We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs.
Ensemble learning is a method of combining multiple trained models to improve model accuracy. We propose the usage of such methods, specifically ensemble average, inside Convolutional Neural Network (CNN) architectures by replacing the single convolutional layers with Inner Average Ensembles (IEA) of multiple convolutional layers. Empirical results on different benchmarking datasets show that CNN models using IEA outperform those with regular convolutional layers. A visual and a similarity score analysis of the features generated from IEA explains why it boosts the model performance.
Technische Universität Darmstadt（达姆施塔特工业大学）；Concordia University（康考迪亚大学）
Image classifiers based on convolutional neural networks are defined, and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Under suitable assumptions on the smoothness and structure of the aposteriori probability a rate of convergence is shown which is independent of the dimension of the image. This proves that in image classification it is possible to circumvent the curse of dimensionality by convolutional neural networks.
Dipartimento di Matematica, Università di Bologna（博洛尼亚大学数学系）
In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what circumstances they tend to perform well and what assumptions are implicitly made in the network. While for fully-connected networks the properties of convergence to Gaussian processes have been studied extensively, little is known about situations in which the output from a convolutional network approaches a multivariate normal distribution.
In this paper, we introduce Channel-wise recurrent convolutional neural networks (RecNets), a family of novel, compact neural network architectures for computer vision tasks inspired by recurrent neural networks (RNNs). RecNets build upon Channel-wise recurrent convolutional (CRC) layers, a novel type of convolutional layer that splits the input channels into disjoint segments and processes them in a recurrent fashion. In this way, we simulate wide, yet compact models, since the number of parameters is vastly reduced via the parameter sharing of the RNN formulation. Experimental results on the…
This paper describes our UNet based deep convolutional neural network approach on the Traffic4cast challenge 2019. Challenges task is to predict future traffic flow volume, heading and speed on high resolution whole city map. We used UNet based deep convolutional neural network to train predictive model for the short term traffic forecast. On each convolution block, layers are densely connected with subsequent layers like a DenseNet. Trained and evaluated on the real world data set collected from three distinct cities in the world, our method achieved best performance in this challenge.
We study the generalization capacity of group convolutional neural networks. We identify precise estimates for the VC dimensions of simple sets of group convolutional neural networks. In particular, we find that for infinite groups and appropriately chosen convolutional kernels, already two-parameter families of convolutional neural networks have an infinite VC dimension, despite being invariant to the action of an infinite group.
We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the global minimum under a planted model assumption, given sufficiently many training samples from a Gaussian distribution. We also identify a phase transition phenomenon in recovering the global minimum for the relaxation.
We study channel number reduction in combination with weight binarization (1-bit weight precision) to trim a convolutional neural network for a keyword spotting (classification) task. We adopt a group-wise splitting method based on the group Lasso penalty to achieve over 50% channel sparsity while maintaining the network performance within 0.25% accuracy loss. We show an effective three-stage procedure to balance accuracy and sparsity in network training.
Convolutional neural networks (CNNs) have achieved breakthrough performances in a wide range of applications including image classification, semantic segmentation, and object detection. Previous research on characterizing the generalization ability of neural networks mostly focuses on fully connected neural networks (FNNs), regarding CNNs as a special case of FNNs without taking into account the special structure of convolutional layers. In this work, we propose a tighter generalization bound for CNNs by exploiting the sparse and permutation structure of its weight matrices. As the generalizat…
University of Notre Dame（圣母大学）；University of Kentucky（肯塔基大学）
We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary structure inference problems of RNA and protein sequences. We develop a CNN architecture that generates and preserves the symmetry structure in the network's convolutional layers. We present parameterizations for the convolutional kernels that produce update rules to maintain symmetry throughout the training. We apply this architecture to the sequential reco…
Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their kernel-based counterparts, Convolutional Kernel Networks (CKNs), and demonstrate that this perception is unfounded both formally and empirically. We show that, given a Convolutional Neural Network, we can design a corresponding Convolutional Kernel Network, easily trainable using a new stochastic gradient algorithm based on an accurate gradient computation, tha…
Kavli IPMU (WPI), University of Tokyo（东京大学卡弗里数物连携宇宙研究机构（世界顶级国际研究中心））
In this work we propose a novel approach to utilize convolutional neural networks for time series forecasting. The time direction of the sequential data with spatial dimensions $D=1,2$ is considered democratically as the input of a spatiotemporal $(D+1)$-dimensional convolutional neural network. Latter then reduces the data stream from $D +1 \to D$ dimensions followed by an incriminator cell which uses this information to forecast the subsequent time step. We empirically compare this strategy to convolutional LSTM's and LSTM's on their performance on the sequential MNIST and the JSB chorals da…
This paper presents the novel way combining the BERT embedding method and the graph convolutional neural network. This combination is employed to solve the text classification problem. Initially, we apply the BERT embedding method to the texts (in the BBC news dataset and the IMDB movie reviews dataset) in order to transform all the texts to numerical vector. Then, the graph convolutional neural network will be applied to these numerical vectors to classify these texts into their ap-propriate classes/labels. Experiments show that the performance of the graph convolutional neural network model …
Chalmers University of Technology（查尔姆斯理工大学）；TU Wien（维也纳工业大学）
Lattice gauge equivariant convolutional neural networks (L-CNNs) are a framework for convolutional neural networks that can be applied to non-Abelian lattice gauge theories without violating gauge symmetry. We demonstrate how L-CNNs can be equipped with global group equivariance. This allows us to extend the formulation to be equivariant not just under translations but under global lattice symmetries such as rotations and reflections. Additionally, we provide a geometric formulation of L-CNNs and show how convolutions in L-CNNs arise as a special case of gauge equivariant neural networks on SU…
Predicting the evolution of a representative sample of a material with microstructure is a fundamental problem in homogenization. In this work we propose a graph convolutional neural network that utilizes the discretized representation of the initial microstructure directly, without segmentation or clustering. Compared to feature-based and pixel-based convolutional neural network models, the proposed method has a number of advantages: (a) it is deep in that it does not require featurization but can benefit from it, (b) it has a simple implementation with standard convolutional filters and laye…
This article presents a new method for forecasting Value at Risk. Convolutional neural networks can do time series forecasting, since they can learn local patterns in time. A simple modification enables them to forecast not the mean, but arbitrary quantiles of the distribution, and thus allows them to be applied to VaR-forecasting. The proposed model can learn from the price history of different assets, and it seems to produce fairly accurate forecasts.
Using electrocardiograms as an example, we demonstrate the characteristic problems that arise when modeling one-dimensional signals containing inaccurate repeating pattern by means of standard convolutional networks. We show that these problems are systemic in nature. They are due to how convolutional networks work with composite objects, parts of which are not fixed rigidly, but have significant mobility. We also demonstrate some counterintuitive effects related to generalization in deep networks.
The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data. We explore artificially constraining the frequency spectra of these filters and data, called band-limiting, during training. The frequency domain constraints apply to both the feed-forward and back-propagation steps. Experimentally, we observe that Convolutional Neural Networks (CNNs) are resilient to this compression scheme and results suggest that CNNs learn to leverage lower-frequency components. In particular, we f…
The Neural Tangent Kernel (NTK) is an important milestone in the ongoing effort to build a theory for deep learning. Its prediction that sufficiently wide neural networks behave as kernel methods, or equivalently as random feature models, has been confirmed empirically for certain wide architectures. It remains an open question how well NTK theory models standard neural network architectures of widths common in practice, trained on complex datasets such as ImageNet. We study this question empirically for two well-known convolutional neural network architectures, namely AlexNet and LeNet, and f…
Hyperparameters tuning is a time-consuming approach, particularly when the architecture of the neural network is decided as part of this process. For instance, in convolutional neural networks (CNNs), the selection of the number and the characteristics of the hidden (convolutional) layers may be decided. This implies that the search process involves the training of all these candidate network architectures. This paper describes a proposal to reuse the weights of hidden (convolutional) layers among different trainings to shorten this process. The rationale is that if a set of convolutional laye…
Image classification is considered, and a hierarchical max-pooling model with additional local pooling is introduced. Here the additional local pooling enables the hierachical model to combine parts of the image which have a variable relative distance towards each other. Various convolutional neural network image classifiers are introduced and compared in view of their rate of convergence. The finite sample size performance of the estimates is analyzed by applying them to simulated and real data.
Convolutional neural networks (CNNs) are a representative class of deep learning algorithms including convolutional computation that perform translation-invariant classification of input data based on their hierarchical architecture. However, classical convolutional neural network learning methods use the steepest descent algorithm for training, and the learning performance is greatly influenced by the initial weight settings of the convolutional and fully connected layers, requiring re-tuning to achieve better performance under different model structures and data. Combining the strengths of t…
China University of Geosciences（中国地质大学）；University of Kentucky（肯塔基大学）
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresponding to a convolutional kernel bounded around $1$. We propose a penalty function that can be used in the optimization of a convolutional neural network to constrain the singular values of the transformation matrix around $1$. We derive an algorithm to carry out the gradient des…
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features, including a bias towards learning oversmoothed and homophilic functions, which are not easily diagnosed due to the complex nature of these algorithms. We propose to bridge this gap in understanding by studying the neural tangent kernel of sheaf convolutional networks--a topological generalization of graph convolutional networks. To this end, we derive a par…
Convolutional neural networks are very popular nowadays. Training neural networks is not an easy task. Each convolution corresponds to a structured transformation matrix. In order to help avoid the exploding/vanishing gradient problem, it is desirable that the singular values of each transformation matrix are not large/small in the training process. We propose three new regularization terms for a convolutional kernel tensor to constrain the singular values of each transformation matrix. We show how to carry out the gradient type methods, which provides new insight about the training of convolu…
Stony Brook University（石溪大学）；The State University of New York Korea（纽约州立大学韩国分校）
We applied pre-defined kernels also known as filters or masks developed for image processing to convolution neural network. Instead of letting neural networks find its own kernels, we used 41 different general-purpose kernels of blurring, edge detecting, sharpening, discrete cosine transformation, etc. for the first layer of the convolution neural networks. This architecture, thus named as general filter convolutional neural network (GFNN), can reduce training time by 30% with a better accuracy compared to the regular convolutional neural network (CNN). GFNN also can be trained to achieve 90% …
Institute of Biomedical Sciences, Academia Sinica（中央研究院生物医学科学研究所）
The paper discusses the limitations of deep learning models in identifying and utilizing features that remain invariant under a bijective transformation on the data entries, which we refer to as combinatorial patterns. We argue that the identification of such patterns may be important for certain applications and suggest providing neural networks with information that fully describes the combinatorial patterns of input entries and allows the network to determine what is relevant for prediction. To demonstrate the feasibility of this approach, we present a combinatorial convolutional neural net…
Shenzhen Polytechnic（深圳职业技术学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Convolutional neural networks have shown impressive abilities in many applications, especially those related to the classification tasks. However, for the regression problem, the abilities of convolutional structures have not been fully understood, and further investigation is needed. In this paper, we consider the mean squared error analysis for deep convolutional neural networks. We show that, for additive ridge functions, convolutional neural networks followed by one fully connected layer with ReLU activation functions can reach optimal mini-max rates (up to a log factor). The input dimensi…
Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden dynamics of a physical system using ordinary differential equation (ODEs) systems (ODEs) and Partial Differential Equation systems (PDEs). Instead of considering the physical system such as image, time -series as a system of multiple layers, this new technique can model a system in the form of Differential Equation (DEs). The proposed method has been assesse…
This work addresses the rising demand for novel tools in statistical and machine learning for "graph-valued random variables" by proposing a fast algorithm to compute the sample Frechet mean, which replaces the concept of sample mean for graphs (or networks). We use convolutional neural networks to learn the morphology of the graphs in a set of graphs. Our experiments on several ensembles of random graphs demonstrate that our method can reliably recover the sample Frechet mean.
Old Dominion University（欧道明大学）；Sun Yat-sen University（中山大学）
Convergence of deep neural networks as the depth of the networks tends to infinity is fundamental in building the mathematical foundation for deep learning. In a previous study, we investigated this question for deep ReLU networks with a fixed width. This does not cover the important convolutional neural networks where the widths are increasing from layer to layer. For this reason, we first study convergence of general ReLU networks with increasing widths and then apply the results obtained to deep convolutional neural networks. It turns out the convergence reduces to convergence of infinite p…
East China University of Science and Technology（华东理工大学）
With the improvement of computer performance and the increase of data volume, the object detection based on convolutional neural network (CNN) has become the main algorithm for object detection. This paper summarizes the research progress of convolutional neural networks and their applications in object detection, and focuses on analyzing and discussing a specific idea and method of applying convolutional neural networks for object detection, pointing out the current deficiencies and future development direction.
We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convo…
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）
The goal of this study was to improve the post-processing of precipitation forecasts using convolutional neural networks (CNNs). Instead of post-processing forecasts on a per-pixel basis, as is usually done when employing machine learning in meteorological post-processing, input forecast images were combined and transformed into probabilistic output forecast images using fully convolutional neural networks. CNNs did not outperform regularized logistic regression. Additionally, an ablation analysis was performed. Combining input forecasts from a global low-resolution weather model and a regiona…
University of Oxford（牛津大学）；Katholische Universität Eichstätt–Ingolstadt（艾希施泰特-英戈尔施塔特天主教大学）
Convolutional neural networks are the most widely used type of neural networks in applications. In mathematical analysis, however, mostly fully-connected networks are studied. In this paper, we establish a connection between both network architectures. Using this connection, we show that all upper and lower bounds concerning approximation rates of {fully-connected} neural networks for functions $f \in \mathcal{C}$ -- for an arbitrary function class $\mathcal{C}$ -- translate to essentially the same bounds concerning approximation rates of convolutional neural networks for functions $f \in {\ma…
Science and Technology on Electronic Information Control Laboratory（电子信息控制科技实验室）
A novel and efficient end-to-end learning model for automatic modulation classification is proposed for wireless spectrum monitoring applications, which automatically learns from the time domain in-phase and quadrature data without requiring the design of hand-crafted expert features. With the intuition of convolutional layers with pooling serving as the role of front-end feature distillation and dimensionality reduction, sequential convolutional recurrent neural networks are developed to take complementary advantage of parallel computing capability of convolutional neural networks and tempora…
The freedom of fast iterations of distributed deep learning tasks is crucial for smaller companies to gain competitive advantages and market shares from big tech giants. HorovodRunner brings this process to relatively accessible spark clusters. There have been, however, no benchmark tests on HorovodRunner per se, nor specifically graph convolutional network (GCN, hereafter), and very limited scalability benchmark tests on Horovod, the predecessor requiring custom built GPU clusters. For the first time, we show that Databricks' HorovodRunner achieves significant lift in scaling efficiency for t…
Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise image models, and thus regularize inverse problems. In this paper, we provide further evidence for this finding by studying variations of convolutional neural networks that map few weight parameters to an image. The networks we consider only consist of convolutional operations, with …
