Enforcing orthogonality in neural networks is an antidote for gradient vanishing/exploding problems, sensitivity by adversarial perturbation, and bounding generalization errors. However, many previous approaches are heuristic, and the orthogonality of convolutional layers is not systematically studied: some of these designs are not exactly orthogonal, while others only consider standard convolutional layers and propose specific classes of their realizations. To address this problem, we propose a theoretical framework for orthogonal convolutional layers, which establishes the equivalence between various orthogonal convolutional layers in the spatial domain and the paraunitary systems in the spectral domain. Since there exists a complete spectral factorization of paraunitary systems, any orthogonal convolution layer can be parameterized as convolutions of spatial filters. Our framework endows high expressive power to various convolutional layers while maintaining their exact orthogonality. Furthermore, our layers are memory and computationally efficient for deep networks compared to previous designs. Our versatile framework, for the first time, enables the study of architecture designs for deep orthogonal networks, such as choices of skip connection, initialization, stride, and dilation. Consequently, we scale up orthogonal networks to deep architectures, including ResNet, WideResNet, and ShuffleNet, substantially increasing the performance over the traditional shallow orthogonal networks.
Convolutional neural networks often dominate fully-connected counterparts in generalization performance, especially on image classification tasks. This is often explained in terms of 'better inductive bias'. However, this has not been made mathematically rigorous, and the hurdle is that the fully connected net can always simulate the convolutional net (for a fixed task). Thus the training algorithm plays a role. The current work describes a natural task on which a provable sample complexity gap can be shown, for standard training algorithms. We construct a single natural distribution on $\math…
Aliasing in Convnets: A Frame-Theoretic Perspective
Acoustics Research Institute, Austrian Academy of Sciences（奥地利科学院声学研究所）；Nantes Université, École Centrale Nantes, CNRS, LS2N（南特大学、中央南特学院、国家科学研究中心、LS2N）；Department of Mathematics, University of Vienna（维也纳大学数学系）；Interdisciplinary Transformation University Austria (IT:U)（奥地利跨学科转型大学（IT:U））
University of New South Wales, Australia（新南威尔士大学，澳大利亚）
Deep learning algorithms have achieved excellent performance lately in a wide range of fields (e.g., computer version). However, a severe challenge faced by deep learning is the high dependency on hyper-parameters. The algorithm results may fluctuate dramatically under the different configuration of hyper-parameters. Addressing the above issue, this paper presents an efficient Orthogonal Array Tuning Method (OATM) for deep learning hyper-parameter tuning. We describe the OATM approach in five detailed steps and elaborate on it using two widely used deep neural network structures (Recurrent Neu…
Recurrent neural networks are extremely powerful yet hard to train. One of their issues is the vanishing gradient problem, whereby propagation of training signals may be exponentially attenuated, freezing training. Use of orthogonal or unitary matrices, whose powers neither explode nor decay, has been proposed to mitigate this issue, but their computational expense has hindered their use. Here we show that in the specific case of convolutional RNNs, we can define a convolutional exponential and that this operation transforms antisymmetric or anti-Hermitian convolution kernels into orthogonal o…
Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
Recent work has highlighted several advantages of enforcing orthogonality in the weight layers of deep networks, such as maintaining the stability of activations, preserving gradient norms, and enhancing adversarial robustness by enforcing low Lipschitz constants. Although numerous methods exist for enforcing the orthogonality of fully-connected layers, those for convolutional layers are more heuristic in nature, often focusing on penalty methods or limited classes of convolutions. In this work, we propose and evaluate an alternative approach to directly parameterize convolutional layers that …
While deep learning models often achieve strong task performance, their successes are hampered by their inability to disentangle spurious correlations from causative factors, such as when they use protected attributes (e.g., race, gender, etc.) to make decisions. In this work, we tackle the problem of debiasing convolutional neural networks (CNNs) in such instances. Building off of existing work on debiasing word embeddings and model interpretability, our Meta Orthogonalization method encourages the CNN representations of different concepts (e.g., gender and class labels) to be orthogonal to o…
An enhanced framework for peak-to-average power ratio ($\mathsf{PAPR}$) reduction and waveform design for Multiple-Input-Multiple-Output ($\mathsf{MIMO}$) orthogonal frequency-division multiplexing ($\mathsf{OFDM}$) systems, based on a convolutional-autoencoder ($\mathsf{CAE}$) architecture, is presented. The end-to-end learning-based autoencoder ($\mathsf{AE}$) for communication networks represents the network by an encoder and decoder, where in between, the learned latent representation goes through a physical communication channel. We introduce a joint learning scheme based on projected gra…
In spite of the advancements made in the periocular recognition, the dataset and periocular recognition in the wild remains a challenge. In this paper, we propose a multilayer fusion approach by means of a pair of shared parameters (dual-stream) convolutional neural network where each network accepts RGB data and a novel colour-based texture descriptor, namely Orthogonal Combination-Local Binary Coded Pattern (OC-LBCP) for periocular recognition in the wild. Specifically, two distinct late-fusion layers are introduced in the dual-stream network to aggregate the RGB data and OC-LBCP. Thus, the …
Feature Map Similarity Reduction in Convolutional Neural Networks
Cranfield University（克兰菲尔德大学）；Centre for Computational Engineering Sciences（计算工程科学中心）；Inria（法国国家信息与自动化技术研究院）；Univ. Bordeaux（波尔多大学）；ESTIA-Institute of Technology（ESTIA技术研究所）
We introduce the novel concept of anti-transfer learning for speech processing with convolutional neural networks. While transfer learning assumes that the learning process for a target task will benefit from re-using representations learned for another task, anti-transfer avoids the learning of representations that have been learned for an orthogonal task, i.e., one that is not relevant and potentially misleading for the target task, such as speaker identity for speech recognition or speech content for emotion recognition. In anti-transfer learning, we penalize similarity between activations …
In conventional machine learning applications, each data attribute is assumed to be orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus there is no distinction of in-between relations of dimensions. However, this is certainly not the case in real world signals which naturally originate from a spatio-temporal configuration. As a result, the conventional vectorization process disrupts all of the spatio-temporal information about the order/place of data whether it be $1$D, $2$D, $3$D, or $4$D. In this paper, the problem of orthogonality is first investigated…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Lipschitz constraints under L2 norm on deep neural networks are useful for provable adversarial robustness bounds, stable training, and Wasserstein distance estimation. While heuristic approaches such as the gradient penalty have seen much practical success, it is challenging to achieve similar practical performance while provably enforcing a Lipschitz constraint. In principle, one can design Lipschitz constrained architectures using the composition property of Lipschitz functions, but Anil et al. recently identified a key obstacle to this approach: gradient norm attenuation. They showed how t…
Training convolutional neural networks with a Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients, stable training, etc. While 1-Lipschitz networks can be designed by imposing a 1-Lipschitz constraint on each layer, training such networks requires each layer to be gradient norm preserving (GNP) to prevent gradients from vanishing. However, existing GNP convolutions suffer from slow training, lead to significant reduction in accuracy and provide no guarantees on their approximations. In this work, we propose a GNP convolution layer …
Incheon National University（仁川大学）；Dain Technology, Inc.
Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of parameters poses many challenges such as limited representational power and the vanishing/exploding gradients problem of recursively shared parameters. In this paper, we present a recursive convolution block design and training method, in which a recursively shareable part, or a filter basis, is separated and learned while effectively avoiding the vanishing/exploding…
In Convolutional Neural Networks (CNNs) information flows across a small neighbourhood of each pixel of an image, preventing long-range integration of features before reaching deep layers in the network. We propose a novel architecture that allows flexible information flow between features $z$ and locations $(x,y)$ across the entire image with a small number of layers. This architecture uses a cycle of three orthogonal convolutions, not only in $(x,y)$ coordinates, but also in $(x,z)$ and $(y,z)$ coordinates. We stack a sequence of such cycles to obtain our deep network, named CycleNet. As thi…
Regularization techniques are widely used to improve the generality, robustness, and efficiency of deep convolutional neural networks (DCNNs). In this paper, we propose a novel approach of regulating DCNN convolutional kernels by a structured filter bank. Comparing with the existing regularization methods, such as $\ell_1$ or $\ell_2$ minimization of DCNN kernel weights and the kernel orthogonality, which ignore sample correlations within a kernel, the use of filter bank in regularization of DCNNs can mold the DCNN kernels to common spatial structures and features (e.g., edges or textures of v…
This paper introduces the architecture of a convolutional autoencoder (CAE) for the task of peak-to-average power ratio (PAPR) reduction and waveform design, for orthogonal frequency division multiplexing (OFDM) systems. The proposed architecture integrates a PAPR reduction block and a non-linear high power amplifier (HPA) model. We apply gradual loss learning for multi-objective optimization. We analyze the models performance by examining the bit error rate (BER), the PAPR and the spectral response, and comparing them with common PAPR reduction algorithms.
In recent years, state-of-the-art methods in computer vision have utilized increasingly deep convolutional neural network architectures (CNNs), with some of the most successful models employing hundreds or even thousands of layers. A variety of pathologies such as vanishing/exploding gradients make training such deep networks challenging. While residual connections and batch normalization do enable training at these depths, it has remained unclear whether such specialized architecture designs are truly necessary to train deep CNNs. In this work, we demonstrate that it is possible to train vani…
Charles Sturt University（查尔斯特大学）；Asia Pacific International College（亚太国际学院）；Worcester State University（伍斯特州立大学）；University of Kurdistan Hewler（库尔德斯坦埃尔比勒大学）
Background and Aim: Each stage of sleep can affect human health, and not getting enough sleep at any stage may lead to sleep disorder like parasomnia, apnea, insomnia, etc. Sleep-related diseases could be diagnosed using Convolutional Neural Network Classifier. However, this classifier has not been successfully implemented into sleep stage classification systems due to high complexity and low accuracy of classification. The aim of this research is to increase the accuracy and reduce the learning time of Convolutional Neural Network Classifier. Methodology: The proposed system used a modified O…
This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop novel orthogonality regularizations on training deep CNNs, utilizing various advanced analytical tools such as mutual coherence and restricted isometry property. These plug-and-play regularizations can be conveniently incorporated into training almost any CNN without extra hassle. We then benchmark their effects on state-of-the-art models: ResNet, WideResNet,…
University of Lugano（卢加诺大学）；Harvard University（哈佛大学）；Tel Aviv University（特拉维夫大学）
Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian eigenvectors and the classical Fourier basis, allowing to formulate the convolution as a multiplication in the spectral domain. One of the key drawback of spectral CNNs is their explicit assumption of an undirected graph, leading to a symmetric Laplacian matrix with orthogonal eigendecomposition. In this work we propose MotifNet, a graph CNN capable of dealing with…
A well-trained Convolutional Neural Network can easily be pruned without significant loss of performance. This is because of unnecessary overlap in the features captured by the network's filters. Innovations in network architecture such as skip/dense connections and Inception units have mitigated this problem to some extent, but these improvements come with increased computation and memory requirements at run-time. We attempt to address this problem from another angle - not by changing the network structure but by altering the training method. We show that by temporarily pruning and then resto…
University of the Philippines Diliman（菲律宾大学迪利曼分校）；Asian Institute of Management（亚洲管理学院）
Single-pixel imaging (SPI) is a novel, unconventional method that goes beyond the notion of traditional cameras but can be computationally expensive and slow for real-time applications. Deep learning has been proposed as an alternative approach for solving the SPI reconstruction problem, but a detailed analysis of its performance and generated basis patterns when used for SPI is limited. We present a modified deep convolutional autoencoder network (DCAN) for SPI on 64x64 pixel images with up to 6.25% compression ratio and apply binary and orthogonality regularizers during training. Training a …
Continual learning could shift the machine learning paradigm from data centric to model centric. A continual learning model needs to scale efficiently to handle semantically different datasets, while avoiding unnecessary growth. We introduce hash-routed convolutional neural networks: a group of convolutional units where data flows dynamically. Feature maps are compared using feature hashing and similar data is routed to the same units. A hash-routed network provides excellent plasticity thanks to its routed nature, while generating stable features through the use of orthogonal feature hashing.…
Hyperbolic graph convolutional networks (GCNs) demonstrate powerful representation ability to model graphs with hierarchical structure. Existing hyperbolic GCNs resort to tangent spaces to realize graph convolution on hyperbolic manifolds, which is inferior because tangent space is only a local approximation of a manifold. In this paper, we propose a hyperbolic-to-hyperbolic graph convolutional network (H2H-GCN) that directly works on hyperbolic manifolds. Specifically, we developed a manifold-preserving graph convolution that consists of a hyperbolic feature transformation and a hyperbolic ne…
In this paper, we study the usage of Convolutional Neural Network (CNN) estimators for the task of Multiple-Input-Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) Channel Estimation (CE). Specifically, the CNN estimators interpolate the channel values of reference signals for estimating the channel of the full OFDM resource element (RE) matrix. We have designed a 2D CNN architecture based on U-net, and a 3D CNN architecture for handling spatial correlation. We investigate the performance of various CNN architectures fora diverse data set generated according to the 5G NR s…
University of Technology Sydney（悉尼科技大学）；Northwestern University（西北大学）
The prevailing thinking is that orthogonal weights are crucial to enforcing dynamical isometry and speeding up training. The increase in learning speed that results from orthogonal initialization in linear networks has been well-proven. However, while the same is believed to also hold for nonlinear networks when the dynamical isometry condition is satisfied, the training dynamics behind this contention have not been thoroughly explored. In this work, we study the dynamics of ultra-wide networks across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural …
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…
School of Artificial Intelligence, Jilin University（吉林大学人工智能学院）；Department of Computer Science, Rice University（莱斯大学计算机科学系）；College of Computer Science and Technology, Jilin University（吉林大学计算机科学与技术学院）
Graph neural networks (GNNs) have received tremendous attention due to their superiority in learning node representations. These models rely on message passing and feature transformation functions to encode the structural and feature information from neighbors. However, stacking more convolutional layers significantly decreases the performance of GNNs. Most recent studies attribute this limitation to the over-smoothing issue, where node embeddings converge to indistinguishable vectors. Through a number of experimental observations, we argue that the main factor degrading the performance is the…
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to nonlinear time-dependent parametrized partial differential equations (PDEs). These might be related to (i) the need to deal with projections onto high dimensional linear approximating trial manifolds, (ii) expensive hyper-reduction strategies, or (iii) the intrinsic difficulty to handle physical complexity with a linear superimposition of modes. All these as…
RRCNN: A novel signal decomposition approach based on recurrent residue convolutional neural network
Guangdong University of Finance and Economics（广东财经大学）；University of L’Aquila（拉奎拉大学）；Istituto di Astrofisica e Planetologia Spaziali, INAF（意大利国家天体物理研究所空间天体物理与行星学研究所）；Istituto Nazionale di Geofisica e Vulcanologia（意大利国家地球物理与火山学研究所）；Georgia Institute of Technology（佐治亚理工学院）
Forward-Only Convolutional Neural Networks with Learnable Channel-Class Assignment
Department of Computer and Data Science, Faculty of Mathematical Sciences, Shahid Beheshti University（肖德行为斯蒂大学计算机与数据科学系）；Cyberspace Research Institute, Shahid Beheshti University（肖德行为斯蒂大学网络空间研究所）；Cybersecurity and Computing Systems Research Group, University of Hertfordshire（赫特福德大学网络安全与计算系统研究组）
Different neural networks trained on the same dataset often learn similar input-output mappings with very different weights. Is there some correspondence between these neural network solutions? For linear networks, it has been shown that different instances of the same network architecture encode the same representational similarity matrix, and their neural activity patterns are connected by orthogonal transformations. However, it is unclear if this holds for non-linear networks. Using a shared response model, we show that different neural networks encode the same input examples as different o…
Non-cooperative communications, where a receiver can automatically distinguish and classify transmitted signal formats prior to detection, are desirable for low-cost and low-latency systems. This work focuses on the deep learning enabled blind classification of multi-carrier signals covering their orthogonal and non-orthogonal varieties. We define two signal groups, in which Type-I includes signals with large feature diversity while Type-II has strong feature similarity. We evaluate time-domain and frequency-domain convolutional neural network (CNN) models in simulation with wireless channel/h…
Massachusetts Institute of Technology（麻省理工学院）；Institute of Science and Technology Austria（奥地利科学技术研究所）；Technische Universität Wien（维也纳工业大学）
Residual mappings have been shown to perform representation learning in the first layers and iterative feature refinement in higher layers. This interplay, combined with their stabilizing effect on the gradient norms, enables them to train very deep networks. In this paper, we take a step further and introduce entangled residual mappings to generalize the structure of the residual connections and evaluate their role in iterative learning representations. An entangled residual mapping replaces the identity skip connections with specialized entangled mappings such as orthogonal, sparse, and stru…
LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers
Department of Mechanical Engineering, Eindhoven University of Technology（埃因霍温理工大学机械工程系）；Institute for Systems Theory and Automatic Control, University of Stuttgart（斯图加特大学系统理论与自动控制研究所）；Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney（悉尼大学澳大利亚机器人中心及航空航天、机械与机电工程学院）
ISCTE – Instituto Universitário de Lisboa（里斯本大学学院）；PDMFC（PDMFC公司）；IT – Instituto de Telecomunicações（电信研究所）；FCT – Universidade Nova de Lisboa（新里斯本大学）；CTTC - Centre Tecnològic de Telecomunicacions de Catalunya（加泰罗尼亚电信技术中心）
When users exchange data with Unmanned Aerial vehicles - (UAVs) over air-to-ground (A2G) wireless communication networks, they expose the link to attacks that could increase packet loss and might disrupt connectivity. For example, in emergency deliveries, losing control information (i.e data related to the UAV control communication) might result in accidents that cause UAV destruction and damage to buildings or other elements in a city. To prevent these problems, these issues must be addressed in 5G and 6G scenarios. This research offers a deep learning (DL) approach for detecting attacks in U…
In this paper, we present a deep neural network-based online multi-speaker localisation algorithm. Following the W-disjoint orthogonality principle in the spectral domain, each time-frequency (TF) bin is dominated by a single speaker, and hence by a single direction of arrival (DOA). A fully convolutional network is trained with instantaneous spatial features to estimate the DOA for each TF bin. The high resolution classification enables the network to accurately and simultaneously localize and track multiple speakers, both static and dynamic. Elaborated experimental study using both simulated…
Training convolutional neural networks (CNNs) with a strict Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients and stable training. While $1$-Lipschitz CNNs can be designed by enforcing a $1$-Lipschitz constraint on each layer, training such networks requires each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. A layer with this property is said to be Gradient Norm Preserving (GNP). In this work, we introduce a procedure to certify the robustness of $1$-L…
University of Helsinki（赫尔辛基大学）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
We propose a novel convolutional neural network (CNN), called $Ψ$DONet, designed for learning pseudodifferential operators ($Ψ$DOs) in the context of linear inverse problems. Our starting point is the Iterative Soft Thresholding Algorithm (ISTA), a well-known algorithm to solve sparsity-promoting minimization problems. We show that, under rather general assumptions on the forward operator, the unfolded iterations of ISTA can be interpreted as the successive layers of a CNN, which in turn provides fairly general network architectures that, for a specific choice of the parameters involved, allow…
Indian Institute of Science（印度科学学院）；Rice University（莱斯大学）
Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical perspective. In this paper, we introduce a learning based approach to wavelet design. We draw a parallel between convolutional autoencoders and wavelet multiresolution approximation, and show how the learning angle provides a coherent computational framework for addressing the design problem. We aim at designing data-independent wavelets by training filterbank autoen…
Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing each layer to have an orthogonal Jacobian matrix (for all inputs) to prevent the gradients from vanishing during backpropagation. However, their performance often significantly lags behind that of heuristic methods to enforce Lipschitz constraints where the resulting CNN is not \textit{provably} 1-Lipschitz. In this work, we reduce this gap by introducing (a…
