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In the space sector, due to environmental conditions and restricted accessibility, robust fault detection methods are imperative for ensuring mission success and safeguarding valuable assets. This work proposes a novel approach leveraging Physics-Informed Real NVP neural networks, renowned for their ability to model complex and high-dimensional distributions, augmented with a self-supervised task based on sensors' data permutation. It focuses on enhancing fault detection within the satellite multivariate time series. The experiments involve various configurations, including pre-training with self-supervision, multi-task learning, and standalone self-supervised training. Results indicate significant performance improvements across all settings. In particular, employing only the self-supervised loss yields the best overall results, suggesting its efficacy in guiding the network to extract relevant features for fault detection. This study presents a promising direction for improving fault detection in space systems and warrants further exploration in other datasets and applications.

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self-attention, positional encoding and feed-forward layer, affect its expressive power, and we study their combined effects through establishing explicit approximation rates. Our study reveals the roles of critical parameters in the Transformer, such as the number of layers and the number of attention heads. These theoretical insights are validated experimentally and offer natural suggestions for alternative architectures.

Cardiac cine magnetic resonance imaging (MRI) is one of the important means to assess cardiac functions and vascular abnormalities. Mitigating artifacts arising during image reconstruction and accelerating cardiac cine MRI acquisition to obtain high-quality images is important. A novel end-to-end deep learning network is developed to improve cardiac cine MRI reconstruction. First, a U-Net is adopted to obtain the initial reconstructed images in k-space. Further to remove the motion artifacts, the motion-guided deformable alignment (MGDA) module with second-order bidirectional propagation is introduced to align the adjacent cine MRI frames by maximizing spatial-temporal information to alleviate motion artifacts. Finally, the multi-resolution fusion (MRF) module is designed to correct the blur and artifacts generated from alignment operation and obtain the last high-quality reconstructed cardiac images. At an 8$\times$ acceleration rate, the numerical measurements on the ACDC dataset are structural similarity index (SSIM) of 78.40%$\pm$.57%, peak signal-to-noise ratio (PSNR) of 30.46$\pm$1.22dB, and normalized mean squared error (NMSE) of 0.0468$\pm$0.0075. On the ACMRI dataset, the results are SSIM of 87.65%$\pm$4.20%, PSNR of 30.04$\pm$1.18dB, and NMSE of 0.0473$\pm$0.0072. The proposed method exhibits high-quality results with richer details and fewer artifacts for cardiac cine MRI reconstruction on different accelerations.

Legged robot locomotion on sand slopes is challenging due to the complex dynamics of granular media and how the lack of solid surfaces can hinder locomotion. A promising strategy, inspired by ghost crabs and other organisms in nature, is to strategically interact with rocks, debris, and other obstacles to facilitate movement. To provide legged robots with this ability, we present a novel approach that leverages avalanche dynamics to indirectly manipulate objects on a granular slope. We use a Vision Transformer (ViT) to process image representations of granular dynamics and robot excavation actions. The ViT predicts object movement, which we use to determine which leg excavation action to execute. We collect training data from 100 real physical trials and, at test time, deploy our trained model in novel settings. Experimental results suggest that our model can accurately predict object movements and achieve a success rate $\geq 80\%$ in a variety of manipulation tasks with up to four obstacles, and can also generalize to objects with different physics properties. To our knowledge, this is the first paper to leverage granular media avalanche dynamics to indirectly manipulate objects on granular slopes. Supplementary material is available at //sites.google.com/view/grain-corl2024/home.

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose \textit{Entropic Optimal Transport (EOT) eigenmaps}, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align the datasets accordingly in a common embedding space. We interpret our approach as an inter-data variant of the classical Laplacian eigenmaps and diffusion maps embeddings, showing that it enjoys many favorable analogous properties. We then analyze a data-generative model where two observed high-dimensional datasets share latent variables on a common low-dimensional manifold, but each dataset is subject to data-specific translation, scaling, nuisance structures, and noise. We show that in a high-dimensional asymptotic regime, the EOT plan recovers the shared manifold structure by approximating a kernel function evaluated at the locations of the latent variables. Subsequently, we provide a geometric interpretation of our embedding by relating it to the eigenfunctions of population-level operators encoding the density and geometry of the shared manifold. Finally, we showcase the performance of our approach for data integration and embedding through simulations and analyses of real-world biological data, demonstrating its advantages over alternative methods in challenging scenarios.

The problem of computing vertex and edge connectivity of a graph are classical problems in algorithmic graph theory. The focus of this paper is on computing these parameters on embedded graphs. A typical example of an embedded graph is a planar graph which can be drawn with no edge crossings. It has long been known that vertex and edge connectivity of planar embedded graphs can be computed in linear time. Very recently, Biedl and Murali extended the techniques from planar graphs to 1-plane graphs without $\times$-crossings, i.e., crossings whose endpoints induce a matching. While the tools used were novel, they were highly tailored to 1-plane graphs, and do not provide much leeway for further extension. In this paper, we develop alternate techniques that are simpler, have wider applications to near-planar graphs, and can be used to test both vertex and edge connectivity. Our technique works for all those embedded graphs where any pair of crossing edges are connected by a path that, roughly speaking, can be covered with few cells of the drawing. Important examples of such graphs include optimal 2-planar and optimal 3-planar graphs, $d$-map graphs, $d$-framed graphs, graphs with bounded crossing number, and $k$-plane graphs with bounded number of $\times$-crossings.

Consecutive matrix multiplications are commonly used in graph neural networks and sparse linear solvers. These operations frequently access the same matrices for both reading and writing. While reusing these matrices improves data locality, it presents a challenge due to the irregular dependencies between iterations across the two multiplication operations. Existing fusion methods often introduce excessive synchronization overhead or overlapped computations with limited benefits. This paper proposes tile fusion, a runtime approach that fuses tiles of the two matrix-matrix multiplications, where at least one of the involved matrices is sparse. Tile fusion aims to improve data locality while providing sufficient workload for cores in shared-memory multi-core processors. For a pair of matrix-matrix multiplications, tile fusion outperforms unfused baseline and MKL implementations with a geometric mean speedup of 1.97$\times$ 1.64$\times$, respectively, on multi-core CPUs.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.