems to a serial binary-class problems. In this paper, we present a heuristic ternary code, named Weight Optimization and Layered Clustering-based ECOC (WOLC-ECOC). It starts with an arbitrary valid ECOC and iterates the following two steps until the training risk converges. The first step, named Layered Clustering based ECOC (LC-ECOC), constructs multiple strong classifiers on the most confu…
WeBank（微众银行）；Harbin Engineering University（哈尔滨工程大学）；University of Hyogo（兵库县立大学）；Gakushuin University（学习院大学）
Quantization of weights of deep neural networks (DNN) has proven to be an effective solution for the purpose of implementing DNNs on edge devices such as mobiles, ASICs and FPGAs, because they have no sufficient resources to support computation involving millions of high precision weights and multiply-accumulate operations. This paper proposes a novel method to compress vectors of high precision weights of DNNs to ternary vectors, namely a cosine similarity based target non-retraining ternary (TNT) compression method. Our method leverages cosine similarity instead of Euclidean distances as com…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Federal Research Center “Computer Science and Control” of Russian Academy of Sciences（俄罗斯科学院计算机科学与控制联邦研究中心）；Smart Engines Service LLC（Smart Engines服务有限责任公司）；Institute for Information Transmission Problems, RAS（俄罗斯科学院信息传输问题研究所）
Low-bit quantized neural networks are of great interest in practical applications because they significantly reduce the consumption of both memory and computational resources. Binary neural networks are memory and computationally efficient as they require only one bit per weight and activation and can be computed using Boolean logic and bit count operations. QNNs with ternary weights and activations and binary weights and ternary activations aim to improve recognition quality compared to BNNs while preserving low bit-width. However, their efficient implementation is usually considered on ASICs…
LoTA-QAF: Lossless Ternary Adaptation for Quantization-Aware Fine-Tuning
Southwestern University of Finance and Economics（西南财经大学）；Artificial Intelligence and Digital Finance Key Laboratory of Sichuan Province（四川省人工智能与数字金融重点实验室）；The Hong Kong University of Science and Technology (Guangzhou)（香港科学与艺术大学（广州））；Sun Yat-sen University（中山大学）；Nanjing University（南京大学）
Recurrent neural networks (RNNs) have shown excellent performance in processing sequence data. However, they are both complex and memory intensive due to their recursive nature. These limitations make RNNs difficult to embed on mobile devices requiring real-time processes with limited hardware resources. To address the above issues, we introduce a method that can learn binary and ternary weights during the training phase to facilitate hardware implementations of RNNs. As a result, using this approach replaces all multiply-accumulate operations by simple accumulations, bringing significant bene…
HadamRNN: Binary and Sparse Ternary Orthogonal RNNs
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Institut de Recherche Technologique Saint Exupéry（圣埃克苏佩里技术研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
NativeTernary: A Self-Delimiting Binary Encoding with Unary Run-Length Hierarchy Markers for Ternary Neural Network Weights, Structured Data, and General Computing Infrastructure
Indian Institute of Technology Bombay（印度理工学院孟买分校）；IIM Udaipur（印度管理学院乌代浦尔分校）
In the past years, Deep convolution neural network has achieved great success in many artificial intelligence applications. However, its enormous model size and massive computation cost have become the main obstacle for deployment of such powerful algorithm in the low power and resource-limited mobile systems. As the countermeasure to this problem, deep neural networks with ternarized weights (i.e. -1, 0, +1) have been widely explored to greatly reduce the model size and computational cost, with limited accuracy degradation. In this work, we propose a novel ternarized neural network training m…
University of Electronic Science and Technology of China（电子科技大学）；Harvard University（哈佛大学）；The Chinese University of Hong Kong（香港中文大学）；National University of Singapore（新加坡国立大学）
To deploy deep neural networks on resource-limited devices, quantization has been widely explored. In this work, we study the extremely low-bit networks which have tremendous speed-up, memory saving with quantized activation and weights. We first bring up three omitted issues in extremely low-bit networks: the squashing range of quantized values; the gradient vanishing during backpropagation and the unexploited hardware acceleration of ternary networks. By reparameterizing quantized activation and weights vector with full precision scale and offset for fixed ternary vector, we decouple the ran…
Activity Sparsity Complements Weight Sparsity for Efficient RNN Inference
Birla Institute of Technology and Science, Pilani – Goa Campus（果阿校区，皮拉尼贝拉理工学院）；TUD Dresden University of Technology（德累斯顿工业大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
We propose a novel fine-grained quantization (FGQ) method to ternarize pre-trained full precision models, while also constraining activations to 8 and 4-bits. Using this method, we demonstrate a minimal loss in classification accuracy on state-of-the-art topologies without additional training. We provide an improved theoretical formulation that forms the basis for a higher quality solution using FGQ. Our method involves ternarizing the original weight tensor in groups of $N$ weights. Using $N=4$, we achieve Top-1 accuracy within $3.7\%$ and $4.2\%$ of the baseline full precision result for Res…
Tsinghua University（清华大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
There is a pressing need to build an architecture that could subsume these networks under a unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discrete. The second one is how to remove the full-precision hidden weights in the training phase to break the bottlenecks of memory/computation consumption. To address the first issue, we present a multi-step neuronal activation discretization method and a derivative approximation tech…
We demonstrate that 1x1-convolutions in 1D time-channel separable convolutions may be replaced by constant, sparse random ternary matrices with weights in $\{-1,0,+1\}$. Such layers do not perform any multiplications and do not require training. Moreover, the matrices may be generated on the chip during computation and therefore do not require any memory access. With the same parameter budget, we can afford deeper and more expressive models, improving the Pareto frontiers of existing models on several tasks. For command recognition on Google Speech Commands v1, we improve the state-of-the-art …
The use of lower precision has emerged as a popular technique to optimize the compute and storage requirements of complex Deep Neural Networks (DNNs). In the quest for lower precision, recent studies have shown that ternary DNNs (which represent weights and activations by signed ternary values) represent a promising sweet spot, achieving accuracy close to full-precision networks on complex tasks. We propose TiM-DNN, a programmable in-memory accelerator that is specifically designed to execute ternary DNNs. TiM-DNN supports various ternary representations including unweighted {-1,0,1}, symmetri…
The computation and storage requirements for Deep Neural Networks (DNNs) are usually high. This issue limits their deployability on ubiquitous computing devices such as smart phones, wearables and autonomous drones. In this paper, we propose ternary neural networks (TNNs) in order to make deep learning more resource-efficient. We train these TNNs using a teacher-student approach based on a novel, layer-wise greedy methodology. Thanks to our two-stage training procedure, the teacher network is still able to use state-of-the-art methods such as dropout and batch normalization to increase accurac…
The University Of Sydney（悉尼大学）；Fulda University Of Applied Sciences（富尔达应用科学大学）；University Of Kassel（卡塞尔大学）
The computational complexity of neural networks for large scale or real-time applications necessitates hardware acceleration. Most approaches assume that the network architecture and parameters are unknown at design time, permitting usage in a large number of applications. This paper demonstrates, for the case where the neural network architecture and ternary weight values are known a priori, that extremely high throughput implementations of neural network inference can be made by customising the datapath and routing to remove unnecessary computations and data movement. This approach is ideall…
Korea Institute of Science and Technology（韩国科学技术研究院）；Seoul National University（首尔大学）；Korea University of Science and Technology（韩国科学技术大学）
In spite of remarkable progress in machine learning techniques, the state-of-the-art machine learning algorithms often keep machines from real-time learning (online learning) due in part to computational complexity in parameter optimization. As an alternative, a learning algorithm to train a memory in real time is proposed, which is named as the Markov chain Hebbian learning algorithm. The algorithm pursues efficient memory use during training in that (i) the weight matrix has ternary elements (-1, 0, 1) and (ii) each update follows a Markov chain--the upcoming update does not need past weight…
We propose a cluster-based quantization method to convert pre-trained full precision weights into ternary weights with minimal impact on the accuracy. In addition, we also constrain the activations to 8-bits thus enabling sub 8-bit full integer inference pipeline. Our method uses smaller clusters of N filters with a common scaling factor to minimize the quantization loss, while also maximizing the number of ternary operations. We show that with a cluster size of N=4 on Resnet-101, can achieve 71.8% TOP-1 accuracy, within 6% of the best full precision results while replacing ~85% of all multipl…
Network pruning has been known to produce compact models without much accuracy degradation. However, how the pruning process affects a network's robustness and the working mechanism behind remain unresolved. In this work, we theoretically prove that the sparsity of network weights is closely associated with model robustness. Through experiments on a variety of adversarial pruning methods, we find that weights sparsity will not hurt but improve robustness, where both weights inheritance from the lottery ticket and adversarial training improve model robustness in network pruning. Based on these …
Jacobs University（雅各布斯大学）；Konya Food and Agriculture University（科尼亚食品农业大学）
In this study, a novel sparsity-driven weighted ensemble classifier (SDWEC) that improves classification accuracy and minimizes the number of classifiers is proposed. Using pre-trained classifiers, an ensemble in which base classifiers votes according to assigned weights is formed. These assigned weights directly affect classifier accuracy. In the proposed method, ensemble weights finding problem is modeled as a cost function with the following terms: (a) a data fidelity term aiming to decrease misclassification rate, (b) a sparsity term aiming to decrease the number of classifiers, and (c) a …
In this paper we apply a compressibility loss that enables learning highly compressible neural network weights. The loss was previously proposed as a measure of negated sparsity of a signal, yet in this paper we show that minimizing this loss also enforces the non-zero parts of the signal to have very low entropy, thus making the entire signal more compressible. For an optimization problem where the goal is to minimize the compressibility loss (the objective), we prove that at any critical point of the objective, the weight vector is a ternary signal and the corresponding value of the objectiv…
Vision transformers (ViTs) have demonstrated great potential in various visual tasks, but suffer from expensive computational and memory cost problems when deployed on resource-constrained devices. In this paper, we introduce a ternary vision transformer (TerViT) to ternarize the weights in ViTs, which are challenged by the large loss surface gap between real-valued and ternary parameters. To address the issue, we introduce a progressive training scheme by first training 8-bit transformers and then TerViT, and achieve a better optimization than conventional methods. Furthermore, we introduce c…
General Motors Advanced Technical Center - Israel（通用汽车以色列先进技术中心）；Department of Electrical Engineering, Technion（以色列理工学院电气工程系）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a challenge. One approach to solving this problem is training networks with binary or ternary weights, thus removing the need to calculate multiplications and significantly reducing memory size. In this work, we introduce LR-nets (Local reparameterization networks), a new method for training neural networks with discrete weights using stochastic parameters. We sh…
University of Washington（华盛顿大学）；Allen Institute for Artificial Intelligence（艾伦人工智能研究所）；Microsoft Research（微软研究院）
Sparsity in Deep Neural Networks (DNNs) is studied extensively with the focus of maximizing prediction accuracy given an overall parameter budget. Existing methods rely on uniform or heuristic non-uniform sparsity budgets which have sub-optimal layer-wise parameter allocation resulting in a) lower prediction accuracy or b) higher inference cost (FLOPs). This work proposes Soft Threshold Reparameterization (STR), a novel use of the soft-threshold operator on DNN weights. STR smoothly induces sparsity while learning pruning thresholds thereby obtaining a non-uniform sparsity budget. Our method a…
The use of deep neural networks in edge computing devices hinges on the balance between accuracy and complexity of computations. Ternary Connect (TC) \cite{lin2015neural} addresses this issue by restricting the parameters to three levels $-1, 0$, and $+1$, thus eliminating multiplications in the forward pass of the network during prediction. We propose Generalized Ternary Connect (GTC), which allows an arbitrary number of levels while at the same time eliminating multiplications by restricting the parameters to integer powers of two. The primary contribution is that GTC learns the number of le…
University of Zürich（苏黎世大学）；ETH Zürich（苏黎世联邦理工学院）；Mila；University of Montreal（蒙特利尔大学）；ServiceNow
Finding neural network weights that generalize well from small datasets is difficult. A promising approach is to learn a weight initialization such that a small number of weight changes results in low generalization error. We show that this form of meta-learning can be improved by letting the learning algorithm decide which weights to change, i.e., by learning where to learn. We find that patterned sparsity emerges from this process, with the pattern of sparsity varying on a problem-by-problem basis. This selective sparsity results in better generalization and less interference in a range of f…
Weight Sparsity Complements Activity Sparsity in Neuromorphic Language Models
TUD Dresden University of Technology（德累斯顿工业大学）；Birla Institute of Technology and Science Pilani – Goa Campus（毕拉理工学院皮拉尼分校果阿校区）；Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI)（可扩展数据分析与人工智能中心）；Centre for Tactile Internet with Human-in-the-Loop (CeTI)（以人为中心的触觉互联网中心）；Ruhr University Bochum（波鸿鲁尔大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）
