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The task of transfer learning using pretrained convolutional neural networks is considered. We propose a convolution-SVD layer to analyze the convolution operators with a singular value decomposition computed in the Fourier domain. Singular vectors extracted from the source domain are transferred to the target domain, whereas the singular values are fine-tuned with a target data set. In this way, dimension reduction is achieved to avoid overfitting, while some flexibility to fine-tune the convolution kernels is maintained. We extend an existing convolution kernel reconstruction algorithm to allow for a reconstruction from an arbitrary set of learned singular values. A generalization bound for a single convolution-SVD layer is devised to show the consistency between training and testing errors. We further introduce a notion of transfer learning gap. We prove that the testing error for a single convolution-SVD layer is bounded in terms of the gap, which motivates us to develop a regularization model with the gap as the regularizer. Numerical experiments are conducted to demonstrate the superiority of the proposed model in solving classification problems and the influence of various parameters. In particular, the regularization is shown to yield a significantly higher prediction accuracy. [ABSTRACT FROM AUTHOR]

Graph Convolution Networks (GCNs) have been shown to be very effective in utilizing pair-wise relationships across samples. They have been successfully applied to solve various machine learning problems in practice. In many applications, the construction of GCNs involves more than one layer. However, their generalization and stability analysis are limited. The main aim of this paper is to analyze GCNs with two layers. The formulation is based on transductive semi-supervised learning and the filtering is done in the eigen-domain. We show the uniform stability of the neural network and the convergence of the generalization gap to zero. The analysis of two-layer GCN is more involved than the single-layer case and requires some new estimates of the neural network's quantities. The analysis confirms the usefulness of GCNs. It also sheds light on the design of the neural network, for instance, how the data should be scaled to achieve the uniform stability of the learning process. Some experimental results on benchmark datasets are presented to illustrate the theory. [ABSTRACT FROM AUTHOR]

This work proposes a novel deep learning (DL) framework to solve the electromagnetic inverse scattering (EMIS) problems. The proposed framework integrates the complex-valued deep convolutional neural network (DConvNet) into the supervised descent method (SDM) to realize both off-line training and on-line “imaging” prediction for EMIS. The offline training consists of two parts: 1) DConvNet training: the training dataset is created, and the proposed DConvNet is trained to realize the EM forward process and 2) SDM training: the trained DConvNet is integrated into the SDM framework, and the average descent directions between the initial prediction and the true label of SDM iterative schemes are learned based on the same dataset in part 1). In the online step, the contrasts (permittivities) reconstruction of scatterers is realized by the SDM iteration process based on learned descent directions, while its forward process is achieved by the trained complex-valued DConvNet. Ultimately, this framework provides a new perspective to integrate the prior information into the EMIS solving process with the maintained accuracy. Unlike the conventional SDM, the novel proposed framework can significantly shorten the computation and realize the real-time imaging. Various numerical examples and discussions are provided to demonstrate the efficiency and accuracy of the proposed novel framework. [ABSTRACT FROM AUTHOR]

This paper proposes a novel inverse method based on the deep convolutional neural network (ConvNet) to extract snow's layer thickness and temperature via passive microwave remote sensing (PMRS). The proposed ConvNet is trained using simulated data obtained through conventional computational electromagnetic methods. Compared with the traditional inverse method, the trained ConvNet can predict the result with higher accuracy. Besides, the proposed method has a strong tolerance for noise. The proposed ConvNet composes three pairs of convolutional and activation layers with one additional fully connected layer to realize regression, i.e., the inversion of snow parameters. The feasibility of the proposed method in learning the inversion of snow parameters is validated by numerical examples. The inversion results indicate that the correlation coefficient ( R 2 ) ratio between the proposed ConvNet and conventional methods reaches 4.8, while the ratio for the root mean square error (RMSE) is only 0.18. Hence, the proposed method experiments with a novel path to improve the inversion of passive microwave remote sensing through deep learning approaches. [ABSTRACT FROM AUTHOR]

Recently, deep-learning-based denoising methods for hyperspectral images (HSIs) have been comprehensively studied and achieved impressive performance because they can effectively extract complex and nonlinear image features. Compared with deep-learning-based methods, the nonlocal similarity-based denoising methods are more suitable for images containing edges or regular textures. We propose a powerful HSI denoising method, termed non-local 3-D convolutional neural network (NL-3DCNN), combining traditional machine learning and deep learning techniques. NL-3DCNN exploits the high spectral correlation of an HSI using subspace representation, and the corresponding representation coefficients are termed eigenimages. The high spatial correlation in eigenimages is exploited by grouping nonlocal similar patches, which are denoised by a 3-D convolutional neural network. The numerical and graphical denoising results of the simulated and real data show that the proposed method is superior to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Precipitation nowcasting is an important task, which can be used in numerous applications. The key challenge of the task lies in radar echo map prediction. Previous studies leverage the convolutional recurrent neural network (ConvRNN) to address the problem. However, the approaches are built upon mean square losses, and the results tend to have inaccurate appearances, shapes, and positions for predictions. To alleviate this problem, we explore the idea of adversarial regularization and systematically compare four types of generative adversarial networks (GANs), which are the combinations of GAN/Wasserstein GAN (WGAN) and its multiscale version. Extensive experiments on a real-world radar dataset and four typical meteorological examples are conducted. The results validate the effectiveness of adversarial regularization. The developed models show superior performances over the existing prediction approaches in the majority of circumstances. Moreover, we find that the WGAN regularization often delivers better results than the GAN regularization due to its robustness, and the multiscale WGAN, in general, performs the best among all the methods. To reproduce the results, we release the source code at https://github.com/luochuyao/MultiScaleGAN and the test system at http://39.97.217.145:80/. [ABSTRACT FROM AUTHOR]

This paper proposes a novel deep learning (DL) based source reconstruction method (SRM). The proposed DL-based SRM employs the deep convolutional asymmetric encoder–decoder structure (DCAEDS), which only demands one-time single-frequency far-field measurement on EM scattered field as its input and further predicts the equivalent source on target scatterers. During the offline training, an EM scattering simulator is designed to compute EM scattered field originated from the predicted equivalent source on target scatterers. The DCAEDS is combined with the EM scattering simulator to optimize the loss function, including two parts: (1) Data-induced loss, which directly evaluates the difference between the prediction of the proposed DCAEDS and the true-labelled equivalent source of target scatterers; (2) Physics-induced loss, which evaluates the difference between received EM scattered field and the computed EM scattered field originated from the prediction of DCAEDS. Moreover, the proposed DL-based SRM can overcome the limitation of conventional methods, involving high computation cost and strong ill-conditions. Consequently, the proposed DL-based SRM can realize the reconstruction of the equivalent current source with higher accuracy and lower computation complexity. Numerical examples illustrate the feasibility of the proposed DL-based SRM, which opens the new path for DL-based EM computation approaches. [ABSTRACT FROM AUTHOR]

Deep neural networks have shown impressive performance in many areas, including computer vision and natural language processing. Millions of parameters in deep neural network limit its deployment in low-end devices due to intensive memory and expensive computational cost. In the literature, several network compression techniques based on tensor decompositions have been proposed to compress deep neural networks. Existing techniques are designed in each network unit by approximating linear response or kernel tensor using various tensor decomposition methods. What is more, research has shown that there exists significant redundancy between different filters and feature channels of kernel tensor in each convolution layer. In this paper, we propose a new algorithm to compress deep neural network by considering both nonlinear response and the multilinear low-rank constraint in the kernel tensor. To overcome the resulted difficulty of nonconvex optimization, we propose a convex relaxation scheme such that it can be solved by alternating direction method of multipliers (ADMM) directly. Thus, the Tucker-2 rank and the feature matrix of Tucker decomposition can be determined simultaneously. The effectiveness of the proposed method is evaluated on CIFAR-10 and large-scale ILSVRC12 datasets for CNNs including ResNet-18, AlexNet and GoogleNet. According to our numerical computation, the proposed method is able to obtain highly reduction in model size with a small loss in accuracy. The compression performance of the proposed method is better than existing methods. [ABSTRACT FROM AUTHOR]