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Although Graph Neural Networks (GNNs) have exhibited the powerful ability to gather graph-structured information from neighborhood nodes via various message-passing mechanisms, the performance of GNNs is limited by poor generalization and fragile robustness caused by noisy and redundant graph data. As a prominent solution, Graph Augmentation Learning (GAL) has recently received increasing attention. Among prior GAL approaches, edge-dropping methods that randomly remove edges from a graph during training are effective techniques to improve the robustness of GNNs. However, randomly dropping edges often results in bypassing critical edges, consequently weakening the effectiveness of message passing. In this paper, we propose a novel adversarial edge-dropping method (ADEdgeDrop) that leverages an adversarial edge predictor guiding the removal of edges, which can be flexibly incorporated into diverse GNN backbones. Employing an adversarial training framework, the edge predictor utilizes the line graph transformed from the original graph to estimate the edges to be dropped, which improves the interpretability of the edge-dropping method. The proposed ADEdgeDrop is optimized alternately by stochastic gradient descent and projected gradient descent. Comprehensive experiments on six graph benchmark datasets demonstrate that the proposed ADEdgeDrop outperforms state-of-the-art baselines across various GNN backbones, demonstrating improved generalization and robustness.

Graphs with abundant attributes are essential in modeling interconnected entities and improving predictions in various real-world applications. Traditional Graph Neural Networks (GNNs), which are commonly used for modeling attributed graphs, need to be re-trained every time when applied to different graph tasks and datasets. Although the emergence of Large Language Models (LLMs) has introduced a new paradigm in natural language processing, the generative potential of LLMs in graph mining remains largely under-explored. To this end, we propose a novel framework MuseGraph, which seamlessly integrates the strengths of GNNs and LLMs and facilitates a more effective and generic approach for graph mining across different tasks and datasets. Specifically, we first introduce a compact graph description via the proposed adaptive input generation to encapsulate key information from the graph under the constraints of language token limitations. Then, we propose a diverse instruction generation mechanism, which distills the reasoning capabilities from LLMs (e.g., GPT-4) to create task-specific Chain-of-Thought-based instruction packages for different graph tasks. Finally, we propose a graph-aware instruction tuning with a dynamic instruction package allocation strategy across tasks and datasets, ensuring the effectiveness and generalization of the training process. Our experimental results demonstrate significant improvements in different graph tasks, showcasing the potential of our MuseGraph in enhancing the accuracy of graph-oriented downstream tasks while keeping the generation powers of LLMs.

Correspondence pruning aims to establish reliable correspondences between two related images and recover relative camera motion. Existing approaches often employ a progressive strategy to handle the local and global contexts, with a prominent emphasis on transitioning from local to global, resulting in the neglect of interactions between different contexts. To tackle this issue, we propose a parallel context learning strategy that involves acquiring bilateral consensus for the two-view correspondence pruning task. In our approach, we design a distinctive self-attention block to capture global context and parallel process it with the established local context learning module, which enables us to simultaneously capture both local and global consensuses. By combining these local and global consensuses, we derive the required bilateral consensus. We also design a recalibration block, reducing the influence of erroneous consensus information and enhancing the robustness of the model. The culmination of our efforts is the Bilateral Consensus Learning Network (BCLNet), which efficiently estimates camera pose and identifies inliers (true correspondences). Extensive experiments results demonstrate that our network not only surpasses state-of-the-art methods on benchmark datasets but also showcases robust generalization abilities across various feature extraction techniques. Noteworthily, BCLNet obtains 3.98\% mAP5$^{\circ}$ gains over the second best method on unknown outdoor dataset, and obviously accelerates model training speed. The source code will be available at: https://github.com/guobaoxiao/BCLNet.

Most of existing correspondence pruning methods only concentrate on gathering the context information as much as possible while neglecting effective ways to utilize such information. In order to tackle this dilemma, in this paper we propose Graph Context Transformation Network (GCT-Net) enhancing context information to conduct consensus guidance for progressive correspondence pruning. Specifically, we design the Graph Context Enhance Transformer which first generates the graph network and then transforms it into multi-branch graph contexts. Moreover, it employs self-attention and cross-attention to magnify characteristics of each graph context for emphasizing the unique as well as shared essential information. To further apply the recalibrated graph contexts to the global domain, we propose the Graph Context Guidance Transformer. This module adopts a confident-based sampling strategy to temporarily screen high-confidence vertices for guiding accurate classification by searching global consensus between screened vertices and remaining ones. The extensive experimental results on outlier removal and relative pose estimation clearly demonstrate the superior performance of GCT-Net compared to state-of-the-art methods across outdoor and indoor datasets. The source code will be available at: https://github.com/guobaoxiao/GCT-Net/.

As researchers strive to narrow the gap between machine intelligence and human through the development of artificial intelligence technologies, it is imperative that we recognize the critical importance of trustworthiness in open-world, which has become ubiquitous in all aspects of daily life for everyone. However, several challenges may create a crisis of trust in current artificial intelligence systems that need to be bridged: 1) Insufficient explanation of predictive results; 2) Inadequate generalization for learning models; 3) Poor adaptability to uncertain environments. Consequently, we explore a neural program to bridge trustworthiness and open-world learning, extending from single-modal to multi-modal scenarios for readers. 1) To enhance design-level interpretability, we first customize trustworthy networks with specific physical meanings; 2) We then design environmental well-being task-interfaces via flexible learning regularizers for improving the generalization of trustworthy learning; 3) We propose to increase the robustness of trustworthy learning by integrating open-world recognition losses with agent mechanisms. Eventually, we enhance various trustworthy properties through the establishment of design-level explainability, environmental well-being task-interfaces and open-world recognition programs. These designed open-world protocols are applicable across a wide range of surroundings, under open-world multimedia recognition scenarios with significant performance improvements observed.

The current work experimentally studies the complex interaction between underwater explosion (UNDEX) bubbles and a free surface. We aim to reveal the dependence of the associated physics on the key factor, namely, the dimensionless detonation depth $\gamma$ (scaled by the maximum equivalent bubble radius). Four typical bubble behavior patterns are identified with the respective range of $\gamma$: (i) bubble bursting at the free surface, (ii) bubble jetting downward, (iii) neutral collapse of the bubble, and (iv) quasi-free-field motion. By comparison of the jet direction and the migration of the bubble centroid, a critical value of $\gamma$ is vital for ignoring the effects of the free surface on UNDEX bubbles. Good agreements are obtained between the experimental data and the unified theory for bubble dynamics by Zhang et al. Additionally, the dependence of the pressure signals in the flow field on $\gamma$ is investigated. The peak pressure, impulse, and energy dissipation in the UNDEX are investigated.

Graph Convolutional Network (GCN) with the powerful capacity to explore graph-structural data has gained noticeable success in recent years. Nonetheless, most of the existing GCN-based models suffer from the notorious over-smoothing issue, owing to which shallow networks are extensively adopted. This may be problematic for complex graph datasets because a deeper GCN should be beneficial to propagating information across remote neighbors. Recent works have devoted effort to addressing over-smoothing problems, including establishing residual connection structure or fusing predictions from multi-layer models. Because of the indistinguishable embeddings from deep layers, it is reasonable to generate more reliable predictions before conducting the combination of outputs from various layers. In light of this, we propose an Alternating Graph-regularized Neural Network (AGNN) composed of Graph Convolutional Layer (GCL) and Graph Embedding Layer (GEL). GEL is derived from the graph-regularized optimization containing Laplacian embedding term, which can alleviate the over-smoothing problem by periodic projection from the low-order feature space onto the high-order space. With more distinguishable features of distinct layers, an improved Adaboost strategy is utilized to aggregate outputs from each layer, which explores integrated embeddings of multi-hop neighbors. The proposed model is evaluated via a large number of experiments including performance comparison with some multi-layer or multi-order graph neural networks, which reveals the superior performance improvement of AGNN compared with state-of-the-art models.

Heterogeneous graph neural networks aim to discover discriminative node embeddings and relations from multi-relational networks.One challenge of heterogeneous graph learning is the design of learnable meta-paths, which significantly influences the quality of learned embeddings.Thus, in this paper, we propose an Attributed Multi-Order Graph Convolutional Network (AMOGCN), which automatically studies meta-paths containing multi-hop neighbors from an adaptive aggregation of multi-order adjacency matrices. The proposed model first builds different orders of adjacency matrices from manually designed node connections. After that, an intact multi-order adjacency matrix is attached from the automatic fusion of various orders of adjacency matrices. This process is supervised by the node semantic information, which is extracted from the node homophily evaluated by attributes. Eventually, we utilize a one-layer simplifying graph convolutional network with the learned multi-order adjacency matrix, which is equivalent to the cross-hop node information propagation with multi-layer graph neural networks. Substantial experiments reveal that AMOGCN gains superior semi-supervised classification performance compared with state-of-the-art competitors.

Graph convolutional networks (GCNs) have been attracting widespread attentions due to their encouraging performance and powerful generalizations. However, few work provide a general view to interpret various GCNs and guide GCNs' designs. In this paper, by revisiting the original GCN, we induce an interpretable regularizer-centerd optimization framework, in which by building appropriate regularizers we can interpret most GCNs, such as APPNP, JKNet, DAGNN, and GNN-LF/HF. Further, under the proposed framework, we devise a dual-regularizer graph convolutional network (dubbed tsGCN) to capture topological and semantic structures from graph data. Since the derived learning rule for tsGCN contains an inverse of a large matrix and thus is time-consuming, we leverage the Woodbury matrix identity and low-rank approximation tricks to successfully decrease the high computational complexity of computing infinite-order graph convolutions. Extensive experiments on eight public datasets demonstrate that tsGCN achieves superior performance against quite a few state-of-the-art competitors w.r.t. classification tasks., Comment: 15 pages, 12 figures

Multi-view data containing complementary and consensus information can facilitate representation learning by exploiting the intact integration of multi-view features. Because most objects in real world often have underlying connections, organizing multi-view data as heterogeneous graphs is beneficial to extracting latent information among different objects. Due to the powerful capability to gather information of neighborhood nodes, in this paper, we apply Graph Convolutional Network (GCN) to cope with heterogeneous-graph data originating from multi-view data, which is still under-explored in the field of GCN. In order to improve the quality of network topology and alleviate the interference of noises yielded by graph fusion, some methods undertake sorting operations before the graph convolution procedure. These GCN-based methods generally sort and select the most confident neighborhood nodes for each vertex, such as picking the top-k nodes according to pre-defined confidence values. Nonetheless, this is problematic due to the non-differentiable sorting operators and inflexible graph embedding learning, which may result in blocked gradient computations and undesired performance. To cope with these issues, we propose a joint framework dubbed Multi-view Graph Convolutional Network with Differentiable Node Selection (MGCN-DNS), which is constituted of an adaptive graph fusion layer, a graph learning module and a differentiable node selection schema. MGCN-DNS accepts multi-channel graph-structural data as inputs and aims to learn more robust graph fusion through a differentiable neural network. The effectiveness of the proposed method is verified by rigorous comparisons with considerable state-of-the-art approaches in terms of multi-view semi-supervised classification tasks.

In practical applications, multi-view data depicting objectives from assorted perspectives can facilitate the accuracy increase of learning algorithms. However, given multi-view data, there is limited work for learning discriminative node relationships and graph information simultaneously via graph convolutional network that has drawn the attention from considerable researchers in recent years. Most of existing methods only consider the weighted sum of adjacency matrices, yet a joint neural network of both feature and graph fusion is still under-explored. To cope with these issues, this paper proposes a joint deep learning framework called Learnable Graph Convolutional Network and Feature Fusion (LGCN-FF), consisting of two stages: feature fusion network and learnable graph convolutional network. The former aims to learn an underlying feature representation from heterogeneous views, while the latter explores a more discriminative graph fusion via learnable weights and a parametric activation function dubbed Differentiable Shrinkage Activation (DSA) function. The proposed LGCN-FF is validated to be superior to various state-of-the-art methods in multi-view semi-supervised classification.

In this paper we discuss the local discontinuous Galerkin methods coupled with two specific explicit-implicit-null time discretizations for solving one-dimensional nonlinear diffusion problems $U_t=(a(U)U_x)_x$. The basic idea is to add and subtract two equal terms $a_0 U_{xx}$ on the right hand side of the partial differential equation, then to treat the term $a_0 U_{xx}$ implicitly and the other terms $(a(U)U_x)_x-a_0 U_{xx}$ explicitly. We give stability analysis for the method on a simplified model by the aid of energy analysis, which gives a guidance for the choice of $a_0$, i.e, $a_0 \ge \max\{a(u)\}/2$ to ensure the unconditional stability of the first order and second order schemes. The optimal error estimate is also derived for the simplified model, and numerical experiments are given to demonstrate the stability, accuracy and performance of the schemes for nonlinear diffusion equations., Comment: it has been accepted for publication in SCIENCE CHINA Mathematics