Graph Neural Networks (GNNs) have shown remarkable success in learning from graph-structured data. However, their application to directed graphs (digraphs) presents unique challenges, primarily due to the inherent asymmetry in node relationships. Traditional GNNs are adept at capturing unidirectional relations but fall short in encoding the mutual path dependencies between nodes, such as asymmetrical shortest paths typically found in digraphs. Recognizing this gap, we introduce Commute Graph Neural Networks (CGNN), an approach that seamlessly integrates node-wise commute time into the message passing scheme. The cornerstone of CGNN is an efficient method for computing commute time using a newly formulated digraph Laplacian. Commute time is then integrated into the neighborhood aggregation process, with neighbor contributions weighted according to their respective commute time to the central node in each layer. It enables CGNN to directly capture the mutual, asymmetric relationships in digraphs. Extensive experiments on 8 benchmarking datasets confirm the superiority of CGNN against 13 state-of-the-art methods.

Federated Learning (FL) on graph-structured data typically faces non-IID challenges, particularly in scenarios where each client holds a distinct subgraph sampled from a global graph. In this paper, we introduce **Fed**erated learning with **Aux**iliary projections (FedAux), a personalized subgraph FL framework that learns to align, compare, and aggregate heterogeneously distributed local models without sharing raw data or node embeddings. In FedAux, each client jointly trains (i) a local GNN and (ii) a learnable auxiliary projection vector (APV) that differentiably projects node embeddings onto a 1D space. A soft-sorting operation followed by a lightweight 1D convolution refines these embeddings in the ordered space, enabling the APV to effectively capture client-specific information. After local training, these APVs serve as compact signatures that the server uses to compute inter‑client similarities and perform similarity‑weighted parameter mixing, yielding personalized models while preserving cross‑client knowledge transfer. Moreover, we provide rigorous theoretical analysis to establish the convergence and rationality of our design. Empirical evaluations across diverse graph benchmarks demonstrate that FedAux substantially outperforms existing baselines in both accuracy and personalization performance. The code is available at [https://github.com/JhuoW/FedAux](https://github.com/JhuoW/FedAux).

Label imbalance and homophily-heterophily mixture are the fundamental problems encountered when applying Graph Neural Networks (GNNs) to Graph Fraud Detection (GFD) tasks. Existing GNN-based GFD models are designed to augment graph structure to accommodate the inductive bias of GNNs towards homophily, by excluding heterophilic neighbors during message passing. In our work, we argue that the key to applying GNNs for GFD is not to exclude but to {\em distinguish} neighbors with different labels. Grounded in this perspective, we introduce Partitioning Message Passing (PMP), an intuitive yet effective message passing paradigm expressly crafted for GFD. Specifically, in the neighbor aggregation stage of PMP, neighbors with different classes are aggregated with distinct node-specific aggregation functions. By this means, the center node can adaptively adjust the information aggregated from its heterophilic and homophilic neighbors, thus avoiding the model gradient being dominated by benign nodes which occupy the majority of the population. We theoretically establish a connection between the spatial formulation of PMP and spectral analysis to characterize that PMP operates an adaptive node-specific spectral graph filter, which demonstrates the capability of PMP to handle heterophily-homophily mixed graphs. Extensive experimental results show that PMP can significantly boost the performance on GFD tasks.

A challenging task in embodied artificial intelligence is enabling the robot to carry out a navigational task following natural language instruction. In the task, the navigator needs to understand objects, directions, as well as room types, which serve as landmarks for navigation. Although it is easy to encode objects and directions with an external encoder like an object detector, current navigators struggle to encode room type information properly due to the low accuracy offered by existing classifiers. This inadequacy poses confusion that navigators find difficult to overcome. Even humans may sometimes fail to determine the exact type of a room since multiple room types may exist in one panorama. To mitigate this problem, we propose to encode room type information in a prompt manner. Specifically, we first establish multi-modal, learnable prompt pools containing knowledge of room types. By querying the prompt pools, the navigator can obtain room-type prompts of the current view, and incorporate them into the navigator using a prompt-based learning method. Experimental results on the REVERIE, R2R and SOON datasets demonstrate the effectiveness of our approach.

Graph neural networks (GNNs) have been successful in a variety of graph-based applications. Recently, it is shown that capturing long-range relationships between nodes helps improve the performance of GNNs. The phenomenon is mostly confirmed in a supervised learning setting. In this article, inspired by contrastive learning (CL), we propose an unsupervised learning pipeline, in which different types of long-range similarity information are injected into the GNN model in an efficient way. We reconstruct the original graph in feature and topology spaces to generate three augmented views. During training, our model alternately picks an augmented view, and maximizes an agreement between the representations of the view and the original graph. Importantly, we identify the issue of diminishing utility of the augmented views as the model gradually learns useful information from the views. Hence, we propose a view update scheme that adaptively adjusts the augmented views, so that the views can continue to provide new information that helps with CL. The updated augmented views and the original graph are jointly used to train a shared GNN encoder by optimizing an efficient channel-level contrastive objective. We conduct extensive experiments on six assortative graphs and three disassortative graphs, which demonstrate the effectiveness of our method.

We consider graph representation learning in an unsupervised manner. Graph neural networks use neighborhood aggregation as a core component that results in feature smoothing among nodes in proximity. While successful in various prediction tasks, such a paradigm falls short of capturing nodes' similarities over a long distance, which proves to be important for high-quality learning. To tackle this problem, we strengthen the graph with three types of additional graph views, in which each node is directly linked to a set of nodes with the highest similarity in terms of node features, neighborhood features or local structures. Not restricted by connectivity in the original graph, the generated views provide new and complementary perspectives from which to look at the relationship between nodes. Inspired by the recent success of contrastive learning approaches, we propose a self-supervised method that aims to learn node representations by maximizing the agreement between representations across generated views and the original graph, without the requirement of any label information. We also propose a channel-level contrast approach that greatly reduces computation cost. Extensive experiments on six assortative graphs and three disassortative graphs demonstrate the effectiveness of our approach.

We consider the graph similarity computation (GSC) task based on graph edit distance (GED) estimation. State-of-the-art methods treat GSC as a learning-based prediction task using Graph Neural Networks (GNNs). To capture fine-grained interactions between pair-wise graphs, these methods mostly contain a node-level matching module in the end-to-end learning pipeline, which causes high computational costs in both the training and inference stages. We show that the expensive node-to-node matching module is not necessary for GSC, and high-quality learning can be attained with a simple yet powerful regularization technique, which we call the Alignment Regularization (AReg). In the training stage, the AReg term imposes a node-graph correspondence constraint on the GNN encoder. In the inference stage, the graph-level representations learned by the GNN encoder are directly used to compute the similarity score without using AReg again to speed up inference. We further propose a multi-scale GED discriminator to enhance the expressive ability of the learned representations. Extensive experiments on real-world datasets demonstrate the effectiveness, efficiency and transferability of our approach.