Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. As they generalize the operations of classical CNNs on grids to arbitrary topologies, GNNs also bring much of the implementation challenges of their Euclidean counterparts. Model size, memory footprint, and energy consumption are common concerns for many real-world applications. Network binarization allocates a single bit to parameters and activations, thus dramatically reducing the memory requirements (up to 32x compared to single-precision floating-point numbers) and maximizing the benefits of fast SIMD instructions on modern hardware for measurable speedups. However, in spite of the large body of work on binarization for classical CNNs, this area remains largely unexplored in geometric deep learning. In this paper, we present and evaluate different strategies for the binarization of graph neural networks. We show that through careful design of the models, and control of the training process, binary graph neural networks can be trained at only a moderate cost in accuracy on challenging benchmarks. In particular, we present the first dynamic graph neural network in Hamming space, able to leverage efficient k-NN search on binary vectors to speed-up the construction of the dynamic graph. We further verify that the binary models offer significant savings on embedded devices. Our code is publicly available on Github.
This paper is on improving the training of binary neural networks in which both activations and weights are binary. While prior methods for neural network binarization binarize each filter independently, we propose to instead parametrize the weight tensor of each layer using matrix or tensor decomposition. The binarization process is then performed using this latent parametrization, via a quantization function (e.g. sign function) applied to the reconstructed weights. A key feature of our method is that while the reconstruction is binarized, the computation in the latent factorized space is do…
Binary neural networks are the extreme case of network quantization, which has long been thought of as a potential edge machine learning solution. However, the significant accuracy gap to the full-precision counterparts restricts their creative potential for mobile applications. In this work, we revisit the potential of binary neural networks and focus on a compelling but unanswered problem: how can a binary neural network achieve the crucial accuracy level (e.g., 80%) on ILSVRC-2012 ImageNet? We achieve this goal by enhancing the optimization process from three complementary perspectives: (1)…
In recent years, deep neural networks have had great success in machine learning and pattern recognition. Architecture size for a neural network contributes significantly to the success of any neural network. In this study, we optimize the selection process by investigating different search algorithms to find a neural network architecture size that yields the highest accuracy. We apply binary search on a very well-defined binary classification network search space and compare the results to those of linear search. We also propose how to relax some of the assumptions regarding the dataset so th…
Beihang University（北京航空航天大学）；University at Buffalo（布法罗大学）
Edge computing is promising to become one of the next hottest topics in artificial intelligence because it benefits various evolving domains such as real-time unmanned aerial systems, industrial applications, and the demand for privacy protection. This paper reviews recent advances on binary neural network (BNN) and 1-bit CNN technologies that are well suitable for front-end, edge-based computing. We introduce and summarize existing work and classify them based on gradient approximation, quantization, architecture, loss functions, optimization method, and binary neural architecture search. We …
Binary Neural Networks (BNNs), neural networks with weights and activations constrained to -1(0) and +1, are an alternative to deep neural networks which offer faster training, lower memory consumption and lightweight models, ideal for use in resource constrained devices while being able to utilize the architecture of their deep neural network counterpart. However, the input binarization step used in BNNs causes a severe accuracy loss. In this paper, we introduce a novel hybrid neural network architecture, Hybrid Binary Neural Network (HyBNN), consisting of a task-independent, general, full-pr…
We consider the compilation of a binary neural network's decision function into tractable representations such as Ordered Binary Decision Diagrams (OBDDs) and Sentential Decision Diagrams (SDDs). Obtaining this function as an OBDD/SDD facilitates the explanation and formal verification of a neural network's behavior. First, we consider the task of verifying the robustness of a neural network, and show how we can compute the expected robustness of a neural network, given an OBDD/SDD representation of it. Next, we consider a more efficient approach for compiling neural networks, based on a pseud…
Binary neural networks (BNN) have been studied extensively since they run dramatically faster at lower memory and power consumption than floating-point networks, thanks to the efficiency of bit operations. However, contemporary BNNs whose weights and activations are both single bits suffer from severe accuracy degradation. To understand why, we investigate the representation ability, speed and bias/variance of BNNs through extensive experiments. We conclude that the error of BNNs is predominantly caused by the intrinsic instability (training time) and non-robustness (train & test time). Inspir…
In this paper, we explore an alternate method for synthesizing neural network architectures, inspired by the brain's stochastic synaptic pruning. During a person's lifetime, numerous distinct neuronal architectures are responsible for performing the same tasks. This indicates that biological neural networks are, to some degree, architecture agnostic. However, artificial networks rely on their fine-tuned weights and hand-crafted architectures for their remarkable performance. This contrast begs the question: Can we build artificial architecture agnostic neural networks? To ground this study we …
Modern hardware design trends have shifted towards specialized hardware acceleration for computationally intensive tasks like machine learning and computer vision. While these complex workloads can be accelerated by commercial GPUs, domain-specific hardware is far more optimal when needing to meet the stringent memory, throughput, and power constraints of mobile and embedded devices. This paper proposes and evaluates a Binary-Enabled Architecture for Neural Network Acceleration (BEANNA), a neural network hardware accelerator capable of processing both floating point and binary network layers. …
BEP: A Binary Error Propagation Algorithm for Binary Neural Networks Training
Department of Electronics, Information and Bioengineering, Politecnico di Milano（电子、信息与生物工程系，米兰理工学院）；Faculty of Informatics and IDSIA, Università della Svizzera italiana（信息学院和IDSIA，瑞士大学）；Department of Computing Sciences and BIDSA, Bocconi University（计算科学系和BIDSA，博科尼大学）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Facebook Research（脸书研究院）
It is widely conjectured that the reason that training algorithms for neural networks are successful because all local minima lead to similar performance, for example, see (LeCun et al., 2015, Choromanska et al., 2015, Dauphin et al., 2014). Performance is typically measured in terms of two metrics: training performance and generalization performance. Here we focus on the training performance of single-layered neural networks for binary classification, and provide conditions under which the training error is zero at all local minima of a smooth hinge loss function. Our conditions are roughly i…
The memristive crossbar aims to implement analog weighted neural network, however, the realistic implementation of such crossbar arrays is not possible due to limited switching states of memristive devices. In this work, we propose the design of an analog deep neural network with binary weight update through backpropagation algorithm using binary state memristive devices. We show that such networks can be successfully used for image processing task and has the advantage of lower power consumption and small on-chip area in comparison with digital counterparts. The proposed network was benchmark…
Hashing techniques, also known as binary code learning, have recently gained increasing attention in large-scale data analysis and storage. Generally, most existing hash clustering methods are single-view ones, which lack complete structure or complementary information from multiple views. For cluster tasks, abundant prior researches mainly focus on learning discrete hash code while few works take original data structure into consideration. To address these problems, we propose a novel binary code algorithm for clustering, which adopts graph embedding to preserve the original data structure, c…
Deploying state-of-the-art CNNs requires power-hungry processors and off-chip memory. This precludes the implementation of CNNs in low-power embedded systems. Recent research shows CNNs sustain extreme quantization, binarizing their weights and intermediate feature maps, thereby saving 8-32\x memory and collapsing energy-intensive sum-of-products into XNOR-and-popcount operations. We present XNORBIN, an accelerator for binary CNNs with computation tightly coupled to memory for aggressive data reuse. Implemented in UMC 65nm technology XNORBIN achieves an energy efficiency of 95 TOp/s/W and an a…
Neural networks and particularly Deep learning have been comparatively little studied from the theoretical point of view. Conversely, Mathematical Morphology is a discipline with solid theoretical foundations. We combine these domains to propose a new type of neural architecture that is theoretically more explainable. We introduce a Binary Morphological Neural Network (BiMoNN) built upon the convolutional neural network. We design it for learning morphological networks with binary inputs and outputs. We demonstrate an equivalence between BiMoNNs and morphological operators that we can use to b…
In the last ten years, Convolutional Neural Networks (CNNs) have formed the basis of deep-learning architectures for most computer vision tasks. However, they are not necessarily optimal. For example, mathematical morphology is known to be better suited to deal with binary images. In this work, we create a morphological neural network that handles binary inputs and outputs. We propose their construction inspired by CNNs to formulate layers adapted to such images by replacing convolutions with erosions and dilations. We give explainable theoretical results on whether or not the resulting learne…
Pohang University of Science and Technology (POSTECH)（浦项科技大学）
Binarization of neural network models is considered as one of the promising methods to deploy deep neural network models on resource-constrained environments such as mobile devices. However, Binary Neural Networks (BNNs) tend to suffer from severe accuracy degradation compared to the full-precision counterpart model. Several techniques were proposed to improve the accuracy of BNNs. One of the approaches is to balance the distribution of binary activations so that the amount of information in the binary activations becomes maximum. Based on extensive analysis, in stark contrast to previous work…
We propose a new algorithm for training deep neural networks (DNNs) with binary weights. In particular, we first cast the problem of training binary neural networks (BiNNs) as a bilevel optimization instance and subsequently construct flexible relaxations of this bilevel program. The resulting training method shares its algorithmic simplicity with several existing approaches to train BiNNs, in particular with the straight-through gradient estimator successfully employed in BinaryConnect and subsequent methods. In fact, our proposed method can be interpreted as an adaptive variant of the origin…
Carnegie Mellon University（卡内基梅隆大学）；Michigan State University（密歇根州立大学）
We propose local binary convolution (LBC), an efficient alternative to convolutional layers in standard convolutional neural networks (CNN). The design principles of LBC are motivated by local binary patterns (LBP). The LBC layer comprises of a set of fixed sparse pre-defined binary convolutional filters that are not updated during the training process, a non-linear activation function and a set of learnable linear weights. The linear weights combine the activated filter responses to approximate the corresponding activated filter responses of a standard convolutional layer. The LBC layer affor…
Hasso Plattner Institute（哈索·普拉特纳研究所）；University of Potsdam（波茨坦大学）
Convolutional neural networks have achieved astonishing results in different application areas. Various methods which allow us to use these models on mobile and embedded devices have been proposed. Especially binary neural networks seem to be a promising approach for these devices with low computational power. However, understanding binary neural networks and training accurate models for practical applications remains a challenge. In our work, we focus on increasing our understanding of the training process and making it accessible to everyone. We publish our code and models based on BMXNet fo…
Compared to Multilayer Neural Networks with real weights, Binary Multilayer Neural Networks (BMNNs) can be implemented more efficiently on dedicated hardware. BMNNs have been demonstrated to be effective on binary classification tasks with Expectation BackPropagation (EBP) algorithm on high dimensional text datasets. In this paper, we investigate the capability of BMNNs using the EBP algorithm on multiclass image classification tasks. The performances of binary neural networks with multiple hidden layers and different numbers of hidden units are examined on MNIST. We also explore the effective…
Université Laval（拉瓦尔大学）；Inria（法国国家信息与自动化研究所）；University College London（伦敦大学学院）
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. Our analysis inherently overcomes the fact that binary activation function is non-differentiable. The performance…
Hasso Plattner Institute（哈索·普拉特纳研究所）；University of Potsdam（波茨坦大学）
Convolutional neural networks have achieved astonishing results in different application areas. Various methods that allow us to use these models on mobile and embedded devices have been proposed. Especially binary neural networks are a promising approach for devices with low computational power. However, training accurate binary models from scratch remains a challenge. Previous work often uses prior knowledge from full-precision models and complex training strategies. In our work, we focus on increasing the performance of binary neural networks without such prior knowledge and a much simpler …
Binary neural networks have attracted tremendous attention due to the efficiency for deploying them on mobile devices. Since the weak expression ability of binary weights and features, their accuracy is usually much lower than that of full-precision (i.e. 32-bit) models. Here we present a new frame work for automatically searching for compact but accurate binary neural networks. In practice, number of channels in each layer will be encoded into the search space and optimized using the evolutionary algorithm. Experiments conducted on benchmark datasets and neural architectures demonstrate that …
École Polytechnique de Montréal（蒙特利尔综合理工学院）；Université de Montréal（蒙特利尔大学）
Deep Neural Networks (DNN) have achieved state-of-the-art results in a wide range of tasks, with the best results obtained with large training sets and large models. In the past, GPUs enabled these breakthroughs because of their greater computational speed. In the future, faster computation at both training and test time is likely to be crucial for further progress and for consumer applications on low-power devices. As a result, there is much interest in research and development of dedicated hardware for Deep Learning (DL). Binary weights, i.e., weights which are constrained to only two possib…
Quantized neural networks have drawn a lot of attention as they reduce the space and computational complexity during the inference. Moreover, there has been folklore that quantization acts as an implicit regularizer and thus can improve the generalizability of neural networks, yet no existing work formalizes this interesting folklore. In this paper, we take the binary weights in a neural network as random variables under stochastic rounding, and study the distribution propagation over different layers in the neural network. We propose a quasi neural network to approximate the distribution prop…
Redwood Center for Theoretical Neuroscience（红木理论神经科学中心）；University of California, Berkeley（加州大学伯克利分校）
Recent research has shown that one can train a neural network with binary weights and activations at train time by augmenting the weights with a high-precision continuous latent variable that accumulates small changes from stochastic gradient descent. However, there is a dearth of theoretical analysis to explain why we can effectively capture the features in our data with binary weights and activations. Our main result is that the neural networks with binary weights and activations trained using the method of Courbariaux, Hubara et al. (2016) work because of the high-dimensional geometry of bi…
The use of neural networks as function approximators has enabled many advances in reinforcement learning (RL). The generalization power of neural networks combined with advances in RL algorithms has reignited the field of artificial intelligence. Despite their power, neural networks are considered black boxes, and their use in safety-critical settings remains a challenge. Recently, neural network verification has emerged as a way to certify safety properties of networks. Verification is a hard problem, and it is difficult to scale to large networks such as the ones used in deep reinforcement l…
National Special Education Resource Center for Children with Autism, Zhejiang Normal University（浙江师范大学国家孤独症儿童特殊教育资源中心）；Institute of Cyber-Systems and Control, Zhejiang University（浙江大学 cyber 系统与控制研究所）；School of Computer Science and Technology, Zhejiang Normal University（浙江师范大学计算机科学与技术学院）
Russian Research Center Huawei Technologies, Russia（华为技术有限公司俄罗斯研究中心）；Department of Computer Science ETH Zurich, Switzerland（苏黎世联邦理工学院计算机科学系）
Despite the growing popularity of deep learning technologies, high memory requirements and power consumption are essentially limiting their application in mobile and IoT areas. While binary convolutional networks can alleviate these problems, the limited bitwidth of weights is often leading to significant degradation of prediction accuracy. In this paper, we present a method for training binary networks that maintains a stable predefined level of their information capacity throughout the training process by applying Shannon entropy based penalty to convolutional filters. The results of experim…
Separation of competing speech is a key challenge in signal processing and a feat routinely performed by the human auditory brain. A long standing benchmark of the spectrogram approach to source separation is known as the ideal binary mask. Here, we train a convolutional deep neural network, on a two-speaker cocktail party problem, to make probabilistic predictions about binary masks. Our results approach ideal binary mask performance, illustrating that relatively simple deep neural networks are capable of robust binary mask prediction. We also illustrate the trade-off between prediction stati…
School of Information Science and Engineering（信息科学与工程学院）；Lanzhou University（兰州大学）
We introduce the chi-square test neural network: a single hidden layer backpropagation neural network using chi-square test theorem to redefine the cost function and the error function. The weights and thresholds are modified using standard backpropagation algorithm. The proposed approach has the advantage of making consistent data distribution over training and testing sets. It can be used for binary classification. The experimental results on real world data sets indicate that the proposed algorithm can significantly improve the classification accuracy comparing to related approaches.
Binarization is an attractive strategy for implementing lightweight Deep Convolutional Neural Networks (CNNs). Despite the unquestionable savings offered, memory footprint above all, it may induce an excessive accuracy loss that prevents a widespread use. This work elaborates on this aspect introducing TentacleNet, a new template designed to improve the predictive performance of binarized CNNs via parallelization. Inspired by the ensemble learning theory, it consists of a compact topology that is end-to-end trainable and organized to minimize memory utilization. Experimental results collected …
Deep generative models provide a powerful set of tools to understand real-world data. But as these models improve, they increase in size and complexity, so their computational cost in memory and execution time grows. Using binary weights in neural networks is one method which has shown promise in reducing this cost. However, whether binary neural networks can be used in generative models is an open problem. In this work we show, for the first time, that we can successfully train generative models which utilize binary neural networks. This reduces the computational cost of the models massively.…
Hasso Plattner Institute (HPI), University of Potsdam（哈索·普拉特纳研究所（HPI），波茨坦大学）
Binary Neural Networks (BNNs) can drastically reduce memory size and accesses by applying bit-wise operations instead of standard arithmetic operations. Therefore it could significantly improve the efficiency and lower the energy consumption at runtime, which enables the application of state-of-the-art deep learning models on low power devices. BMXNet is an open-source BNN library based on MXNet, which supports both XNOR-Networks and Quantized Neural Networks. The developed BNN layers can be seamlessly applied with other standard library components and work in both GPU and CPU mode. BMXNet is …
Hasso Plattner Institute, University of Potsdam（波茨坦大学哈索·普拉特纳研究所）；AI Labs, Alibaba Group（阿里巴巴集团人工智能实验室）
Binary Neural Networks (BNNs) are neural networks which use binary weights and activations instead of the typical 32-bit floating point values. They have reduced model sizes and allow for efficient inference on mobile or embedded devices with limited power and computational resources. However, the binarization of weights and activations leads to feature maps of lower quality and lower capacity and thus a drop in accuracy compared to traditional networks. Previous work has increased the number of channels or used multiple binary bases to alleviate these problems. In this paper, we instead prese…
Recent advances in neuroscience have revealed many principles about neural processing. In particular, many biological systems were found to reconfigure/recruit single neurons to generate multiple kinds of decisions. Such findings have the potential to advance our understanding of the design and optimization process of artificial neural networks. Previous work demonstrated that dense neural networks are needed to shape complex decision surfaces required for AI-level recognition tasks. We investigate the ability to model high dimensional recognition problems using single or several neurons netwo…
This paper proposes an improved training algorithm for binary neural networks in which both weights and activations are binary numbers. A key but fairly overlooked feature of the current state-of-the-art method of XNOR-Net is the use of analytically calculated real-valued scaling factors for re-weighting the output of binary convolutions. We argue that analytic calculation of these factors is sub-optimal. Instead, in this work, we make the following contributions: (a) we propose to fuse the activation and weight scaling factors into a single one that is learned discriminatively via backpropaga…
Despite the outstanding performance of deep neural networks in different applications, they are still computationally extensive and require a great number of memories. This motivates more research on reducing the resources required for implementing such networks. An efficient approach addressed for this purpose is matrix factorization, which has been shown to be effective on different networks. In this paper, we utilize binary matrix factorization and show its great efficiency in reducing the required number of resources in deep neural networks. In effect, this technique can lead to the practi…
The Pennsylvania State University（宾夕法尼亚州立大学）；School of Electrical Engineering and Computer Science（电气工程与计算机科学学院）；University Park（大学公园（此处为校区名，按要求提取到学院级别，原机构为宾夕法尼亚州立大学，学院为其下属，按规则提取到大学级别即可））
On-chip edge intelligence has necessitated the exploration of algorithmic techniques to reduce the compute requirements of current machine learning frameworks. This work aims to bridge the recent algorithmic progress in training Binary Neural Networks and Spiking Neural Networks - both of which are driven by the same motivation and yet synergies between the two have not been fully explored. We show that training Spiking Neural Networks in the extreme quantization regime results in near full precision accuracies on large-scale datasets like CIFAR-$100$ and ImageNet. An important implication of …
We propose and study a new projection formula for training binary weight convolutional neural networks. The projection formula measures the error in approximating a full precision (32 bit) vector by a 1-bit vector in the l_1 norm instead of the standard l_2 norm. The l_1 projector is in closed analytical form and involves a median computation instead of an arithmatic average in the l_2 projector. Experiments on 10 keywords classification show that the l_1 (median) BinaryConnect (BC) method outperforms the regular BC, regardless of cold or warm start. The binary network trained by median BC and…
Beihang University（北京航空航天大学）；University of Electronic Science and Technology of China（电子科技大学）；University of Trento（特伦托大学）
The binary neural network, largely saving the storage and computation, serves as a promising technique for deploying deep models on resource-limited devices. However, the binarization inevitably causes severe information loss, and even worse, its discontinuity brings difficulty to the optimization of the deep network. To address these issues, a variety of algorithms have been proposed, and achieved satisfying progress in recent years. In this paper, we present a comprehensive survey of these algorithms, mainly categorized into the native solutions directly conducting binarization, and the opti…
Nanjing University of Science and Technology（南京理工大学）
Recently the deep learning techniques have achieved success in multi-label classification due to its automatic representation learning ability and the end-to-end learning framework. Existing deep neural networks in multi-label classification can be divided into two kinds: binary relevance neural network (BRNN) and threshold dependent neural network (TDNN). However, the former needs to train a set of isolate binary networks which ignore dependencies between labels and have heavy computational load, while the latter needs an additional threshold function mechanism to transform the multi-class pr…
We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory size and accesses, and can replace arithmetic operations with more efficient bitwise operations, leading to much faster test-time inference and lower power consumption. However, previous works on binarizing CNNs usually result in severe prediction accuracy degradation. In this paper, we address this issue with two major innovations: (1) approximating full-pr…
The interpretation of seismic data is vital for characterizing sediments' shape in areas of geological study. In seismic interpretation, deep learning becomes useful for reducing the dependence on handcrafted facies segmentation geometry and the time required to study geological areas. This work presents a Deep Neural Network for Facies Segmentation (DNFS) to obtain state-of-the-art results for seismic facies segmentation. DNFS is trained using a combination of cross-entropy and Jaccard loss functions. Our results show that DNFS obtains highly detailed predictions for seismic facies segmentati…
Artificial Neural Network (ANN)-based inference on battery-powered devices can be made more energy-efficient by restricting the synaptic weights to be binary, hence eliminating the need to perform multiplications. An alternative, emerging, approach relies on the use of Spiking Neural Networks (SNNs), biologically inspired, dynamic, event-driven models that enhance energy efficiency via the use of binary, sparse, activations. In this paper, an SNN model is introduced that combines the benefits of temporally sparse binary activations and of binary weights. Two learning rules are derived, the fir…
Low bit-width weights and activations are an effective way of combating the increasing need for both memory and compute power of Deep Neural Networks. In this work, we present a probabilistic training method for Neural Network with both binary weights and activations, called BLRNet. By embracing stochasticity during training, we circumvent the need to approximate the gradient of non-differentiable functions such as sign(), while still obtaining a fully Binary Neural Network at test time. Moreover, it allows for anytime ensemble predictions for improved performance and uncertainty estimates by …
