Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Study

In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural (integer-order) ordinary differential equation (ODE) models by implementing the time-fractional Caputo derivative. Utilizing fractional calculus allows our model to consider long-term memory during the feature updating process, diverging from the memoryless Markovian updates seen in traditional graph neural ODE models. The superiority of graph neural FDE models over graph neural ODE models has been established in environments free from attacks or perturbations. While traditional graph neural ODE models have been verified to possess a degree of stability and resilience in the presence of adversarial attacks in existing literature, the robustness of graph neural FDE models, especially under adversarial conditions, remains largely unexplored. This paper undertakes a detailed assessment of the robustness of graph neural FDE models. We establish a theoretical foundation outlining the robustness characteristics of graph neural FDE models, highlighting that they maintain more stringent output perturbation bounds in the face of input and graph topology disturbances, compared to their integer-order counterparts. Our empirical evaluations further confirm the enhanced robustness of graph neural FDE models, highlighting their potential in adversarially robust applications.

PosDiffNet: Positional Neural Diffusion for Point Cloud Registration in a Large Field of View with Perturbations

Point cloud registration is a crucial technique in 3D computer vision with a wide range of applications. However, this task can be challenging, particularly in large fields of view with dynamic objects, environmental noise, or other perturbations. To address this challenge, we propose a model called PosDiffNet. Our approach performs hierarchical registration based on window-level, patch-level, and point-level correspondence. We leverage a graph neural partial differential equation (PDE) based on Beltrami flow to obtain high-dimensional features and position embeddings for point clouds. We incorporate position embeddings into a Transformer module based on a neural ordinary differential equation (ODE) to efficiently represent patches within points. We employ the multi-level correspondence derived from the high feature similarity scores to facilitate alignment between point clouds. Subsequently, we use registration methods such as SVD-based algorithms to predict the transformation using corresponding point pairs. We evaluate PosDiffNet on several 3D point cloud datasets, verifying that it achieves state-of-the-art (SOTA) performance for point cloud registration in large fields of view with perturbations. The implementation code of experiments is available at https://github.com/AI-IT-AVs/PosDiffNet.

DistilVPR: Cross-Modal Knowledge Distillation for Visual Place Recognition

The utilization of multi-modal sensor data in visual place recognition (VPR) has demonstrated enhanced performance compared to single-modal counterparts. Nonetheless, integrating additional sensors comes with elevated costs and may not be feasible for systems that demand lightweight operation, thereby impacting the practical deployment of VPR. To address this issue, we resort to knowledge distillation, which empowers single-modal students to learn from cross-modal teachers without introducing additional sensors during inference. Despite the notable advancements achieved by current distillation approaches, the exploration of feature relationships remains an under-explored area. In order to tackle the challenge of cross-modal distillation in VPR, we present DistilVPR, a novel distillation pipeline for VPR. We propose leveraging feature relationships from multiple agents, including self-agents and cross-agents for teacher and student neural networks. Furthermore, we integrate various manifolds, characterized by different space curvatures for exploring feature relationships. This approach enhances the diversity of feature relationships, including Euclidean, spherical, and hyperbolic relationship modules, thereby enhancing the overall representational capacity. The experiments demonstrate that our proposed pipeline achieves state-of-the-art performance compared to other distillation baselines. We also conduct necessary ablation studies to show design effectiveness. The code is released at: https://github.com/sijieaaa/DistilVPR

Image Patch-Matching with Graph-Based Learning in Street Scenes

Matching landmark patches from a real-time image captured by an on-vehicle camera with landmark patches in an image database plays an important role in various computer perception tasks for autonomous driving. Current methods focus on local matching for regions of interest and do not take into account spatial neighborhood relationships among the image patches, which typically correspond to objects in the environment. In this paper, we construct a spatial graph with the graph vertices corresponding to patches and edges capturing the spatial neighborhood information. We propose a joint feature and metric learning model with graph-based learning. We provide a theoretical basis for the graph-based loss by showing that the information distance between the distributions conditioned on matched and unmatched pairs is maximized under our framework. We evaluate our model using several street-scene datasets and demonstrate that our approach achieves state-of-the-art matching results.

RobustMat: Neural Diffusion for Street Landmark Patch Matching under Challenging Environments

For autonomous vehicles (AVs), visual perception techniques based on sensors like cameras play crucial roles in information acquisition and processing. In various computer perception tasks for AVs, it may be helpful to match landmark patches taken by an onboard camera with other landmark patches captured at a different time or saved in a street scene image database. To perform matching under challenging driving environments caused by changing seasons, weather, and illumination, we utilize the spatial neighborhood information of each patch. We propose an approach, named RobustMat, which derives its robustness to perturbations from neural differential equations. A convolutional neural ODE diffusion module is used to learn the feature representation for the landmark patches. A graph neural PDE diffusion module then aggregates information from neighboring landmark patches in the street scene. Finally, feature similarity learning outputs the final matching score. Our approach is evaluated on several street scene datasets and demonstrated to achieve state-of-the-art matching results under environmental perturbations.

SGA: A Graph Augmentation Method for Signed Graph Neural Networks

Signed Graph Neural Networks (SGNNs) are vital for analyzing complex patterns in real-world signed graphs containing positive and negative links. However, three key challenges hinder current SGNN-based signed graph representation learning: sparsity in signed graphs leaves latent structures undiscovered, unbalanced triangles pose representation difficulties for SGNN models, and real-world signed graph datasets often lack supplementary information like node labels and features. These constraints limit the potential of SGNN-based representation learning. We address these issues with data augmentation techniques. Despite many graph data augmentation methods existing for unsigned graphs, none are tailored for signed graphs. Our paper introduces the novel Signed Graph Augmentation framework (SGA), comprising three main components. First, we employ the SGNN model to encode the signed graph, extracting latent structural information for candidate augmentation structures. Second, we evaluate these candidate samples (edges) and select the most beneficial ones for modifying the original training set. Third, we propose a novel augmentation perspective that assigns varying training difficulty to training samples, enabling the design of a new training strategy. Extensive experiments on six real-world datasets (Bitcoin-alpha, Bitcoin-otc, Epinions, Slashdot, Wiki-elec, and Wiki-RfA) demonstrate that SGA significantly improves performance across multiple benchmarks. Our method outperforms baselines by up to 22.2% in AUC for SGCN on Wiki-RfA, 33.3% in F1-binary, 48.8% in F1-micro, and 36.3% in F1-macro for GAT on Bitcoin-alpha in link sign prediction.

Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at https://github.com/zknus/NeurIPS-2023-HANG-Robustness.

Enhancing Student Performance Prediction on Learnersourced Questions with SGNN-LLM Synergy

As an emerging education strategy, learnersourcing offers the potential for personalized learning content creation, but also grapples with the challenge of predicting student performance due to inherent noise in student-generated data. While graph-based methods excel in capturing dense learner-question interactions, they falter in cold start scenarios, characterized by limited interactions, as seen when questions lack substantial learner responses. In response, we introduce an innovative strategy that synergizes the potential of integrating Signed Graph Neural Networks (SGNNs) and Large Language Model (LLM) embeddings. Our methodology employs a signed bipartite graph to comprehensively model student answers, complemented by a contrastive learning framework that enhances noise resilience. Furthermore, LLM's contribution lies in generating foundational question embeddings, proving especially advantageous in addressing cold start scenarios characterized by limited graph data interactions. Validation across five real-world datasets sourced from the PeerWise platform underscores our approach's effectiveness. Our method outperforms baselines, showcasing enhanced predictive accuracy and robustness.

Graph Neural Convection-Diffusion with Heterophily

Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at \url{https://github.com/zknus/Graph-Diffusion-CDE}.

Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at \url{https://github.com/zknus/Hamiltonian-GNN}.