On the Robustness of Convolutional Neural Networks to Internal Architecture and Weight Perturbations
Cornell University（康奈尔大学）；Augsburg University（奥格斯堡大学）；Technische Universität München（慕尼黑工业大学）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Boston Children’s Hospital（波士顿儿童医院）；Harvard Medical School（哈佛医学院）
Deep convolutional neural networks are generally regarded as robust function approximators. So far, this intuition is based on perturbations to external stimuli such as the images to be classified. Here we explore the robustness of convolutional neural networks to perturbations to the internal weights and architecture of the network itself. We show that convolutional networks are surprisingly robust to a number of internal perturbations in the higher convolutional layers but the bottom convolutional layers are much more fragile. For instance, Alexnet shows less than a 30% decrease in classification performance when randomly removing over 70% of weight connections in the top convolutional or dense layers but performance is almost at chance with the same perturbation in the first convolutional layer. Finally, we suggest further investigations which could continue to inform the robustness of convolutional networks to internal perturbations.
We review three recently-proposed classifier quality metrics and consider their suitability for large-scale classification challenges such as applying convolutional neural networks to the 1000-class ImageNet dataset. These metrics, referred to as the "geometric accuracy," "decisiveness," and "robustness," are based on the generalized mean ($ρ$ equals 0, 1, and -2/3, respectively) of the classifier's self-reported and measured probabilities of correct classification. We also propose some minor clarifications to standardize the metric definitions. With these updates, we show some examples of cal…
University of Groningen（格罗宁根大学）；University of Malaga（马拉加大学）
We propose a new layer in Convolutional Neural Networks (CNNs) to increase their robustness to several types of noise perturbations of the input images. We call this a push-pull layer and compute its response as the combination of two half-wave rectified convolutions, with kernels of opposite polarity. It is based on a biologically-motivated non-linear model of certain neurons in the visual system that exhibit a response suppression phenomenon, known as push-pull inhibition. We validate our method by substituting the first convolutional layer of the LeNet-5 and WideResNet architectures with ou…
Modern deep convolutional networks (CNNs) are often criticized for not generalizing under distributional shifts. However, several recent breakthroughs in transfer learning suggest that these networks can cope with severe distribution shifts and successfully adapt to new tasks from a few training examples. In this work we study the interplay between out-of-distribution and transfer performance of modern image classification CNNs for the first time and investigate the impact of the pre-training data size, the model scale, and the data preprocessing pipeline. We find that increasing both the trai…
New York University（纽约大学）；Facebook AI Research（Facebook人工智能研究）；CIFAR（加拿大高级研究所（CIFAR））
We propose a retrieval-augmented convolutional network and propose to train it with local mixup, a novel variant of the recently proposed mixup algorithm. The proposed hybrid architecture combining a convolutional network and an off-the-shelf retrieval engine was designed to mitigate the adverse effect of off-manifold adversarial examples, while the proposed local mixup addresses on-manifold ones by explicitly encouraging the classifier to locally behave linearly on the data manifold. Our evaluation of the proposed approach against five readily-available adversarial attacks on three datasets--…
Center for Data Science, New York University（纽约大学数据科学中心）；Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Department of EECS, UC Berkeley（加州大学伯克利分校电气工程与计算机科学系）；Electrical and Computer Engineering, University of Denver（丹佛大学电气与计算机工程系）；Department of EECS, University of Michigan（密歇根大学电气工程与计算机科学系）
Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve robustness. For ConvNets, most existing methods are based on penalizing or normalizing weight matrices derived from concatenating or flattening the convolutional kernels. These methods often destroy or ignore the benign convolutional structure of the kernels; therefore, they are often expensive or impractical for deep ConvNets. In contrast, we introduce a simple…
Traditional convolutional neural networks (CNN) are stationary and feedforward. They neither change their parameters during evaluation nor use feedback from higher to lower layers. Real brains, however, do. So does our Deep Attention Selective Network (dasNet) architecture. DasNets feedback structure can dynamically alter its convolutional filter sensitivities during classification. It harnesses the power of sequential processing to improve classification performance, by allowing the network to iteratively focus its internal attention on some of its convolutional filters. Feedback is trained t…
Shandong University（山东大学）；University of Leeds（利兹大学）
This research proposes a Ground Penetrating Radar (GPR) data processing method for non-destructive detection of tunnel lining internal defects, called defect segmentation. To perform this critical step of automatic tunnel lining detection, the method uses a CNN called Segnet combined with the Lovász softmax loss function to map the internal defect structure with GPR synthetic data, which improves the accuracy, automation and efficiency of defects detection. The novel method we present overcomes several difficulties of traditional GPR data interpretation as demonstrated by an evaluation on both…
Recently, the generalization behavior of Convolutional Neural Networks (CNN) is gradually transparent through explanation techniques with the frequency components decomposition. However, the importance of the phase spectrum of the image for a robust vision system is still ignored. In this paper, we notice that the CNN tends to converge at the local optimum which is closely related to the high-frequency components of the training images, while the amplitude spectrum is easily disturbed such as noises or common corruptions. In contrast, more empirical studies found that humans rely on more phase…
We introduce a novel artificial neural network architecture that integrates robustness to adversarial input in the network structure. The main idea of our approach is to force the network to make predictions on what the given instance of the class under consideration would look like and subsequently test those predictions. By forcing the network to redraw the relevant parts of the image and subsequently comparing this new image to the original, we are having the network give a "proof" of the presence of the object.
In general, convolutional neural networks (CNNs) are easy to train, but their essential properties, such as generalization error and adversarial robustness, are hard to control. Recent research demonstrated that singular values of convolutional layers significantly affect such elusive properties and offered several methods for controlling them. Nevertheless, these methods present an intractable computational challenge or resort to coarse approximations. In this paper, we offer a principled approach to alleviating constraints of the prior art at the expense of an insignificant reduction in laye…
K. N. Toosi University of Technology（K. N. 图什理工大学）；Emory School of Medicine（埃默里大学医学院）
Deep Convolutional Neural Networks (DCNNs) have attracted extensive attention and been applied in many areas, including medical image analysis and clinical diagnosis. One major challenge is to conceive a DCNN model with remarkable performance on both internal and external data. We demonstrate that DCNNs may not generalize to new data, but increasing the quality and heterogeneity of the training data helps to improve the generalizibility factor. We use InceptionResNetV2 and DenseNet121 architectures to predict the risk of 5 common chest pathologies. The experiments were conducted on three publi…
Recent works show that Graph Neural Networks (GNNs) are highly non-robust with respect to adversarial attacks on both the graph structure and the node attributes, making their outcomes unreliable. We propose the first method for certifiable (non-)robustness of graph convolutional networks with respect to perturbations of the node attributes. We consider the case of binary node attributes (e.g. bag-of-words) and perturbations that are L_0-bounded. If a node has been certified with our method, it is guaranteed to be robust under any possible perturbation given the attack model. Likewise, we can …
Machine learning technologies using deep neural networks (DNNs), especially convolutional neural networks (CNNs), have made automated, accurate, and fast medical image analysis a reality for many applications, and some DNN-based medical image analysis systems have even been FDA-cleared. Despite the progress, challenges remain to build DNNs as reliable as human expert doctors. It is known that DNN classifiers may not be robust to noises: by adding a small amount of noise to an input image, a DNN classifier may make a wrong classification of the noisy image (i.e., in-distribution adversarial sam…
City University of Hong Kong（香港城市大学）；Shanghai Jiao Tong University（上海交通大学）
Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node-removals or edge-removals. The measure of network controllability is quantified by the number of external control inputs needed to recover or to retain the controllability after the occurrence of an unexpected attack. The measure of the network controllability robustness, on the other hand, is quantified by a sequence of values that record the remaining controllability of the…
Offenburg University（奥芬堡大学）；Fraunhofer ITWM（弗劳恩霍夫工业数学研究所）；Fraunhofer Research Center ML（弗劳恩霍夫机器学习研究中心）
Deep learning models are intrinsically sensitive to distribution shifts in the input data. In particular, small, barely perceivable perturbations to the input data can force models to make wrong predictions with high confidence. An common defense mechanism is regularization through adversarial training which injects worst-case perturbations back into training to strengthen the decision boundaries, and to reduce overfitting. In this context, we perform an investigation of 3x3 convolution filters that form in adversarially-trained models. Filters are extracted from 71 public models of the linf-R…
The upcoming Surface Water Ocean Topography (SWOT) satellite altimetry mission is expected to yield two-dimensional high-resolution measurements of Sea Surface Height (SSH), thus allowing for a better characterization of the mesoscale and submesoscale eddy field. However, to fulfill the promises of this mission, filtering the tidal component of the SSH measurements is necessary. This challenging problem is crucial since the posterior studies done by physical oceanographers using SWOT data will depend heavily on the selected filtering schemes. In this paper, we cast this problem into a supervis…
Rotation-Robust Regression with Convolutional Model Trees
Department of Automation, Harbin Institute of Technology, Shenzhen, China（自动化系，哈尔滨工业大学，深圳）；Department of Computing Science, University of Alberta, Edmonton, Canada（计算机科学系，阿尔伯塔大学，爱德蒙顿）
We propose Absum, which is a regularization method for improving adversarial robustness of convolutional neural networks (CNNs). Although CNNs can accurately recognize images, recent studies have shown that the convolution operations in CNNs commonly have structural sensitivity to specific noise composed of Fourier basis functions. By exploiting this sensitivity, they proposed a simple black-box adversarial attack: Single Fourier attack. To reduce structural sensitivity, we can use regularization of convolution filter weights since the sensitivity of linear transform can be assessed by the nor…
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院MIT-IBM沃森人工智能实验室）
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP-complete problem, obtaining a non-trivial lower bound of minimum distortion as a provable robustness guarantee is possible. However, most previous works only focused on simple fully-connected layers (multilayer perceptrons) and were limited to ReLU activations. This motivates us…
This paper proposes a fusion strategy for multistream convolutional networks, the Lattice Cross Fusion. This approach crosses signals from convolution layers performing mathematical operation-based fusions right before pooling layers. Results on a purposely worsened CIFAR-10, a popular image classification data set, with a modified AlexNet-LCNN version show that this novel method outperforms by 46% the baseline single stream network, with faster convergence, stability, and robustness.
National Taiwan University（国立台湾大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Soochow University（东吴大学）；National Sun Yat-sen University（国立中山大学）
Deep learning (DL) has been applied extensively in a wide range of fields. However, it has been shown that DL models are susceptible to a certain kinds of perturbations called \emph{adversarial attacks}. To fully unlock the power of DL in critical fields such as financial trading, it is necessary to address such issues. In this paper, we present a method of constructing perturbed examples and use these examples to boost the robustness of the model. Our algorithm increases the stability of DL models for candlestick classification with respect to perturbations in the input data.
Energy-Regularized Spatial Masking: A Novel Approach to Enhancing Robustness and Interpretability in Vision Models
DAVID Lab, UVSQ, Paris-Saclay University（DAVID实验室，UVSQ，巴黎-萨克雷大学）；LIPN, UMR CNRS 7030, Sorbonne Paris Nord University（LIPN，UMR CNRS 7030，索邦巴黎北大学）；LISN, Paris-Saclay University（LISN，巴黎-萨克雷大学）
University of Bucharest（布加勒斯特大学）；SecurifAI；Romanian Young Academy（罗马尼亚青年科学院）
Recent studies revealed that convolutional neural networks do not generalize well to small image transformations, e.g. rotations by a few degrees or translations of a few pixels. To improve the robustness to such transformations, we propose to introduce data augmentation at intermediate layers of the neural architecture, in addition to the common data augmentation applied on the input images. By introducing small perturbations to activation maps (features) at various levels, we develop the capacity of the neural network to cope with such transformations. We conduct experiments on three image c…
Antifragility Predicts the Robustness and Evolvability of Biological Networks through Multi-class Classification with a Convolutional Neural Network
University of Copenhagen（哥本哈根大学）；Graz University of Technology（格拉茨工业大学）；Sorbonne Université（索邦大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；ITMO University（ITMO大学）
Indian Institute of Information Technology, Sri City（斯里城印度信息技术学院）
Convolutional neural networks (CNNs) have shown very promising performance in recent years for different problems, including object recognition, face recognition, medical image analysis, etc. However, generally the trained CNN models are tested over the test set which is very similar to the trained set. The generalizability and robustness of the CNN models are very important aspects to make it to work for the unseen data. In this letter, we study the performance of CNN models over the high and low frequency information of the images. We observe that the trained CNN fails to generalize over the…
From Code to Field: Evaluating the Robustness of Convolutional Neural Networks for Disease Diagnosis in Mango Leaves
Institutetext: Instituto de Computação, Universidade Federal de Alagoas, Maceió, AL, 57072-970, Brazil（计算机学院，阿拉加斯联邦大学）；Institutetext: Centro de Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-900, Brazil（技术中心，里奥格兰德杜北联邦大学）
Adversarial training is the most promising method for learning robust models against adversarial examples. A recent study has shown that knowledge distillation between the same architectures is effective in improving the performance of adversarial training. Exploiting knowledge distillation is a new approach to improve adversarial training and has attracted much attention. However, its performance is still insufficient. Therefore, we propose Adversarial Robust Distillation with Internal Representation~(ARDIR) to utilize knowledge distillation even more effectively. In addition to the output of…
Motivation: Thanks to the recent advances in structural biology, nowadays three-dimensional structures of various proteins are solved on a routine basis. A large portion of these contain structural repetitions or internal symmetries. To understand the evolution mechanisms of these proteins and how structural repetitions affect the protein function, we need to be able to detect such proteins very robustly. As deep learning is particularly suited to deal with spatially organized data, we applied it to the detection of proteins with structural repetitions. Results: We present DeepSymmetry, a vers…
As more and more artificial intelligence (AI) technologies move from the laboratory to real-world applications, the open-set and robustness challenges brought by data from the real world have received increasing attention. Data augmentation is a widely used method to improve model performance, and some recent works have also confirmed its positive effect on the robustness of AI models. However, most of the existing data augmentation methods are heuristic, lacking the exploration of their internal mechanisms. We apply the explainable artificial intelligence (XAI) method, explore the internal me…
Comprehensive Analysis of Network Robustness Evaluation Based on Convolutional Neural Networks with Spatial Pyramid Pooling
School of Systems Science and Engineering, Sun Yat-sen University（中山大学系统科学与工程学院）；School of Cyber Science and Technology, University of Science and Technology of China（中国科学技术大学网络空间安全学院）
Medical Center - University of Freiburg（弗莱堡大学医学中心）
Recently, there is increasing interest and research on the interpretability of machine learning models, for example how they transform and internally represent EEG signals in Brain-Computer Interface (BCI) applications. This can help to understand the limits of the model and how it may be improved, in addition to possibly provide insight about the data itself. Schirrmeister et al. (2017) have recently reported promising results for EEG decoding with deep convolutional neural networks (ConvNets) trained in an end-to-end manner and, with a causal visualization approach, showed that they learn to…
School of Computer Science（计算机科学学院）；Carnegie Mellon University（卡内基梅隆大学）
We investigate the relationship between the frequency spectrum of image data and the generalization behavior of convolutional neural networks (CNN). We first notice CNN's ability in capturing the high-frequency components of images. These high-frequency components are almost imperceptible to a human. Thus the observation leads to multiple hypotheses that are related to the generalization behaviors of CNN, including a potential explanation for adversarial examples, a discussion of CNN's trade-off between robustness and accuracy, and some evidence in understanding training heuristics.
South China Agricultural University（华南农业大学）；Pazhou Lab（琶洲实验室）
Since the Lipschitz properties of convolutional neural networks (CNNs) are widely considered to be related to adversarial robustness, we theoretically characterize the $\ell_1$ norm and $\ell_\infty$ norm of 2D multi-channel convolutional layers and provide efficient methods to compute the exact $\ell_1$ norm and $\ell_\infty$ norm. Based on our theorem, we propose a novel regularization method termed norm decay, which can effectively reduce the norms of convolutional layers and fully-connected layers. Experiments show that norm-regularization methods, including norm decay, weight decay, and s…
Rochester Institute of Technology（罗切斯特理工学院）；University of South Florida（南佛罗里达大学）
In this work, we develop convolutional neural generative coding (Conv-NGC), a generalization of predictive coding to the case of convolution/deconvolution-based computation. Specifically, we concretely implement a flexible neurobiologically-motivated algorithm that progressively refines latent state feature maps in order to dynamically form a more accurate internal representation/reconstruction model of natural images. The performance of the resulting sensory processing system is evaluated on complex datasets such as Color-MNIST, CIFAR-10, and Street House View Numbers (SVHN). We study the eff…
Huawei（华为）；École Polytechnique（巴黎综合理工学院）；Institute Polytechnique de Paris（巴黎理工学院）；AUEB（雅典经济与商业大学）
The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a G…
Kyoto University（京都大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）；University of Tsukuba（筑波大学）；Hokkaido University（北海道大学）；RIKEN（理化学研究所）
Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work has been done in the field of machine learning and data mining. The recent advances in graph neural networks have made automatic and flexible feature extraction from graphs possible and have improved the predictive performance significantly. In this paper, we go further with this line of research and address a more general problem of learning with a graph of g…
Sun Yat-sen University（中山大学）；Emory University（埃默里大学）
Recent studies have shown that Graph Convolutional Networks (GCNs) are vulnerable to adversarial attacks on the graph structure. Although multiple works have been proposed to improve their robustness against such structural adversarial attacks, the reasons for the success of the attacks remain unclear. In this work, we theoretically and empirically demonstrate that structural adversarial examples can be attributed to the non-robust aggregation scheme (i.e., the weighted mean) of GCNs. Specifically, our analysis takes advantage of the breakdown point which can quantitatively measure the robustn…
Recent work has extensively shown that randomized perturbations of neural networks can improve robustness to adversarial attacks. The literature is, however, lacking a detailed compare-and-contrast of the latest proposals to understand what classes of perturbations work, when they work, and why they work. We contribute a detailed evaluation that elucidates these questions and benchmarks perturbation based defenses consistently. In particular, we show five main results: (1) all input perturbation defenses, whether random or deterministic, are equivalent in their efficacy, (2) attacks transfer b…
Clouds frequently cover the Earth's surface and pose an omnipresent challenge to optical Earth observation methods. The vast majority of remote sensing approaches either selectively choose single cloud-free observations or employ a pre-classification strategy to identify and mask cloudy pixels. We follow a different strategy and treat cloud coverage as noise that is inherent to the observed satellite data. In prior work, we directly employed a straightforward \emph{convolutional long short-term memory} network for vegetation classification without explicit cloud filtering and achieved state-of…
We study how effective data augmentation is at capturing the inductive bias of carefully designed network architectures for spatial translation invariance. We evaluate various image classification architectures (antialiased, convolutional, vision transformer, and fully connected MLP networks) and data augmentation techniques towards generalization to large translation shifts. We observe that: (a) without data augmentation, all architectures, including convolutional networks with antialiased modification suffer some degradation in performance when evaluated on translated test distributions. Und…
School of Computer Science and Technology（计算机科学与技术学院）
Graph Convolutional Representation (GCR) has achieved impressive performance for graph data representation. However, existing GCR is generally defined on the input fixed graph which may restrict the representation capacity and also be vulnerable to the structural attacks and noises. To address this issue, we propose a novel Latent Graph Convolutional Representation (LatGCR) for robust graph data representation and learning. Our LatGCR is derived based on reformulating graph convolutional representation from the aspect of graph neighborhood reconstruction. Given an input graph $\textbf{A}$, Lat…
National Physical Laboratory（英国国家物理实验室）；University of Surrey（萨里大学）
The electrocardiogram (ECG) is one of the most widespread diagnostic tools in healthcare and supports the diagnosis of cardiovascular disorders. Deep learning methods are a successful and popular technique to detect indications of disorders from an ECG signal. However, there are open questions around the robustness of these methods to various factors, including physiological ECG noise. In this study we generate clean and noisy versions of an ECG dataset before applying Symmetric Projection Attractor Reconstruction (SPAR) and scalogram image transformations. A pretrained convolutional neural ne…
A Learning Convolutional Neural Network Approach for Network Robustness Prediction
Lingnan University（岭南大学）；Sichuan Normal University（四川师范大学）；Shanghai Jiao Tong University（上海交通大学）；Shanghai Research Institute for Intelligent Autonomous Systems（上海智能自主系统研究院）；Tongji University（同济大学）；City University of Hong Kong（香港城市大学）
A counter-intuitive property of convolutional neural networks (CNNs) is their inherent susceptibility to adversarial examples, which severely hinders the application of CNNs in security-critical fields. Adversarial examples are similar to original examples but contain malicious perturbations. Adversarial training is a simple and effective defense method to improve the robustness of CNNs to adversarial examples. The mechanisms behind adversarial examples and adversarial training are worth exploring. Therefore, this work investigates similarities and differences between normally trained CNNs (NT…
The handwritten string recognition is still a challengeable task, though the powerful deep learning tools were introduced. In this paper, based on TAO-FCN, we proposed an end-to-end system for handwritten string recognition. Compared with the conventional methods, there is no preprocess nor manually designed rules employed. With enough labelled data, it is easy to apply the proposed method to different applications. Although the performance of the proposed method may not be comparable with the state-of-the-art approaches, it's usability and robustness are more meaningful for practical applicat…
Very-high-resolution (VHR) images can provide abundant ground details and spatial geometric information. Change detection in multi-temporal VHR images plays a significant role in urban expansion and area internal change analysis. Nevertheless, traditional change detection methods can neither take full advantage of spatial context information nor cope with the complex internal heterogeneity of VHR images. In this paper, a powerful feature extraction model entitled multi-scale feature convolution unit (MFCU) is adopted for change detection in multi-temporal VHR images. MFCU can extract multi-sca…
RoHNAS: A Neural Architecture Search Framework with Conjoint Optimization for Adversarial Robustness and Hardware Efficiency of Convolutional and Capsule Networks
Embedded Computing Systems Group, Institute of Computer Engineering, Technische Universität Wien (TU Wien), Vienna, Austria（嵌入式计算系统组，计算机工程学院，维也纳技术大学）；Evolvable Hardware Research Group, Faculty of Information Technology, Brno University of Technology, Brno, Czechia（可进化硬件研究组，信息技术学院，布拉格技术大学）；VLSI Lab, Department of Electronics and Telecommunications, Politecnico di Torino, Turin, Italy（非常规集成电路实验室，电子与电信系，托里尼 Politecnico）；eBrain Lab, Division of Engineering, New York University Abu Dhabi, UAE（eBrain 实验室，工程系，纽约大学阿布扎克分校）
Measuring model performance is a key issue for deep learning practitioners. However, we often lack the ability to explain why a specific architecture attains superior predictive accuracy for a given data set. Often, validation accuracy is used as a performance heuristic quantifying how well a network generalizes to unseen data, but it does not capture anything about the information flow in the model. Mutual information can be used as a measure of the quality of internal representations in deep learning models, and the information plane may provide insights into whether the model exploits the a…
Robust Mixture-of-Expert Training for Convolutional Neural Networks
Michigan State University（密歇根州立大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；MIT（麻省理工学院）；Harvard University（哈佛大学）；UC Santa Barbara（加州大学圣巴巴拉分校）；Carnegie Mellon University（卡内基梅隆大学）；UIUC（伊利诺伊大学厄巴纳-香槟分校）；IBM Research（IBM研究院）
Convolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between the three components (R,G,B) of a pixel, and the global relations describing edges or shapes, making it efficient with small or heterogeneous datasets. Quaternion-valued convolutional neural networks (QCNN) solved this problematic by introducing multidimensional algebra to CNN. This paper proposes to explore the fundamental reason of the success of QCNN over …
