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The Sun constantly releases radiation and plasma into the heliosphere. Sporadically, the Sun launches solar eruptions such as flares and coronal mass ejections (CMEs). CMEs carry away a huge amount of mass and magnetic flux with them. An Earth-directed CME can cause serious consequences to the human system. It can destroy power grids/pipelines, satellites, and communications. Therefore, accurately monitoring and predicting CMEs is important to minimize damages to the human system. In this study we propose an ensemble learning approach, named CMETNet, for predicting the arrival time of CMEs from the Sun to the Earth. We collect and integrate eruptive events from two solar cycles, #23 and #24, from 1996 to 2021 with a total of 363 geoeffective CMEs. The data used for making predictions include CME features, solar wind parameters and CME images obtained from the SOHO/LASCO C2 coronagraph. Our ensemble learning framework comprises regression algorithms for numerical data analysis and a convolutional neural network for image processing. Experimental results show that CMETNet performs better than existing machine learning methods reported in the literature, with a Pearson product-moment correlation coefficient of 0.83 and a mean absolute error of 9.75 h. 

Data augmentation is a powerful technique to improve performance in applications such as image and text classification tasks. Yet, there is little rigorous understanding of why and how various augmentations work. In this work, we consider a family of linear transformations and study their effects on the ridge estimator in an over-parametrized linear regression setting. First, we show that trans-formations which preserve the labels of the data can improve estimation by enlarging the span of the training data. Second, we show that transformations which mix data can improve estimation by playing a regularization effect. Finally, we validate our theoretical insights on MNIST. Based on the insights, we propose an augmentation scheme that searches over the space of transformations by how uncertain the model is about the transformed data. We validate our proposed scheme on image and text datasets. For example, our method outperforms RandAugment by 1.24% on CIFAR-100 using Wide-ResNet-28-10. Furthermore, we achieve comparable accuracy to the SoTA Adversarial AutoAugment on CIFAR-10, CIFAR-100, SVHN, and ImageNet datasets. 

We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the ℓp ball of radius ϵ when p>2. Although random smoothing has been well understood for the ℓ2 case using the Gaussian distribution, much remains unknown concerning the existence of a noise distribution that works for the case of p>2. This has been posed as an open problem by Cohen et al. (2019) and includes many significant paradigms such as the ℓ∞ threat model. In this work, we show that any noise distribution D over R^d that provides ℓp robustness for all base classifiers with p>2 must satisfy E[η_i^2]= Ω(d^(1−2/p) ϵ^2 (1−δ)/δ^2) for 99% of the features (pixels) of vector η∼D, where ϵ is the robust radius and δ is the score gap between the highest-scored class and the runner-up. Therefore, for high-dimensional images with pixel values bounded in [0,255], the required noise will eventually dominate the useful information in the images, leading to trivial smoothed classifiers. 

We show a hardness result for random smoothing to achieve certified adversarial robustness against attacks in the ℓp ball of radius ϵ when p>2. Although random smoothing has been well understood for the ℓ2 case using the Gaussian distribution, much remains unknown concerning the existence of a noise distribution that works for the case of p>2. This has been posed as an open problem by Cohen et al. (2019) and includes many significant paradigms such as the ℓ∞ threat model. In this work, we show that any noise distribution D over Rd that provides ℓp robustness for all base classifiers with p>2 must satisfy E[η_i^2]=Ω(d^(1−2/p) ϵ^2(1−δ)/δ^2) for 99% of the features (pixels) of vector η∼D, where ϵ is the robust radius and δ is the score gap between the highest-scored class and the runner-up. Therefore, for high-dimensional images with pixel values bounded in [0,255], the required noise will eventually dominate the useful information in the images, leading to trivial smoothed classifiers. 

Current methods for training robust networks lead to a drop in test accuracy, which has led prior works to posit that a robustness-accuracy tradeoff may be inevitable in deep learning. We take a closer look at this phenomenon and first show that real image datasets are actually separated. With this property in mind, we then prove that robustness and accuracy should both be achievable for benchmark datasets through locally Lipschitz functions, and hence, there should be no inherent tradeoff between robustness and accuracy. Through extensive experiments with robustness methods, we argue that the gap between theory and practice arises from two limitations of current methods: either they fail to impose local Lipschitzness or they are insufficiently generalized. We explore combining dropout with robust training methods and obtain better generalization. We conclude that achieving robustness and accuracy in practice may require using methods that impose local Lipschitzness and augmenting them with deep learning generalization techniques.