Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces. The anisotropic Besov space is characterized by direction-dependent smoothness and includes several function classes that have been investigated thus far. We demonstrate that the approximation error and estimation error of deep learning only depend on the average value of the smoothness parameters in all directions. Consequently, the curse of dimensionality can be avoided if the smoothness of the target function is highly anisotropic. Unlike existing studies, our analysis does not require a low-dimensional structure of the input data. We also investigate the minimax optimality of deep learning and compare its performance with that of the kernel method (more generally, linear estimators). The results show that deep learning has better dependence on the input dimensionality if the target function possesses anisotropic smoothness, and it achieves an adaptive rate for functions with spatially inhomogeneous smoothness.

Graph Neural Networks (GNNs) have received extensive research attention for their promising performance in graph machine learning. Despite their extraordinary predictive accuracy, existing approaches, such as GCN and GPRGNN, are not robust in the face of homophily changes on test graphs, rendering these models vulnerable to graph structural attacks and with limited capacity in generalizing to graphs of varied homophily levels. Although many methods have been proposed to improve the robustness of GNN models, the majority of these techniques are restricted to the spatial domain and employ complicated defense mechanisms, such as learning new graph structures or calculating edge attention. In this paper, we study the problem of designing simple and robust GNN models in the spectral domain. We propose EvenNet, a spectral GNN corresponding to an even-polynomial graph filter. Based on our theoretical analysis in both spatial and spectral domains, we demonstrate that EvenNet outperforms full-order models in generalizing across homophilic and heterophilic graphs, implying that ignoring odd-hop neighbors improves the robustness of GNNs. We conduct experiments on both synthetic and real-world datasets to demonstrate the effectiveness of EvenNet. Notably, EvenNet outperforms existing defense models against structural attacks without introducing additional computational costs and maintains competitiveness in traditional node classification tasks on homophilic and heterophilic graphs.

In this paper, we introduce a novel approach to fine-grained cross-view geolocalization.

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims at recovering the underlying rotations directly. We provide strong theoretical guarantees for ReSync under the random corruption setting. Specifically, we first show that the initialization procedure of ReSyncyields a proper initial point that lies in a local region around the ground-truth rotations. We next establish the weak sharpness property of the aforementioned formulation and then utilize this property to derive the local linear convergence of ReSyncto the ground-truth rotations. By combining these guarantees, we conclude that ReSync converges linearly to the ground-truth rotations under appropriate conditions. Experiment results demonstrate the effectiveness of ReSync.

We construct SEIDNet based on PyTorch1. There are 26 convolutional layers for extracting the visual feature map from the rainy image. The feature masking contains two convolutional layers. It computes the rain (or object) feature map. There is a pair of batch normalization and ReLU layers between the adjacent convolutional layers. The size of kernels in each convolutional layer is 3 3. Vid generates 3 3kernel for deraining each pixel.

Image rain removal requires the accurate separation between the pixels of the rain streaks and object textures. But the confusing appearances of rains and objects lead to the misunderstanding of pixels, thus remaining the rain streaks or missing the object details in the result. In this paper, we propose SEIDNet equipped with the generative Status Estimation and Information Decoupling for rain removal. In the status estimation, we embed the pixel-wise statuses into the status space, where each status indicates a pixel of the rain or object. The status space allows sampling multiple statuses for a pixel, thus capturing the confusing rain or object. In the information decoupling, we respect the pixel-wise statuses, decoupling the appearance information of rain and object from the pixel. Based on the decoupled information, we construct the kernel space, where multiple kernels are sampled for the pixel to remove the rain and recover the object appearance. We evaluate SEIDNet on the public datasets, achieving state-of-the-art performances of image rain removal. The experimental results also demonstrate the generalization of SEIDNet, which can be easily extended to achieve state-of-the-art performances on other image restoration tasks (e.g., snow, haze, and shadow removal).

In this paper, we focus on multi-task classification, where related classification tasks share the same label space and are learned simultaneously. In particular, we tackle a new setting, which is more realistic than currently addressed in the literature, where categories shift from training to test data. Hence, individual tasks do not contain complete training data for the categories in the test set. To generalize to such test data, it is crucial for individual tasks to leverage knowledge from related tasks. To this end, we propose learning an association graph to transfer knowledge among tasks for missing classes.