Daily Papers

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of labels, it is impossible to first identify a graph as homophilic or heterophilic before a suitable GNN model can be found. Hence, clustering on real-world graph with various levels of homophily poses a new challenge to the graph research community. To fill this gap, we propose a novel graph clustering method, which contains three key components: graph reconstruction, a mixed filter, and dual graph clustering network. To be graph-agnostic, we empirically construct two graphs which are high homophily and heterophily from each data. The mixed filter based on the new graphs extracts both low-frequency and high-frequency information. To reduce the adverse coupling between node attribute and topological structure, we separately map them into two subspaces in dual graph clustering network. Extensive experiments on 11 benchmark graphs demonstrate our promising performance. In particular, our method dominates others on heterophilic graphs.

Graph Neural Networks (GNNs) have emerged as powerful tools to encode graph-structured data. Due to their broad applications, there is an increasing need to develop tools to explain how GNNs make decisions given graph-structured data. Existing learning-based GNN explanation approaches are task-specific in training and hence suffer from crucial drawbacks. Specifically, they are incapable of producing explanations for a multitask prediction model with a single explainer. They are also unable to provide explanations in cases where the GNN is trained in a self-supervised manner, and the resulting representations are used in future downstream tasks. To address these limitations, we propose a Task-Agnostic GNN Explainer (TAGE) that is independent of downstream models and trained under self-supervision with no knowledge of downstream tasks. TAGE enables the explanation of GNN embedding models with unseen downstream tasks and allows efficient explanation of multitask models. Our extensive experiments show that TAGE can significantly speed up the explanation efficiency by using the same model to explain predictions for multiple downstream tasks while achieving explanation quality as good as or even better than current state-of-the-art GNN explanation approaches. Our code is pubicly available as part of the DIG library at https://github.com/divelab/DIG/tree/main/dig/xgraph/TAGE/.

GNNs, like other deep learning models, are data and computation hungry. There is a pressing need to scale training of GNNs on large datasets to enable their usage on low-resource environments. Graph distillation is an effort in that direction with the aim to construct a smaller synthetic training set from the original training data without significantly compromising model performance. While initial efforts are promising, this work is motivated by two key observations: (1) Existing graph distillation algorithms themselves rely on training with the full dataset, which undermines the very premise of graph distillation. (2) The distillation process is specific to the target GNN architecture and hyper-parameters and thus not robust to changes in the modeling pipeline. We circumvent these limitations by designing a distillation algorithm called Mirage for graph classification. Mirage is built on the insight that a message-passing GNN decomposes the input graph into a multiset of computation trees. Furthermore, the frequency distribution of computation trees is often skewed in nature, enabling us to condense this data into a concise distilled summary. By compressing the computation data itself, as opposed to emulating gradient flows on the original training set-a prevalent approach to date-Mirage transforms into an unsupervised and architecture-agnostic distillation algorithm. Extensive benchmarking on real-world datasets underscores Mirage's superiority, showcasing enhanced generalization accuracy, data compression, and distillation efficiency when compared to state-of-the-art baselines.

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

Graph representation learning is a fundamental research theme and can be generalized to benefit multiple downstream tasks from the node and link levels to the higher graph level. In practice, it is desirable to develop task-agnostic general graph representation learning methods that are typically trained in an unsupervised manner. Related research reveals that the power of graph representation learning methods depends on whether they can differentiate distinct graph structures as different embeddings and map isomorphic graphs to consistent embeddings (i.e., the isomorphic consistency of graph models). However, for task-agnostic general graph representation learning, existing unsupervised graph models, represented by the variational graph auto-encoders (VGAEs), can only keep the isomorphic consistency within the subgraphs of 1-hop neighborhoods and thus usually manifest inferior performance on the more difficult higher-level tasks. To overcome the limitations of existing unsupervised methods, in this paper, we propose the Isomorphic-Consistent VGAE (IsoC-VGAE) for multi-level task-agnostic graph representation learning. We first devise a decoding scheme to provide a theoretical guarantee of keeping the isomorphic consistency under the settings of unsupervised learning. We then propose the Inverse Graph Neural Network (Inv-GNN) decoder as its intuitive realization, which trains the model via reconstructing the GNN node embeddings with multi-hop neighborhood information, so as to maintain the high-order isomorphic consistency within the VGAE framework. We conduct extensive experiments on the representative graph learning tasks at different levels, including node classification, link prediction and graph classification, and the results verify that our proposed model generally outperforms both the state-of-the-art unsupervised methods and representative supervised methods.

Large Language Models (LLMs) have shown strong inductive reasoning ability across various domains, but their reliability is hindered by the outdated knowledge and hallucinations. Retrieval-Augmented Generation mitigates these issues by grounding LLMs with external knowledge; however, most existing RAG pipelines rely on unstructured text, limiting interpretability and structured reasoning. Knowledge graphs, which represent facts as relational triples, offer a more structured and compact alternative. Recent studies have explored integrating knowledge graphs with LLMs for knowledge graph question answering (KGQA), with a significant proportion adopting the retrieve-then-reasoning paradigm. In this framework, graph-based retrievers have demonstrated strong empirical performance, yet they still face challenges in generalization ability. In this work, we propose RAPL, a novel framework for efficient and effective graph retrieval in KGQA. RAPL addresses these limitations through three aspects: (1) a two-stage labeling strategy that combines heuristic signals with parametric models to provide causally grounded supervision; (2) a model-agnostic graph transformation approach to capture both intra- and inter-triple interactions, thereby enhancing representational capacity; and (3) a path-based reasoning strategy that facilitates learning from the injected rational knowledge, and supports downstream reasoner through structured inputs. Empirically, RAPL outperforms state-of-the-art methods by 2.66%-20.34%, and significantly reduces the performance gap between smaller and more powerful LLM-based reasoners, as well as the gap under cross-dataset settings, highlighting its superior retrieval capability and generalizability. Codes are available at: https://github.com/tianyao-aka/RAPL.

Geometric Deep Learning has recently attracted significant interest in a wide range of machine learning fields, including document analysis. The application of Graph Neural Networks (GNNs) has become crucial in various document-related tasks since they can unravel important structural patterns, fundamental in key information extraction processes. Previous works in the literature propose task-driven models and do not take into account the full power of graphs. We propose Doc2Graph, a task-agnostic document understanding framework based on a GNN model, to solve different tasks given different types of documents. We evaluated our approach on two challenging datasets for key information extraction in form understanding, invoice layout analysis and table detection. Our code is freely accessible on https://github.com/andreagemelli/doc2graph.

Traditional 2D pose estimation models are limited by their category-specific design, making them suitable only for predefined object categories. This restriction becomes particularly challenging when dealing with novel objects due to the lack of relevant training data. To address this limitation, category-agnostic pose estimation (CAPE) was introduced. CAPE aims to enable keypoint localization for arbitrary object categories using a single model, requiring minimal support images with annotated keypoints. This approach not only enables object pose generation based on arbitrary keypoint definitions but also significantly reduces the associated costs, paving the way for versatile and adaptable pose estimation applications. We present a novel approach to CAPE that leverages the inherent geometrical relations between keypoints through a newly designed Graph Transformer Decoder. By capturing and incorporating this crucial structural information, our method enhances the accuracy of keypoint localization, marking a significant departure from conventional CAPE techniques that treat keypoints as isolated entities. We validate our approach on the MP-100 benchmark, a comprehensive dataset comprising over 20,000 images spanning more than 100 categories. Our method outperforms the prior state-of-the-art by substantial margins, achieving remarkable improvements of 2.16% and 1.82% under 1-shot and 5-shot settings, respectively. Furthermore, our method's end-to-end training demonstrates both scalability and efficiency compared to previous CAPE approaches.

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches rely on various local heuristics for enforcing the acyclicity constraint. In this paper, we introduce a fundamentally different strategy: We formulate the structure learning problem as a purely continuous optimization problem over real matrices that avoids this combinatorial constraint entirely. This is achieved by a novel characterization of acyclicity that is not only smooth but also exact. The resulting problem can be efficiently solved by standard numerical algorithms, which also makes implementation effortless. The proposed method outperforms existing ones, without imposing any structural assumptions on the graph such as bounded treewidth or in-degree. Code implementing the proposed algorithm is open-source and publicly available at https://github.com/xunzheng/notears.

Programming languages possess rich semantic information such as data flow that is represented by graphs and not available from the surface form of source code. Recent code language models have scaled to billions of parameters, but model source code solely as text tokens while ignoring any other structural information. Conversely, models that do encode structural information of code make modifications to the Transformer architecture, limiting their scale and compatibility with pretrained LLMs. In this work, we take the best of both worlds with GALLa - Graph Aligned Large Language Model. GALLa utilizes graph neural networks and cross-modal alignment technologies to inject the structural information of code into LLMs as an auxiliary task during finetuning. This framework is both model-agnostic and task-agnostic, as it can be applied to any code LLM for any code downstream task, and requires the structural graph data only at training time from a corpus unrelated to the finetuning data, while incurring no cost at inference time over the baseline LLM. Experiments on five code tasks with four different baseline LLMs ranging in size from 350M to 8B validate the effectiveness of GALLa, demonstrating consistent improvement over the baseline, even for powerful models such as LLaMA3.

Learning a shared policy that guides the locomotion of different agents is of core interest in Reinforcement Learning (RL), which leads to the study of morphology-agnostic RL. However, existing benchmarks are highly restrictive in the choice of starting point and target point, constraining the movement of the agents within 2D space. In this work, we propose a novel setup for morphology-agnostic RL, dubbed Subequivariant Graph RL in 3D environments (3D-SGRL). Specifically, we first introduce a new set of more practical yet challenging benchmarks in 3D space that allows the agent to have full Degree-of-Freedoms to explore in arbitrary directions starting from arbitrary configurations. Moreover, to optimize the policy over the enlarged state-action space, we propose to inject geometric symmetry, i.e., subequivariance, into the modeling of the policy and Q-function such that the policy can generalize to all directions, improving exploration efficiency. This goal is achieved by a novel SubEquivariant Transformer (SET) that permits expressive message exchange. Finally, we evaluate the proposed method on the proposed benchmarks, where our method consistently and significantly outperforms existing approaches on single-task, multi-task, and zero-shot generalization scenarios. Extensive ablations are also conducted to verify our design. Code and videos are available on our project page: https://alpc91.github.io/SGRL/.

Graph Neural Networks (GNNs) are a powerful tool for machine learning on graphs.GNNs combine node feature information with the graph structure by recursively passing neural messages along edges of the input graph. However, incorporating both graph structure and feature information leads to complex models, and explaining predictions made by GNNs remains unsolved. Here we propose GNNExplainer, the first general, model-agnostic approach for providing interpretable explanations for predictions of any GNN-based model on any graph-based machine learning task. Given an instance, GNNExplainer identifies a compact subgraph structure and a small subset of node features that have a crucial role in GNN's prediction. Further, GNNExplainer can generate consistent and concise explanations for an entire class of instances. We formulate GNNExplainer as an optimization task that maximizes the mutual information between a GNN's prediction and distribution of possible subgraph structures. Experiments on synthetic and real-world graphs show that our approach can identify important graph structures as well as node features, and outperforms baselines by 17.1% on average. GNNExplainer provides a variety of benefits, from the ability to visualize semantically relevant structures to interpretability, to giving insights into errors of faulty GNNs.

Graph Neural Networks (GNNs) are a powerful technique for machine learning on graph-structured data, yet they pose challenges in interpretability. Existing GNN explanation methods usually yield technical outputs, such as subgraphs and feature importance scores, that are difficult for non-data scientists to understand and thereby violate the purpose of explanations. Motivated by recent Explainable AI (XAI) research, we propose GraphXAIN, a method that generates natural language narratives explaining GNN predictions. GraphXAIN is a model- and explainer-agnostic method that uses Large Language Models (LLMs) to translate explanatory subgraphs and feature importance scores into coherent, story-like explanations of GNN decision-making processes. Evaluations on real-world datasets demonstrate GraphXAIN's ability to improve graph explanations. A survey of machine learning researchers and practitioners reveals that GraphXAIN enhances four explainability dimensions: understandability, satisfaction, convincingness, and suitability for communicating model predictions. When combined with another graph explainer method, GraphXAIN further improves trustworthiness, insightfulness, confidence, and usability. Notably, 95% of participants found GraphXAIN to be a valuable addition to the GNN explanation method. By incorporating natural language narratives, our approach serves both graph practitioners and non-expert users by providing clearer and more effective explanations.

Graph unlearning has emerged as a pivotal method to delete information from a pre-trained graph neural network (GNN). One may delete nodes, a class of nodes, edges, or a class of edges. An unlearning method enables the GNN model to comply with data protection regulations (i.e., the right to be forgotten), adapt to evolving data distributions, and reduce the GPU-hours carbon footprint by avoiding repetitive retraining. Existing partitioning and aggregation-based methods have limitations due to their poor handling of local graph dependencies and additional overhead costs. More recently, GNNDelete offered a model-agnostic approach that alleviates some of these issues. Our work takes a novel approach to address these challenges in graph unlearning through knowledge distillation, as it distills to delete in GNN (D2DGN). It is a model-agnostic distillation framework where the complete graph knowledge is divided and marked for retention and deletion. It performs distillation with response-based soft targets and feature-based node embedding while minimizing KL divergence. The unlearned model effectively removes the influence of deleted graph elements while preserving knowledge about the retained graph elements. D2DGN surpasses the performance of existing methods when evaluated on various real-world graph datasets by up to 43.1% (AUC) in edge and node unlearning tasks. Other notable advantages include better efficiency, better performance in removing target elements, preservation of performance for the retained elements, and zero overhead costs. Notably, our D2DGN surpasses the state-of-the-art GNNDelete in AUC by 2.4%, improves membership inference ratio by +1.3, requires 10.2times10^6 fewer FLOPs per forward pass and up to 3.2times faster.

Scene Graph Generation (SGG) aims to detect all the visual relation triplets <sub, pred, obj> in a given image. With the emergence of various advanced techniques for better utilizing both the intrinsic and extrinsic information in each relation triplet, SGG has achieved great progress over the recent years. However, due to the ubiquitous long-tailed predicate distributions, today's SGG models are still easily biased to the head predicates. Currently, the most prevalent debiasing solutions for SGG are re-balancing methods, e.g., changing the distributions of original training samples. In this paper, we argue that all existing re-balancing strategies fail to increase the diversity of the relation triplet features of each predicate, which is critical for robust SGG. To this end, we propose a novel Compositional Feature Augmentation (CFA) strategy, which is the first unbiased SGG work to mitigate the bias issue from the perspective of increasing the diversity of triplet features. Specifically, we first decompose each relation triplet feature into two components: intrinsic feature and extrinsic feature, which correspond to the intrinsic characteristics and extrinsic contexts of a relation triplet, respectively. Then, we design two different feature augmentation modules to enrich the feature diversity of original relation triplets by replacing or mixing up either their intrinsic or extrinsic features from other samples. Due to its model-agnostic nature, CFA can be seamlessly incorporated into various SGG frameworks. Extensive ablations have shown that CFA achieves a new state-of-the-art performance on the trade-off between different metrics.

The goal of this paper is to detect objects by exploiting their interrelationships. Contrary to existing methods, which learn objects and relations separately, our key idea is to learn the object-relation distribution jointly. We first propose a novel way of creating a graphical representation of an image from inter-object relation priors and initial class predictions, we call a context-likelihood graph. We then learn the joint distribution with an energy-based modeling technique which allows to sample and refine the context-likelihood graph iteratively for a given image. Our formulation of jointly learning the distribution enables us to generate a more accurate graph representation of an image which leads to a better object detection performance. We demonstrate the benefits of our context-likelihood graph formulation and the energy-based graph refinement via experiments on the Visual Genome and MS-COCO datasets where we achieve a consistent improvement over object detectors like DETR and Faster-RCNN, as well as alternative methods modeling object interrelationships separately. Our method is detector agnostic, end-to-end trainable, and especially beneficial for rare object classes.

Human mobility prediction is a fundamental task essential for various applications in urban planning, location-based services and intelligent transportation systems. Existing methods often ignore activity information crucial for reasoning human preferences and routines, or adopt a simplified representation of the dependencies between time, activities and locations. To address these issues, we present Hierarchical Graph Attention Recurrent Network (HGARN) for human mobility prediction. Specifically, we construct a hierarchical graph based on past mobility records and employ a Hierarchical Graph Attention Module to capture complex time-activity-location dependencies. This way, HGARN can learn representations with rich human travel semantics to model user preferences at the global level. We also propose a model-agnostic history-enhanced confidence (MAHEC) label to incorporate each user's individual-level preferences. Finally, we introduce a Temporal Module, which employs recurrent structures to jointly predict users' next activities and their associated locations, with the former used as an auxiliary task to enhance the latter prediction. For model evaluation, we test the performance of HGARN against existing state-of-the-art methods in both the recurring (i.e., returning to a previously visited location) and explorative (i.e., visiting a new location) settings. Overall, HGARN outperforms other baselines significantly in all settings based on two real-world human mobility data benchmarks. These findings confirm the important role that human activities play in determining mobility decisions, illustrating the need to develop activity-aware intelligent transportation systems. Source codes of this study are available at https://github.com/YihongT/HGARN.

Identification and categorization of social media posts generated during disasters are crucial to reduce the sufferings of the affected people. However, lack of labeled data is a significant bottleneck in learning an effective categorization system for a disaster. This motivates us to study the problem as unsupervised domain adaptation (UDA) between a previous disaster with labeled data (source) and a current disaster (target). However, if the amount of labeled data available is limited, it restricts the learning capabilities of the model. To handle this challenge, we utilize limited labeled data along with abundantly available unlabeled data, generated during a source disaster to propose a novel two-part graph neural network. The first-part extracts domain-agnostic global information by constructing a token level graph across domains and the second-part preserves local instance-level semantics. In our experiments, we show that the proposed method outperforms state-of-the-art techniques by 2.74% weighted F_1 score on average on two standard public dataset in the area of disaster management. We also report experimental results for granular actionable multi-label classification datasets in disaster domain for the first time, on which we outperform BERT by 3.00% on average w.r.t weighted F_1. Additionally, we show that our approach can retain performance when very limited labeled data is available.

Category-Agnostic Pose Estimation (CAPE) localizes keypoints across diverse object categories with a single model, using one or a few annotated support images. Recent works have shown that using a pose graph (i.e., treating keypoints as nodes in a graph rather than isolated points) helps handle occlusions and break symmetry. However, these methods assume a static pose graph with equal-weight edges, leading to suboptimal results. We introduce EdgeCape, a novel framework that overcomes these limitations by predicting the graph's edge weights which optimizes localization. To further leverage structural priors, we propose integrating Markovian Structural Bias, which modulates the self-attention interaction between nodes based on the number of hops between them. We show that this improves the model's ability to capture global spatial dependencies. Evaluated on the MP-100 benchmark, which includes 100 categories and over 20K images, EdgeCape achieves state-of-the-art results in the 1-shot setting and leads among similar-sized methods in the 5-shot setting, significantly improving keypoint localization accuracy. Our code is publicly available.

We present a novel meta-learning approach for 6D pose estimation on unknown objects. In contrast to ``instance-level" and ``category-level" pose estimation methods, our algorithm learns object representation in a category-agnostic way, which endows it with strong generalization capabilities across object categories. Specifically, we employ a neural process-based meta-learning approach to train an encoder to capture texture and geometry of an object in a latent representation, based on very few RGB-D images and ground-truth keypoints. The latent representation is then used by a simultaneously meta-trained decoder to predict the 6D pose of the object in new images. Furthermore, we propose a novel geometry-aware decoder for the keypoint prediction using a Graph Neural Network (GNN), which explicitly takes geometric constraints specific to each object into consideration. To evaluate our algorithm, extensive experiments are conducted on the \linemod dataset, and on our new fully-annotated synthetic datasets generated from Multiple Categories in Multiple Scenes (MCMS). Experimental results demonstrate that our model performs well on unseen objects with very different shapes and appearances. Remarkably, our model also shows robust performance on occluded scenes although trained fully on data without occlusion. To our knowledge, this is the first work exploring cross-category level 6D pose estimation.

Conventional 2D pose estimation models are constrained by their design to specific object categories. This limits their applicability to predefined objects. To overcome these limitations, category-agnostic pose estimation (CAPE) emerged as a solution. CAPE aims to facilitate keypoint localization for diverse object categories using a unified model, which can generalize from minimal annotated support images. Recent CAPE works have produced object poses based on arbitrary keypoint definitions annotated on a user-provided support image. Our work departs from conventional CAPE methods, which require a support image, by adopting a text-based approach instead of the support image. Specifically, we use a pose-graph, where nodes represent keypoints that are described with text. This representation takes advantage of the abstraction of text descriptions and the structure imposed by the graph. Our approach effectively breaks symmetry, preserves structure, and improves occlusion handling. We validate our novel approach using the MP-100 benchmark, a comprehensive dataset spanning over 100 categories and 18,000 images. Under a 1-shot setting, our solution achieves a notable performance boost of 1.07\%, establishing a new state-of-the-art for CAPE. Additionally, we enrich the dataset by providing text description annotations, further enhancing its utility for future research.

The scene graph generation (SGG) task involves detecting objects within an image and predicting predicates that represent the relationships between the objects. However, in SGG benchmark datasets, each subject-object pair is annotated with a single predicate even though a single predicate may exhibit diverse semantics (i.e., semantic diversity), existing SGG models are trained to predict the one and only predicate for each pair. This in turn results in the SGG models to overlook the semantic diversity that may exist in a predicate, thus leading to biased predictions. In this paper, we propose a novel model-agnostic Semantic Diversity-aware Prototype-based Learning (DPL) framework that enables unbiased predictions based on the understanding of the semantic diversity of predicates. Specifically, DPL learns the regions in the semantic space covered by each predicate to distinguish among the various different semantics that a single predicate can represent. Extensive experiments demonstrate that our proposed model-agnostic DPL framework brings significant performance improvement on existing SGG models, and also effectively understands the semantic diversity of predicates.

Long-range dependencies are critical for effective graph representation learning, yet most existing datasets focus on small graphs tailored to inductive tasks, offering limited insight into long-range interactions. Current evaluations primarily compare models employing global attention (e.g., graph transformers) with those using local neighborhood aggregation (e.g., message-passing neural networks) without a direct measurement of long-range dependency. In this work, we introduce City-Networks, a novel large-scale transductive learning dataset derived from real-world city roads. This dataset features graphs with over 10^5 nodes and significantly larger diameters than those in existing benchmarks, naturally embodying long-range information. We annotate the graphs using an eccentricity-based approach, ensuring that the classification task inherently requires information from distant nodes. Furthermore, we propose a model-agnostic measurement based on the Jacobians of neighbors from distant hops, offering a principled quantification of long-range dependencies. Finally, we provide theoretical justifications for both our dataset design and the proposed measurement - particularly by focusing on over-smoothing and influence score dilution - which establishes a robust foundation for further exploration of long-range interactions in graph neural networks.

Compressing a predefined deep neural network (DNN) into a compact sub-network with competitive performance is crucial in the efficient machine learning realm. This topic spans various techniques, from structured pruning to neural architecture search, encompassing both pruning and erasing operators perspectives. Despite advancements, existing methods suffers from complex, multi-stage processes that demand substantial engineering and domain knowledge, limiting their broader applications. We introduce the third-generation Only-Train-Once (OTOv3), which first automatically trains and compresses a general DNN through pruning and erasing operations, creating a compact and competitive sub-network without the need of fine-tuning. OTOv3 simplifies and automates the training and compression process, minimizes the engineering efforts required from users. It offers key technological advancements: (i) automatic search space construction for general DNNs based on dependency graph analysis; (ii) Dual Half-Space Projected Gradient (DHSPG) and its enhanced version with hierarchical search (H2SPG) to reliably solve (hierarchical) structured sparsity problems and ensure sub-network validity; and (iii) automated sub-network construction using solutions from DHSPG/H2SPG and dependency graphs. Our empirical results demonstrate the efficacy of OTOv3 across various benchmarks in structured pruning and neural architecture search. OTOv3 produces sub-networks that match or exceed the state-of-the-arts. The source code will be available at https://github.com/tianyic/only_train_once.

Multimodal contrastive learning aims to train a general-purpose feature extractor, such as CLIP, on vast amounts of raw, unlabeled paired image-text data. This can greatly benefit various complex downstream tasks, including cross-modal image-text retrieval and image classification. Despite its promising prospect, the security issue of cross-modal pre-trained encoder has not been fully explored yet, especially when the pre-trained encoder is publicly available for commercial use. In this work, we propose AdvCLIP, the first attack framework for generating downstream-agnostic adversarial examples based on cross-modal pre-trained encoders. AdvCLIP aims to construct a universal adversarial patch for a set of natural images that can fool all the downstream tasks inheriting the victim cross-modal pre-trained encoder. To address the challenges of heterogeneity between different modalities and unknown downstream tasks, we first build a topological graph structure to capture the relevant positions between target samples and their neighbors. Then, we design a topology-deviation based generative adversarial network to generate a universal adversarial patch. By adding the patch to images, we minimize their embeddings similarity to different modality and perturb the sample distribution in the feature space, achieving unviersal non-targeted attacks. Our results demonstrate the excellent attack performance of AdvCLIP on two types of downstream tasks across eight datasets. We also tailor three popular defenses to mitigate AdvCLIP, highlighting the need for new defense mechanisms to defend cross-modal pre-trained encoders.

This work presents UNO, a unified monocular visual odometry framework that enables robust and adaptable pose estimation across diverse environments, platforms, and motion patterns. Unlike traditional methods that rely on deployment-specific tuning or predefined motion priors, our approach generalizes effectively across a wide range of real-world scenarios, including autonomous vehicles, aerial drones, mobile robots, and handheld devices. To this end, we introduce a Mixture-of-Experts strategy for local state estimation, with several specialized decoders that each handle a distinct class of ego-motion patterns. Moreover, we introduce a fully differentiable Gumbel-Softmax module that constructs a robust inter-frame correlation graph, selects the optimal expert decoder, and prunes erroneous estimates. These cues are then fed into a unified back-end that combines pre-trained, scale-independent depth priors with a lightweight bundling adjustment to enforce geometric consistency. We extensively evaluate our method on three major benchmark datasets: KITTI (outdoor/autonomous driving), EuRoC-MAV (indoor/aerial drones), and TUM-RGBD (indoor/handheld), demonstrating state-of-the-art performance.

We propose a simple approach for weighting self-connecting edges in a Graph Convolutional Network (GCN) and show its impact on depression detection from transcribed clinical interviews. To this end, we use a GCN for modeling non-consecutive and long-distance semantics to classify the transcriptions into depressed or control subjects. The proposed method aims to mitigate the limiting assumptions of locality and the equal importance of self-connections vs. edges to neighboring nodes in GCNs, while preserving attractive features such as low computational cost, data agnostic, and interpretability capabilities. We perform an exhaustive evaluation in two benchmark datasets. Results show that our approach consistently outperforms the vanilla GCN model as well as previously reported results, achieving an F1=0.84 on both datasets. Finally, a qualitative analysis illustrates the interpretability capabilities of the proposed approach and its alignment with previous findings in psychology.

Scene Graph Generation (SGG) aims to extract <subject, predicate, object> relationships in images for vision understanding. Although recent works have made steady progress on SGG, they still suffer long-tail distribution issues that tail-predicates are more costly to train and hard to distinguish due to a small amount of annotated data compared to frequent predicates. Existing re-balancing strategies try to handle it via prior rules but are still confined to pre-defined conditions, which are not scalable for various models and datasets. In this paper, we propose a Cross-modal prediCate boosting (CaCao) framework, where a visually-prompted language model is learned to generate diverse fine-grained predicates in a low-resource way. The proposed CaCao can be applied in a plug-and-play fashion and automatically strengthen existing SGG to tackle the long-tailed problem. Based on that, we further introduce a novel Entangled cross-modal prompt approach for open-world predicate scene graph generation (Epic), where models can generalize to unseen predicates in a zero-shot manner. Comprehensive experiments on three benchmark datasets show that CaCao consistently boosts the performance of multiple scene graph generation models in a model-agnostic way. Moreover, our Epic achieves competitive performance on open-world predicate prediction. The data and code for this paper are publicly available.

Scene graph generation (SGG) models have suffered from inherent problems regarding the benchmark datasets such as the long-tailed predicate distribution and missing annotation problems. In this work, we aim to alleviate the long-tailed problem of SGG by utilizing unannotated triplets. To this end, we introduce a Self-Training framework for SGG (ST-SGG) that assigns pseudo-labels for unannotated triplets based on which the SGG models are trained. While there has been significant progress in self-training for image recognition, designing a self-training framework for the SGG task is more challenging due to its inherent nature such as the semantic ambiguity and the long-tailed distribution of predicate classes. Hence, we propose a novel pseudo-labeling technique for SGG, called Class-specific Adaptive Thresholding with Momentum (CATM), which is a model-agnostic framework that can be applied to any existing SGG models. Furthermore, we devise a graph structure learner (GSL) that is beneficial when adopting our proposed self-training framework to the state-of-the-art message-passing neural network (MPNN)-based SGG models. Our extensive experiments verify the effectiveness of ST-SGG on various SGG models, particularly in enhancing the performance on fine-grained predicate classes.

The expressivity of Graph Neural Networks (GNNs) is dependent on the aggregation functions they employ. Theoretical works have pointed towards Sum aggregation GNNs subsuming every other GNNs, while certain practical works have observed a clear advantage to using Mean and Max. An examination of the theoretical guarantee identifies two caveats. First, it is size-restricted, that is, the power of every specific GNN is limited to graphs of a specific size. Successfully processing larger graphs may require an other GNN, and so on. Second, it concerns the power to distinguish non-isomorphic graphs, not the power to approximate general functions on graphs, and the former does not necessarily imply the latter. It is desired that a GNN's usability will not be limited to graphs of any specific size. Therefore, we explore the realm of unrestricted-size expressivity. We prove that basic functions, which can be computed exactly by Mean or Max GNNs, are inapproximable by any Sum GNN. We prove that under certain restrictions, every Mean or Max GNN can be approximated by a Sum GNN, but even there, a combination of (Sum, [Mean/Max]) is more expressive than Sum alone. Lastly, we prove further expressivity limitations for GNNs with a broad class of aggregations.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 14 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96\%.

Node classification is a classical graph machine learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs where edges tend to connect nodes of the same class. Graphs without this property are called heterophilous, and it is typically assumed that specialized methods are required to achieve strong performance on such graphs. In this work, we challenge this assumption. First, we show that the standard datasets used for evaluating heterophily-specific models have serious drawbacks, making results obtained by using them unreliable. The most significant of these drawbacks is the presence of a large number of duplicate nodes in the datasets Squirrel and Chameleon, which leads to train-test data leakage. We show that removing duplicate nodes strongly affects GNN performance on these datasets. Then, we propose a set of heterophilous graphs of varying properties that we believe can serve as a better benchmark for evaluating the performance of GNNs under heterophily. We show that standard GNNs achieve strong results on these heterophilous graphs, almost always outperforming specialized models. Our datasets and the code for reproducing our experiments are available at https://github.com/yandex-research/heterophilous-graphs

A subgraph is constructed by using a subset of vertices and edges of a given graph. There exist many graph properties that are hereditary for subgraphs. Hence, researchers from different communities have paid a great deal of attention in studying numerous subgraph problems, on top of the ordinary graph problems. Many algorithms are proposed in studying subgraph problems, where one common approach is by extracting the patterns and structures of a given graph. Due to the complex structures of certain types of graphs and to improve overall performances of the existing frameworks, machine learning techniques have recently been employed in dealing with various subgraph problems. In this article, we present a comprehensive review on five well known subgraph problems that have been tackled by using machine learning methods. They are subgraph isomorphism (both counting and matching), maximum common subgraph, community detection and community search problems. We provide an outline of each proposed method, and examine its designs and performances. We also explore non-learning-based algorithms for each problem and a brief discussion is given. We then suggest some promising research directions in this area, hoping that relevant subgraph problems can be tackled by using a similar strategy. Since there is a huge growth in employing machine learning techniques in recent years, we believe that this survey will serve as a good reference point to relevant research communities.

A key requirement for graph neural networks is that they must process a graph in a way that does not depend on how the graph is described. Traditionally this has been taken to mean that a graph network must be equivariant to node permutations. Here we show that instead of equivariance, the more general concept of naturality is sufficient for a graph network to be well-defined, opening up a larger class of graph networks. We define global and local natural graph networks, the latter of which are as scalable as conventional message passing graph neural networks while being more flexible. We give one practical instantiation of a natural network on graphs which uses an equivariant message network parameterization, yielding good performance on several benchmarks.

Recently, there has been a surge of interest in employing neural networks for graph generation, a fundamental statistical learning problem with critical applications like molecule design and community analysis. However, most approaches encounter significant limitations when generating large-scale graphs. This is due to their requirement to output the full adjacency matrices whose size grows quadratically with the number of nodes. In response to this challenge, we introduce a new, simple, and scalable graph representation named gap encoded edge list (GEEL) that has a small representation size that aligns with the number of edges. In addition, GEEL significantly reduces the vocabulary size by incorporating the gap encoding and bandwidth restriction schemes. GEEL can be autoregressively generated with the incorporation of node positional encoding, and we further extend GEEL to deal with attributed graphs by designing a new grammar. Our findings reveal that the adoption of this compact representation not only enhances scalability but also bolsters performance by simplifying the graph generation process. We conduct a comprehensive evaluation across ten non-attributed and two molecular graph generation tasks, demonstrating the effectiveness of GEEL.

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are limited in their expressive power. These models are no more powerful than the 1-dimensional Weisfeiler-Leman (1-WL) algorithm in terms of distinguishing non-isomorphic graphs. In this paper, we propose Path Neural Networks (PathNNs), a model that updates node representations by aggregating paths emanating from nodes. We derive three different variants of the PathNN model that aggregate single shortest paths, all shortest paths and all simple paths of length up to K. We prove that two of these variants are strictly more powerful than the 1-WL algorithm, and we experimentally validate our theoretical results. We find that PathNNs can distinguish pairs of non-isomorphic graphs that are indistinguishable by 1-WL, while our most expressive PathNN variant can even distinguish between 3-WL indistinguishable graphs. The different PathNN variants are also evaluated on graph classification and graph regression datasets, where in most cases, they outperform the baseline methods.

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

Acceleration of graph applications on GPUs has found large interest due to the ubiquitous use of graph processing in various domains. The inherent irregularity in graph applications leads to several challenges for parallelization. A key challenge, which we address in this paper, is that of load-imbalance. If the work-assignment to threads uses node-based graph partitioning, it can result in skewed task-distribution, leading to poor load-balance. In contrast, if the work-assignment uses edge-based graph partitioning, the load-balancing is better, but the memory requirement is relatively higher. This makes it unsuitable for large graphs. In this work, we propose three techniques for improved load-balancing of graph applications on GPUs. Each technique brings in unique advantages, and a user may have to employ a specific technique based on the requirement. Using Breadth First Search and Single Source Shortest Paths as our processing kernels, we illustrate the effectiveness of each of the proposed techniques in comparison to the existing node-based and edge-based mechanisms.

Can we model non-Euclidean graphs as pure language or even Euclidean vectors while retaining their inherent information? The non-Euclidean property have posed a long term challenge in graph modeling. Despite recent GNN and Graphformer efforts encoding graphs as Euclidean vectors, recovering original graph from the vectors remains a challenge. We introduce GraphsGPT, featuring a Graph2Seq encoder that transforms non-Euclidean graphs into learnable graph words in a Euclidean space, along with a GraphGPT decoder that reconstructs the original graph from graph words to ensure information equivalence. We pretrain GraphsGPT on 100M molecules and yield some interesting findings: (1) Pretrained Graph2Seq excels in graph representation learning, achieving state-of-the-art results on 8/9 graph classification and regression tasks. (2) Pretrained GraphGPT serves as a strong graph generator, demonstrated by its ability to perform both unconditional and conditional graph generation. (3) Graph2Seq+GraphGPT enables effective graph mixup in the Euclidean space, overcoming previously known non-Euclidean challenge. (4) Our proposed novel edge-centric GPT pretraining task is effective in graph fields, underscoring its success in both representation and generation.

Graph databases are gaining momentum thanks to the flexibility and expressiveness of their data models and query languages. A standardization activity driven by the ISO/IEC standardization body is also ongoing and has already conducted to the specification of the first versions of two standard graph query languages, namely SQL/PGQ and GQL, respectively in 2023 and 2024. Apart from the standards, there exists a panoply of concrete graph query languages provided by current graph database systems, each offering different query features. A common limitation of current graph query engines is the absence of an algebraic approach for evaluating path queries. To address this, we introduce an abstract algebra for evaluating path queries, allowing paths to be treated as first-class entities within the query processing pipeline. We demonstrate that our algebra can express a core fragment of path queries defined in GQL and SQL/PGQ, thereby serving as a formal framework for studying both standards and supporting their implementation in current graph database systems. We also show that evaluation trees for path algebra expressions can function as logical plans for evaluating path queries and enable the application of query optimization techniques. Our algebraic framework has the potential to act as a lingua franca for path query evaluation, enabling different implementations to be expressed and compared.

Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified communities and connectivities, and evaluated clustering coefficients and betweenness centrality of pivotal nodes, uncovering fascinating knowledge architectures. The graph has an inherently scale-free nature, is highly connected, and can be used for graph reasoning by taking advantage of transitive and isomorphic properties that reveal unprecedented interdisciplinary relationships that can be used to answer queries, identify gaps in knowledge, propose never-before-seen material designs, and predict material behaviors. We compute deep node embeddings for combinatorial node similarity ranking for use in a path sampling strategy links dissimilar concepts that have previously not been related. One comparison revealed structural parallels between biological materials and Beethoven's 9th Symphony, highlighting shared patterns of complexity through isomorphic mapping. In another example, the algorithm proposed a hierarchical mycelium-based composite based on integrating path sampling with principles extracted from Kandinsky's 'Composition VII' painting. The resulting material integrates an innovative set of concepts that include a balance of chaos/order, adjustable porosity, mechanical strength, and complex patterned chemical functionalization. We uncover other isomorphisms across science, technology and art, revealing a nuanced ontology of immanence that reveal a context-dependent heterarchical interplay of constituents. Graph-based generative AI achieves a far higher degree of novelty, explorative capacity, and technical detail, than conventional approaches and establishes a widely useful framework for innovation by revealing hidden connections.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of graph representation learning with a variety of recent publications but they lack a common foundation about what constitutes a good positional or structural encoding, and what differentiates them. In this paper, we summarize the different types of encodings with a clearer definition and categorize them as being local, global or relative. The prior GTs are constrained to small graphs with a few hundred nodes, here we propose the first architecture with a complexity linear in the number of nodes and edges O(N+E) by decoupling the local real-edge aggregation from the fully-connected Transformer. We argue that this decoupling does not negatively affect the expressivity, with our architecture being a universal function approximator on graphs. Our GPS recipe consists of choosing 3 main ingredients: (i) positional/structural encoding, (ii) local message-passing mechanism, and (iii) global attention mechanism. We provide a modular framework GraphGPS that supports multiple types of encodings and that provides efficiency and scalability both in small and large graphs. We test our architecture on 16 benchmarks and show highly competitive results in all of them, show-casing the empirical benefits gained by the modularity and the combination of different strategies.

Graph learning has become indispensable for interpreting and harnessing relational data in diverse fields, ranging from recommendation systems to social network analysis. In this context, a variety of GNNs have emerged as promising methodologies for encoding the structural information of graphs. By effectively capturing the graph's underlying structure, these GNNs have shown great potential in enhancing performance in graph learning tasks, such as link prediction and node classification. However, despite their successes, a significant challenge persists: these advanced methods often face difficulties in generalizing to unseen graph data that significantly differs from the training instances. In this work, our aim is to advance the graph learning paradigm by developing a general graph foundation model. This model is designed to understand the complex topological patterns present in diverse graph data, enabling it to excel in zero-shot graph learning tasks across different downstream datasets. To achieve this goal, we address several key technical challenges in our OpenGraph model. Firstly, we propose a unified graph tokenizer to adapt our graph model to generalize well on unseen graph data, even when the underlying graph properties differ significantly from those encountered during training. Secondly, we develop a scalable graph transformer as the foundational encoder, which effectively captures node-wise dependencies within the global topological context. Thirdly, we introduce a data augmentation mechanism enhanced by a LLM to alleviate the limitations of data scarcity in real-world scenarios. Extensive experiments validate the effectiveness of our framework. By adapting our OpenGraph to new graph characteristics and comprehending the nuances of diverse graphs, our approach achieves remarkable zero-shot graph learning performance across various settings and domains.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

Graphs are essential data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which predict properties or classes for the entire graph, are critical for applications, such as molecular property prediction and subgraph counting. Graph Neural Networks (GNNs) have shown promise in these tasks, but their evaluations are often limited to narrow datasets, tasks, and inconsistent experimental setups, restricting their generalizability. To address these limitations, we propose a unified evaluation framework for graph-level GNNs. This framework provides a standardized setting to evaluate GNNs across diverse datasets, various graph tasks (e.g., graph classification and regression), and challenging scenarios, including noisy, imbalanced, and few-shot graphs. Additionally, we propose a novel GNN model with enhanced expressivity and generalization capabilities. Specifically, we enhance the expressivity of GNNs through a k-path rooted subgraph approach, enabling the model to effectively count subgraphs (e.g., paths and cycles). Moreover, we introduce a unified graph contrastive learning algorithm for graphs across diverse domains, which adaptively removes unimportant edges to augment graphs, thereby significantly improving generalization performance. Extensive experiments demonstrate that our model achieves superior performance against fourteen effective baselines across twenty-seven graph datasets, establishing it as a robust and generalizable model for graph-level tasks.

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenkovi\'c, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. Roughly speaking, the shortcut partition guarantees that for every two vertices u and v in the graph, there exists a path between u and v that intersects only a few clusters. They proved that any planar graph admits a shortcut partition and gave several applications, including a construction of tree cover for arbitrary planar graphs with stretch 1+varepsilon and O(1) many trees for any fixed varepsilon in (0,1). However, the construction heavily exploits planarity in multiple steps, and is thus inherently limited to planar graphs. In this work, we breach the "planarity barrier" to construct a shortcut partition for K_r-minor-free graphs for any r. To this end, we take a completely different approach -- our key contribution is a novel deterministic variant of the cop decomposition in minor-free graphs [And86, AGG14]. Our shortcut partition for K_r-minor-free graphs yields several direct applications. Most notably, we construct the first optimal distance oracle for K_r-minor-free graphs, with 1+varepsilon stretch, linear space, and constant query time for any fixed varepsilon in (0,1). The previous best distance oracle [AG06] uses O(nlog n) space and O(log n) query time, and its construction relies on Robertson-Seymour structural theorem and other sophisticated tools. We also obtain the first tree cover of O(1) size for minor-free graphs with stretch 1+varepsilon, while the previous best (1+varepsilon)-tree cover has size O(log^2 n) [BFN19].

Contrastive learning has recently achieved remarkable success in many domains including graphs. However contrastive loss, especially for graphs, requires a large number of negative samples which is unscalable and computationally prohibitive with a quadratic time complexity. Sub-sampling is not optimal and incorrect negative sampling leads to sampling bias. In this work, we propose a meta-node based approximation technique that can (a) proxy all negative combinations (b) in quadratic cluster size time complexity, (c) at graph level, not node level, and (d) exploit graph sparsity. By replacing node-pairs with additive cluster-pairs, we compute the negatives in cluster-time at graph level. The resulting Proxy approximated meta-node Contrastive (PamC) loss, based on simple optimized GPU operations, captures the full set of negatives, yet is efficient with a linear time complexity. By avoiding sampling, we effectively eliminate sample bias. We meet the criterion for larger number of samples, thus achieving block-contrastiveness, which is proven to outperform pair-wise losses. We use learnt soft cluster assignments for the meta-node constriction, and avoid possible heterophily and noise added during edge creation. Theoretically, we show that real world graphs easily satisfy conditions necessary for our approximation. Empirically, we show promising accuracy gains over state-of-the-art graph clustering on 6 benchmarks. Importantly, we gain substantially in efficiency; up to 3x in training time, 1.8x in inference time and over 5x in GPU memory reduction.

Many real-world graphs frequently present challenges for graph learning due to the presence of both heterophily and heterogeneity. However, existing benchmarks for graph learning often focus on heterogeneous graphs with homophily or homogeneous graphs with heterophily, leaving a gap in understanding how methods perform on graphs that are both heterogeneous and heterophilic. To bridge this gap, we introduce H2GB, a novel graph benchmark that brings together the complexities of both the heterophily and heterogeneity properties of graphs. Our benchmark encompasses 9 diverse real-world datasets across 5 domains, 28 baseline model implementations, and 26 benchmark results. In addition, we present a modular graph transformer framework UnifiedGT and a new model variant, H2G-former, that excels at this challenging benchmark. By integrating masked label embeddings, cross-type heterogeneous attention, and type-specific FFNs, H2G-former effectively tackles graph heterophily and heterogeneity. Extensive experiments across 26 baselines on H2GB reveal inadequacies of current models on heterogeneous heterophilic graph learning, and demonstrate the superiority of our H2G-former over existing solutions. Both the benchmark and the framework are available on GitHub (https://github.com/junhongmit/H2GB) and PyPI (https://pypi.org/project/H2GB), and documentation can be found at https://junhongmit.github.io/H2GB/.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in the following sense: we consider the cost as a function of sample size for any target function, even if the sample size is not large enough for consistency or the target is outside the RKHS. We analyze the cost of overfitting under a Gaussian universality ansatz using recently derived (non-rigorous) risk estimates in terms of the task eigenstructure. Our analysis provides a more refined characterization of benign, tempered and catastrophic overfitting (cf. Mallinar et al. 2022).

Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their O(V) depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of O(log V) depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.

Since the pioneering work on the lottery ticket hypothesis for graph neural networks (GNNs) was proposed in Chen et al. (2021), the study on finding graph lottery tickets (GLT) has become one of the pivotal focus in the GNN community, inspiring researchers to discover sparser GLT while achieving comparable performance to original dense networks. In parallel, the graph structure has gained substantial attention as a crucial factor in GNN training dynamics, also elucidated by several recent studies. Despite this, contemporary studies on GLT, in general, have not fully exploited inherent pathways in the graph structure and identified tickets in an iterative manner, which is time-consuming and inefficient. To address these limitations, we introduce TEDDY, a one-shot edge sparsification framework that leverages structural information by incorporating edge-degree information. Following edge sparsification, we encourage the parameter sparsity during training via simple projected gradient descent on the ell_0 ball. Given the target sparsity levels for both the graph structure and the model parameters, our TEDDY facilitates efficient and rapid realization of GLT within a single training. Remarkably, our experimental results demonstrate that TEDDY significantly surpasses conventional iterative approaches in generalization, even when conducting one-shot sparsification that solely utilizes graph structures, without taking feature information into account.

Graph Contrastive Learning (GCL) has emerged as a popular training approach for learning node embeddings from augmented graphs without labels. Despite the key principle that maximizing the similarity between positive node pairs while minimizing it between negative node pairs is well established, some fundamental problems are still unclear. Considering the complex graph structure, are some nodes consistently well-trained and following this principle even with different graph augmentations? Or are there some nodes more likely to be untrained across graph augmentations and violate the principle? How to distinguish these nodes and further guide the training of GCL? To answer these questions, we first present experimental evidence showing that the training of GCL is indeed imbalanced across all nodes. To address this problem, we propose the metric "node compactness", which is the lower bound of how a node follows the GCL principle related to the range of augmentations. We further derive the form of node compactness theoretically through bound propagation, which can be integrated into binary cross-entropy as a regularization. To this end, we propose the PrOvable Training (POT) for GCL, which regularizes the training of GCL to encode node embeddings that follows the GCL principle better. Through extensive experiments on various benchmarks, POT consistently improves the existing GCL approaches, serving as a friendly plugin.

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

Heterophilic Graph Neural Networks (HGNNs) have shown promising results for semi-supervised learning tasks on graphs. Notably, most real-world heterophilic graphs are composed of a mixture of nodes with different neighbor patterns, exhibiting local node-level homophilic and heterophilic structures. However, existing works are only devoted to designing better HGNN backbones or architectures for node classification tasks on heterophilic and homophilic graph benchmarks simultaneously, and their analyses of HGNN performance with respect to nodes are only based on the determined data distribution without exploring the effect caused by this structural difference between training and testing nodes. How to learn invariant node representations on heterophilic graphs to handle this structure difference or distribution shifts remains unexplored. In this paper, we first discuss the limitations of previous graph-based invariant learning methods from the perspective of data augmentation. Then, we propose HEI, a framework capable of generating invariant node representations through incorporating heterophily information to infer latent environments without augmentation, which are then used for invariant prediction, under heterophilic graph structure distribution shifts. We theoretically show that our proposed method can achieve guaranteed performance under heterophilic graph structure distribution shifts. Extensive experiments on various benchmarks and backbones can also demonstrate the effectiveness of our method compared with existing state-of-the-art baselines.

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While functional generative models are theoretically domain- and discretization-agnostic, current implementations heavily rely on the Fourier Neural Operator (FNO), limiting their applicability to regular grids and rectangular domains. To overcome these critical limitations, we introduce the Mesh-Informed Neural Operator (MINO). By leveraging graph neural operators and cross-attention mechanisms, MINO offers a principled, domain- and discretization-agnostic backbone for generative modeling in function spaces. This advancement significantly expands the scope of such models to more diverse applications in generative, inverse, and regression tasks. Furthermore, MINO provides a unified perspective on integrating neural operators with general advanced deep learning architectures. Finally, we introduce a suite of standardized evaluation metrics that enable objective comparison of functional generative models, addressing another critical gap in the field.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

The origins of the colours of Trans-Neptunian Objects (TNOs) represent a crucial unresolved question, central to understanding the history of our Solar System. Recent observational surveys revealed correlations between the eccentricity and inclination of TNOs, and their colours. This rekindled the long-standing debate on whether these colours reflect the conditions of TNO formation or their subsequent evolution. We address this question using a model-agnostic, data-driven approach that unanimously converges to a common causal graph from the analysis of two different datasets, each from two different conditional independence test methods. For evaluation, we demonstrate how our model is consistent with the currently-accepted paradigms of TNOs' dynamical histories, without involving any orbital modelling or physics-based assumptions. Our causal model (with no knowledge of the existence of Neptune) predicts the need for an unknown confounding variable, consistent with Neptune's effects. The model predicts that the colour of TNOs is the root cause of their inclination distribution, rather than the other way around. This strongly suggests that the colours of TNOs reflect an underlying dynamical property, most likely their formation location. Our model excludes formation scenarios that invoke substantial colour modification by subsequent evolution. We conclude that the colours of TNOs are predominantly primordial.

The expressivity of Graph Neural Networks (GNNs) has been studied broadly in recent years to reveal the design principles for more powerful GNNs. Graph canonization is known as a typical approach to distinguish non-isomorphic graphs, yet rarely adopted when developing expressive GNNs. This paper proposes to maximize the expressivity of GNNs by graph canonization, then the power of such GNNs is studies from the perspective of model stability. A stable GNN will map similar graphs to close graph representations in the vectorial space, and the stability of GNNs is critical to generalize their performance to unseen graphs. We theoretically reveal the trade-off of expressivity and stability in graph-canonization-enhanced GNNs. Then we introduce a notion of universal graph canonization as the general solution to address the trade-off and characterize a widely applicable sufficient condition to solve the universal graph canonization. A comprehensive set of experiments demonstrates the effectiveness of the proposed method. In many popular graph benchmark datasets, graph canonization successfully enhances GNNs and provides highly competitive performance, indicating the capability and great potential of proposed method in general graph representation learning. In graph datasets where the sufficient condition holds, GNNs enhanced by universal graph canonization consistently outperform GNN baselines and successfully improve the SOTA performance up to 31%, providing the optimal solution to numerous challenging real-world graph analytical tasks like gene network representation learning in bioinformatics.

Knowledge Graph (KG) reasoning, which aims to infer new facts from structured knowledge repositories, plays a vital role in Natural Language Processing (NLP) systems. Its effectiveness critically depends on constructing informative and contextually relevant reasoning paths. However, existing graph neural networks (GNNs) often adopt rigid, query-agnostic path-exploration strategies, limiting their ability to adapt to diverse linguistic contexts and semantic nuances. To address these limitations, we propose MoKGR, a mixture-of-experts framework that personalizes path exploration through two complementary components: (1) a mixture of length experts that adaptively selects and weights candidate path lengths according to query complexity, providing query-specific reasoning depth; and (2) a mixture of pruning experts that evaluates candidate paths from a complementary perspective, retaining the most informative paths for each query. Through comprehensive experiments on diverse benchmark, MoKGR demonstrates superior performance in both transductive and inductive settings, validating the effectiveness of personalized path exploration in KGs reasoning.

Unsupervised Multiplex Graph Learning (UMGL) aims to learn node representations on various edge types without manual labeling. However, existing research overlooks a key factor: the reliability of the graph structure. Real-world data often exhibit a complex nature and contain abundant task-irrelevant noise, severely compromising UMGL's performance. Moreover, existing methods primarily rely on contrastive learning to maximize mutual information across different graphs, limiting them to multiplex graph redundant scenarios and failing to capture view-unique task-relevant information. In this paper, we focus on a more realistic and challenging task: to unsupervisedly learn a fused graph from multiple graphs that preserve sufficient task-relevant information while removing task-irrelevant noise. Specifically, our proposed Information-aware Unsupervised Multiplex Graph Fusion framework (InfoMGF) uses graph structure refinement to eliminate irrelevant noise and simultaneously maximizes view-shared and view-unique task-relevant information, thereby tackling the frontier of non-redundant multiplex graph. Theoretical analyses further guarantee the effectiveness of InfoMGF. Comprehensive experiments against various baselines on different downstream tasks demonstrate its superior performance and robustness. Surprisingly, our unsupervised method even beats the sophisticated supervised approaches. The source code and datasets are available at https://github.com/zxlearningdeep/InfoMGF.

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable k-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

Recently, subgraph GNNs have emerged as an important direction for developing expressive graph neural networks (GNNs). While numerous architectures have been proposed, so far there is still a limited understanding of how various design paradigms differ in terms of expressive power, nor is it clear what design principle achieves maximal expressiveness with minimal architectural complexity. To address these fundamental questions, this paper conducts a systematic study of general node-based subgraph GNNs through the lens of Subgraph Weisfeiler-Lehman Tests (SWL). Our central result is to build a complete hierarchy of SWL with strictly growing expressivity. Concretely, we prove that any node-based subgraph GNN falls into one of the six SWL equivalence classes, among which SSWL achieves the maximal expressive power. We also study how these equivalence classes differ in terms of their practical expressiveness such as encoding graph distance and biconnectivity. Furthermore, we give a tight expressivity upper bound of all SWL algorithms by establishing a close relation with localized versions of WL and Folklore WL (FWL) tests. Our results provide insights into the power of existing subgraph GNNs, guide the design of new architectures, and point out their limitations by revealing an inherent gap with the 2-FWL test. Finally, experiments demonstrate that SSWL-inspired subgraph GNNs can significantly outperform prior architectures on multiple benchmarks despite great simplicity.

Molecular relational learning, whose goal is to learn the interaction behavior between molecular pairs, got a surge of interest in molecular sciences due to its wide range of applications. Recently, graph neural networks have recently shown great success in molecular relational learning by modeling a molecule as a graph structure, and considering atom-level interactions between two molecules. Despite their success, existing molecular relational learning methods tend to overlook the nature of chemistry, i.e., a chemical compound is composed of multiple substructures such as functional groups that cause distinctive chemical reactions. In this work, we propose a novel relational learning framework, called CGIB, that predicts the interaction behavior between a pair of graphs by detecting core subgraphs therein. The main idea is, given a pair of graphs, to find a subgraph from a graph that contains the minimal sufficient information regarding the task at hand conditioned on the paired graph based on the principle of conditional graph information bottleneck. We argue that our proposed method mimics the nature of chemical reactions, i.e., the core substructure of a molecule varies depending on which other molecule it interacts with. Extensive experiments on various tasks with real-world datasets demonstrate the superiority of CGIB over state-of-the-art baselines. Our code is available at https://github.com/Namkyeong/CGIB.

Graph mining workloads aim to extract structural properties of a graph by exploring its subgraph structures. General purpose graph mining systems provide a generic runtime to explore subgraph structures of interest with the help of user-defined functions that guide the overall exploration process. However, the state-of-the-art graph mining systems remain largely oblivious to the shape (or pattern) of the subgraphs that they mine. This causes them to: (a) explore unnecessary subgraphs; (b) perform expensive computations on the explored subgraphs; and, (c) hold intermediate partial subgraphs in memory; all of which affect their overall performance. Furthermore, their programming models are often tied to their underlying exploration strategies, which makes it difficult for domain users to express complex mining tasks. In this paper, we develop Peregrine, a pattern-aware graph mining system that directly explores the subgraphs of interest while avoiding exploration of unnecessary subgraphs, and simultaneously bypassing expensive computations throughout the mining process. We design a pattern-based programming model that treats "graph patterns" as first class constructs and enables Peregrine to extract the semantics of patterns, which it uses to guide its exploration. Our evaluation shows that Peregrine outperforms state-of-the-art distributed and single machine graph mining systems, and scales to complex mining tasks on larger graphs, while retaining simplicity and expressivity with its "pattern-first" programming approach.

While machine learning on graphs has demonstrated promise in drug design and molecular property prediction, significant benchmarking challenges hinder its further progress and relevance. Current benchmarking practices often lack focus on transformative, real-world applications, favoring narrow domains like two-dimensional molecular graphs over broader, impactful areas such as combinatorial optimization, relational databases, or chip design. Additionally, many benchmark datasets poorly represent the underlying data, leading to inadequate abstractions and misaligned use cases. Fragmented evaluations and an excessive focus on accuracy further exacerbate these issues, incentivizing overfitting rather than fostering generalizable insights. These limitations have prevented the development of truly useful graph foundation models. This position paper calls for a paradigm shift toward more meaningful benchmarks, rigorous evaluation protocols, and stronger collaboration with domain experts to drive impactful and reliable advances in graph learning research, unlocking the potential of graph learning.

Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not fully characterize the joint distribution given the graph structure. In this work, we propose novel edgewise metrics, namely the edgewise expected calibration error (ECE) and the agree/disagree ECEs, which provide criteria for uncertainty estimation on graphs beyond the nodewise setting. Our experiments demonstrate that the proposed edgewise metrics can complement the nodewise results and yield additional insights. Moreover, we show that GNN models which consider the structured prediction problem on graphs tend to have better uncertainty estimations, which illustrates the benefit of going beyond the nodewise setting.

Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify "implicitly-defined" GNNs as a class of architectures which is provably robust to partially asynchronous "hogwild" inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.

Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of their capability are scarce, despite their empirical effectiveness in state-of-the-art recommender models. Recently, research has explored the expressiveness of GNNs in general, demonstrating that message passing GNNs are at most as powerful as the Weisfeiler-Lehman test, and that GNNs combined with random node initialization are universal. Nevertheless, the concept of "expressiveness" for GNNs remains vaguely defined. Most existing works adopt the graph isomorphism test as the metric of expressiveness, but this graph-level task may not effectively assess a model's ability in recommendation, where the objective is to distinguish nodes of different closeness. In this paper, we provide a comprehensive theoretical analysis of the expressiveness of GNNs in recommendation, considering three levels of expressiveness metrics: graph isomorphism (graph-level), node automorphism (node-level), and topological closeness (link-level). We propose the topological closeness metric to evaluate GNNs' ability to capture the structural distance between nodes, which aligns closely with the objective of recommendation. To validate the effectiveness of this new metric in evaluating recommendation performance, we introduce a learning-less GNN algorithm that is optimal on the new metric and can be optimal on the node-level metric with suitable modification. We conduct extensive experiments comparing the proposed algorithm against various types of state-of-the-art GNN models to explore the explainability of the new metric in the recommendation task. For reproducibility, implementation codes are available at https://github.com/HKUDS/GTE.

Benefiting from the message passing mechanism, Graph Neural Networks (GNNs) have been successful on flourish tasks over graph data. However, recent studies have shown that attackers can catastrophically degrade the performance of GNNs by maliciously modifying the graph structure. A straightforward solution to remedy this issue is to model the edge weights by learning a metric function between pairwise representations of two end nodes, which attempts to assign low weights to adversarial edges. The existing methods use either raw features or representations learned by supervised GNNs to model the edge weights. However, both strategies are faced with some immediate problems: raw features cannot represent various properties of nodes (e.g., structure information), and representations learned by supervised GNN may suffer from the poor performance of the classifier on the poisoned graph. We need representations that carry both feature information and as mush correct structure information as possible and are insensitive to structural perturbations. To this end, we propose an unsupervised pipeline, named STABLE, to optimize the graph structure. Finally, we input the well-refined graph into a downstream classifier. For this part, we design an advanced GCN that significantly enhances the robustness of vanilla GCN without increasing the time complexity. Extensive experiments on four real-world graph benchmarks demonstrate that STABLE outperforms the state-of-the-art methods and successfully defends against various attacks.

Graph neural networks (GNNs), in general, are built on the assumption of a static set of features characterizing each node in a graph. This assumption is often violated in practice. Existing methods partly address this issue through feature imputation. However, these techniques (i) assume uniformity of feature set across nodes, (ii) are transductive by nature, and (iii) fail to work when features are added or removed over time. In this work, we address these limitations through a novel GNN framework called GRAFENNE. GRAFENNE performs a novel allotropic transformation on the original graph, wherein the nodes and features are decoupled through a bipartite encoding. Through a carefully chosen message passing framework on the allotropic transformation, we make the model parameter size independent of the number of features and thereby inductive to both unseen nodes and features. We prove that GRAFENNE is at least as expressive as any of the existing message-passing GNNs in terms of Weisfeiler-Leman tests, and therefore, the additional inductivity to unseen features does not come at the cost of expressivity. In addition, as demonstrated over four real-world graphs, GRAFENNE empowers the underlying GNN with high empirical efficacy and the ability to learn in continual fashion over streaming feature sets.

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine learning is witnessing a paradigm transition from shallow methods to more sophisticated deep learning approaches. The capabilities of foundation models to generalize and adapt motivate graph machine learning researchers to discuss the potential of developing a new graph learning paradigm. This paradigm envisions models that are pre-trained on extensive graph data and can be adapted for various graph tasks. Despite this burgeoning interest, there is a noticeable lack of clear definitions and systematic analyses pertaining to this new domain. To this end, this article introduces the concept of Graph Foundation Models (GFMs), and offers an exhaustive explanation of their key characteristics and underlying technologies. We proceed to classify the existing work related to GFMs into three distinct categories, based on their dependence on graph neural networks and large language models. In addition to providing a thorough review of the current state of GFMs, this article also outlooks potential avenues for future research in this rapidly evolving domain.

It has been shown that a message passing neural networks (MPNNs), a popular family of neural networks for graph-structured data, are at most as expressive as the first-order Weisfeiler-Leman (1-WL) graph isomorphism test, which has motivated the development of more expressive architectures. In this work, we analyze if the limited expressiveness is actually a limiting factor for MPNNs and other WL-based models in standard graph datasets. Interestingly, we find that the expressiveness of WL is sufficient to identify almost all graphs in most datasets. Moreover, we find that the classification accuracy upper bounds are often close to 100\%. Furthermore, we find that simple WL-based neural networks and several MPNNs can be fitted to several datasets. In sum, we conclude that the performance of WL/MPNNs is not limited by their expressiveness in practice.

Graph representation learning is fundamental for analyzing graph-structured data. Exploring invariant graph representations remains a challenge for most existing graph representation learning methods. In this paper, we propose a cross-view graph consistency learning (CGCL) method that learns invariant graph representations for link prediction. First, two complementary augmented views are derived from an incomplete graph structure through a bidirectional graph structure augmentation scheme. This augmentation scheme mitigates the potential information loss that is commonly associated with various data augmentation techniques involving raw graph data, such as edge perturbation, node removal, and attribute masking. Second, we propose a CGCL model that can learn invariant graph representations. A cross-view training scheme is proposed to train the proposed CGCL model. This scheme attempts to maximize the consistency information between one augmented view and the graph structure reconstructed from the other augmented view. Furthermore, we offer a comprehensive theoretical CGCL analysis. This paper empirically and experimentally demonstrates the effectiveness of the proposed CGCL method, achieving competitive results on graph datasets in comparisons with several state-of-the-art algorithms.

Masked graph autoencoders have emerged as a powerful graph self-supervised learning method that has yet to be fully explored. In this paper, we unveil that the existing discrete edge masking and binary link reconstruction strategies are insufficient to learn topologically informative representations, from the perspective of message propagation on graph neural networks. These limitations include blocking message flows, vulnerability to over-smoothness, and suboptimal neighborhood discriminability. Inspired by these understandings, we explore non-discrete edge masks, which are sampled from a continuous and dispersive probability distribution instead of the discrete Bernoulli distribution. These masks restrict the amount of output messages for each edge, referred to as "bandwidths". We propose a novel, informative, and effective topological masked graph autoencoder using bandwidth masking and a layer-wise bandwidth prediction objective. We demonstrate its powerful graph topological learning ability both theoretically and empirically. Our proposed framework outperforms representative baselines in both self-supervised link prediction (improving the discrete edge reconstructors by at most 20%) and node classification on numerous datasets, solely with a structure-learning pretext. Our implementation is available at https://github.com/Newiz430/Bandana.

Realistic graphs contain both (1) rich self-features of nodes and (2) informative structures of neighborhoods, jointly handled by a Graph Neural Network (GNN) in the typical setup. We propose to decouple the two modalities by Mixture of weak and strong experts (Mowst), where the weak expert is a light-weight Multi-layer Perceptron (MLP), and the strong expert is an off-the-shelf GNN. To adapt the experts' collaboration to different target nodes, we propose a "confidence" mechanism based on the dispersion of the weak expert's prediction logits. The strong expert is conditionally activated in the low-confidence region when either the node's classification relies on neighborhood information, or the weak expert has low model quality. We reveal interesting training dynamics by analyzing the influence of the confidence function on loss: our training algorithm encourages the specialization of each expert by effectively generating soft splitting of the graph. In addition, our "confidence" design imposes a desirable bias toward the strong expert to benefit from GNN's better generalization capability. Mowst is easy to optimize and achieves strong expressive power, with a computation cost comparable to a single GNN. Empirically, Mowst on 4 backbone GNN architectures show significant accuracy improvement on 6 standard node classification benchmarks, including both homophilous and heterophilous graphs (https://github.com/facebookresearch/mowst-gnn).

The growing importance of understanding and addressing algorithmic bias in artificial intelligence (AI) has led to a surge in research on AI fairness, which often assumes that the underlying data is independent and identically distributed (IID). However, real-world data frequently exists in non-IID graph structures that capture connections among individual units. To effectively mitigate bias in AI systems, it is essential to bridge the gap between traditional fairness literature, designed for IID data, and the prevalence of non-IID graph data. This survey reviews recent advancements in fairness amidst non-IID graph data, including the newly introduced fair graph generation and the commonly studied fair graph classification. In addition, available datasets and evaluation metrics for future research are identified, the limitations of existing work are highlighted, and promising future directions are proposed.

In disentangled representation learning, the goal is to achieve a compact representation that consists of all interpretable generative factors in the observational data. Learning disentangled representations for graphs becomes increasingly important as graph data rapidly grows. Existing approaches often rely on Variational Auto-Encoder (VAE) or its causal structure learning-based refinement, which suffer from sub-optimality in VAEs due to the independence factor assumption and unavailability of concept labels, respectively. In this paper, we propose an unsupervised solution, dubbed concept-free causal disentanglement, built on a theoretically provable tight upper bound approximating the optimal factor. This results in an SCM-like causal structure modeling that directly learns concept structures from data. Based on this idea, we propose Concept-free Causal VGAE (CCVGAE) by incorporating a novel causal disentanglement layer into Variational Graph Auto-Encoder. Furthermore, we prove concept consistency under our concept-free causal disentanglement framework, hence employing it to enhance the meta-learning framework, called concept-free causal Meta-Graph (CC-Meta-Graph). We conduct extensive experiments to demonstrate the superiority of the proposed models: CCVGAE and CC-Meta-Graph, reaching up to 29% and 11% absolute improvements over baselines in terms of AUC, respectively.

Graph representation learning nowadays becomes fundamental in analyzing graph-structured data. Inspired by recent success of contrastive methods, in this paper, we propose a novel framework for unsupervised graph representation learning by leveraging a contrastive objective at the node level. Specifically, we generate two graph views by corruption and learn node representations by maximizing the agreement of node representations in these two views. To provide diverse node contexts for the contrastive objective, we propose a hybrid scheme for generating graph views on both structure and attribute levels. Besides, we provide theoretical justification behind our motivation from two perspectives, mutual information and the classical triplet loss. We perform empirical experiments on both transductive and inductive learning tasks using a variety of real-world datasets. Experimental experiments demonstrate that despite its simplicity, our proposed method consistently outperforms existing state-of-the-art methods by large margins. Moreover, our unsupervised method even surpasses its supervised counterparts on transductive tasks, demonstrating its great potential in real-world applications.

Subgraph matching is a fundamental building block for graph-based applications and is challenging due to its high-order combinatorial nature. Existing studies usually tackle it by combinatorial optimization or learning-based methods. However, they suffer from exponential computational costs or searching the matching without theoretical guarantees. In this paper, we develop D2Match by leveraging the efficiency of Deep learning and Degeneracy for subgraph matching. More specifically, we first prove that subgraph matching can degenerate to subtree matching, and subsequently is equivalent to finding a perfect matching on a bipartite graph. We can then yield an implementation of linear time complexity by the built-in tree-structured aggregation mechanism on graph neural networks. Moreover, circle structures and node attributes can be easily incorporated in D2Match to boost the matching performance. Finally, we conduct extensive experiments to show the superior performance of our D2Match and confirm that our D2Match indeed exploits the subtrees and differs from existing GNNs-based subgraph matching methods that depend on memorizing the data distribution divergence

Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and architecture developments, it suffers from several significant limitations. These include a complex definition that lacks direct guidance for model improvement and a WL hierarchy that is too coarse to study current GNNs. This paper introduces an alternative expressive power hierarchy based on the ability of GNNs to calculate equivariant polynomials of a certain degree. As a first step, we provide a full characterization of all equivariant graph polynomials by introducing a concrete basis, significantly generalizing previous results. Each basis element corresponds to a specific multi-graph, and its computation over some graph data input corresponds to a tensor contraction problem. Second, we propose algorithmic tools for evaluating the expressiveness of GNNs using tensor contraction sequences, and calculate the expressive power of popular GNNs. Finally, we enhance the expressivity of common GNN architectures by adding polynomial features or additional operations / aggregations inspired by our theory. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks.

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is still on primary stage. In this paper, we move towards this goal from the perspective of generalization. To be specific, we first establish high probability bounds of generalization gap and gradients in transductive learning with consideration of stochastic optimization. After that, we provide high probability bounds of generalization gap for popular GNNs. The theoretical results reveal the architecture specific factors affecting the generalization gap. Experimental results on benchmark datasets show the consistency between theoretical results and empirical evidence. Our results provide new insights in understanding the generalization of GNNs.

Graph neural networks (GNNs) are effective models for representation learning on relational data. However, standard GNNs are limited in their expressive power, as they cannot distinguish graphs beyond the capability of the Weisfeiler-Leman graph isomorphism heuristic. In order to break this expressiveness barrier, GNNs have been enhanced with random node initialization (RNI), where the idea is to train and run the models with randomized initial node features. In this work, we analyze the expressive power of GNNs with RNI, and prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties. This universality result holds even with partially randomized initial node features, and preserves the invariance properties of GNNs in expectation. We then empirically analyze the effect of RNI on GNNs, based on carefully constructed datasets. Our empirical findings support the superior performance of GNNs with RNI over standard GNNs.

Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods, however, are known to suffer from two major limitations: over-squashing and poor capturing of long-range dependencies. Recently, Graph Transformers (GTs) emerged as a powerful alternative to Message-Passing Neural Networks (MPNNs). GTs, however, have quadratic computational cost, lack inductive biases on graph structures, and rely on complex Positional/Structural Encodings (SE/PE). In this paper, we show that while Transformers, complex message-passing, and SE/PE are sufficient for good performance in practice, neither is necessary. Motivated by the recent success of State Space Models (SSMs), such as Mamba, we present Graph Mamba Networks (GMNs), a general framework for a new class of GNNs based on selective SSMs. We discuss and categorize the new challenges when adopting SSMs to graph-structured data, and present four required and one optional steps to design GMNs, where we choose (1) Neighborhood Tokenization, (2) Token Ordering, (3) Architecture of Bidirectional Selective SSM Encoder, (4) Local Encoding, and dispensable (5) PE and SE. We further provide theoretical justification for the power of GMNs. Experiments demonstrate that despite much less computational cost, GMNs attain an outstanding performance in long-range, small-scale, large-scale, and heterophilic benchmark datasets.

Graph Neural Networks (GNNs) are widely deployed in vast fields, but they often struggle to maintain accurate representations as graphs evolve. We theoretically establish a lower bound, proving that under mild conditions, representation distortion inevitably occurs over time. To estimate the temporal distortion without human annotation after deployment, one naive approach is to pre-train a recurrent model (e.g., RNN) before deployment and use this model afterwards, but the estimation is far from satisfactory. In this paper, we analyze the representation distortion from an information theory perspective, and attribute it primarily to inaccurate feature extraction during evolution. Consequently, we introduce Smart, a straightforward and effective baseline enhanced by an adaptive feature extractor through self-supervised graph reconstruction. In synthetic random graphs, we further refine the former lower bound to show the inevitable distortion over time and empirically observe that Smart achieves good estimation performance. Moreover, we observe that Smart consistently shows outstanding generalization estimation on four real-world evolving graphs. The ablation studies underscore the necessity of graph reconstruction. For example, on OGB-arXiv dataset, the estimation metric MAPE deteriorates from 2.19% to 8.00% without reconstruction.

Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, multi-layer architectures, which are required to propagate knowledge to distant nodes in the graph, dilute the knowledge by performing extensive Laplacian smoothing at each layer and thereby consequently decrease performance. In order to still enjoy the benefit brought by the graph structure while preventing dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node to improve information propagation in the graph. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches.

Graph neural networks (GNNs) emerged recently as a standard toolkit for learning from data on graphs. Current GNN designing works depend on immense human expertise to explore different message-passing mechanisms, and require manual enumeration to determine the proper message-passing depth. Inspired by the strong searching capability of neural architecture search (NAS) in CNN, this paper proposes Graph Neural Architecture Search (GNAS) with novel-designed search space. The GNAS can automatically learn better architecture with the optimal depth of message passing on the graph. Specifically, we design Graph Neural Architecture Paradigm (GAP) with tree-topology computation procedure and two types of fine-grained atomic operations (feature filtering and neighbor aggregation) from message-passing mechanism to construct powerful graph network search space. Feature filtering performs adaptive feature selection, and neighbor aggregation captures structural information and calculates neighbors' statistics. Experiments show that our GNAS can search for better GNNs with multiple message-passing mechanisms and optimal message-passing depth. The searched network achieves remarkable improvement over state-of-the-art manual designed and search-based GNNs on five large-scale datasets at three classical graph tasks. Codes can be found at https://github.com/phython96/GNAS-MP.

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.

Scene graph generation (SGG) aims to predict graph-structured descriptions of input images, in the form of objects and relationships between them. This task is becoming increasingly useful for progress at the interface of vision and language. Here, it is important - yet challenging - to perform well on novel (zero-shot) or rare (few-shot) compositions of objects and relationships. In this paper, we identify two key issues that limit such generalization. Firstly, we show that the standard loss used in this task is unintentionally a function of scene graph density. This leads to the neglect of individual edges in large sparse graphs during training, even though these contain diverse few-shot examples that are important for generalization. Secondly, the frequency of relationships can create a strong bias in this task, such that a blind model predicting the most frequent relationship achieves good performance. Consequently, some state-of-the-art models exploit this bias to improve results. We show that such models can suffer the most in their ability to generalize to rare compositions, evaluating two different models on the Visual Genome dataset and its more recent, improved version, GQA. To address these issues, we introduce a density-normalized edge loss, which provides more than a two-fold improvement in certain generalization metrics. Compared to other works in this direction, our enhancements require only a few lines of code and no added computational cost. We also highlight the difficulty of accurately evaluating models using existing metrics, especially on zero/few shots, and introduce a novel weighted metric.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

Graph neural networks (GNNs) have been demonstrated to be powerful in modeling graph-structured data. However, training GNNs usually requires abundant task-specific labeled data, which is often arduously expensive to obtain. One effective way to reduce the labeling effort is to pre-train an expressive GNN model on unlabeled data with self-supervision and then transfer the learned model to downstream tasks with only a few labels. In this paper, we present the GPT-GNN framework to initialize GNNs by generative pre-training. GPT-GNN introduces a self-supervised attributed graph generation task to pre-train a GNN so that it can capture the structural and semantic properties of the graph. We factorize the likelihood of the graph generation into two components: 1) Attribute Generation and 2) Edge Generation. By modeling both components, GPT-GNN captures the inherent dependency between node attributes and graph structure during the generative process. Comprehensive experiments on the billion-scale Open Academic Graph and Amazon recommendation data demonstrate that GPT-GNN significantly outperforms state-of-the-art GNN models without pre-training by up to 9.1% across various downstream tasks.

A k-clique is a dense graph, consisting of k fully-connected nodes, that finds numerous applications, such as community detection and network analysis. In this paper, we study a new problem, that finds a maximum set of disjoint k-cliques in a given large real-world graph with a user-defined fixed number k, which can contribute to a good performance of teaming collaborative events in online games. However, this problem is NP-hard when k geq 3, making it difficult to solve. To address that, we propose an efficient lightweight method that avoids significant overheads and achieves a k-approximation to the optimal, which is equipped with several optimization techniques, including the ordering method, degree estimation in the clique graph, and a lightweight implementation. Besides, to handle dynamic graphs that are widely seen in real-world social networks, we devise an efficient indexing method with careful swapping operations, leading to the efficient maintenance of a near-optimal result with frequent updates in the graph. In various experiments on several large graphs, our proposed approaches significantly outperform the competitors by up to 2 orders of magnitude in running time and 13.3\% in the number of computed disjoint k-cliques, which demonstrates the superiority of the proposed approaches in terms of efficiency and effectiveness.

Graph Neural Networks (GNNs) have been widely applied to different tasks such as bioinformatics, drug design, and social networks. However, recent studies have shown that GNNs are vulnerable to adversarial attacks which aim to mislead the node or subgraph classification prediction by adding subtle perturbations. Detecting these attacks is challenging due to the small magnitude of perturbation and the discrete nature of graph data. In this paper, we propose a general adversarial edge detection pipeline EDoG without requiring knowledge of the attack strategies based on graph generation. Specifically, we propose a novel graph generation approach combined with link prediction to detect suspicious adversarial edges. To effectively train the graph generative model, we sample several sub-graphs from the given graph data. We show that since the number of adversarial edges is usually low in practice, with low probability the sampled sub-graphs will contain adversarial edges based on the union bound. In addition, considering the strong attacks which perturb a large number of edges, we propose a set of novel features to perform outlier detection as the preprocessing for our detection. Extensive experimental results on three real-world graph datasets including a private transaction rule dataset from a major company and two types of synthetic graphs with controlled properties show that EDoG can achieve above 0.8 AUC against four state-of-the-art unseen attack strategies without requiring any knowledge about the attack type; and around 0.85 with knowledge of the attack type. EDoG significantly outperforms traditional malicious edge detection baselines. We also show that an adaptive attack with full knowledge of our detection pipeline is difficult to bypass it.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

Weighted graphs are ubiquitous throughout biology, chemistry, and the social sciences, motivating the development of generative models for abstract weighted graph data using deep neural networks. However, most current deep generative models are either designed for unweighted graphs and are not easily extended to weighted topologies or incorporate edge weights without consideration of a joint distribution with topology. Furthermore, learning a distribution over weighted graphs must account for complex nonlocal dependencies between both the edges of the graph and corresponding weights of each edge. We develop an autoregressive model BiGG-E, a nontrivial extension of the BiGG model, that learns a joint distribution over weighted graphs while still exploiting sparsity to generate a weighted graph with n nodes and m edges in O((n + m)log n) time. Simulation studies and experiments on a variety of benchmark datasets demonstrate that BiGG-E best captures distributions over weighted graphs while remaining scalable and computationally efficient.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their expansive application in sensitive domains requires a comprehensive understanding of their decision-making processes -- necessitating a framework for GNN explainability. An explanation function for GNNs takes a pre-trained GNN along with a graph as input, to produce a `sufficient statistic' subgraph with respect to the graph label. A main challenge in studying GNN explainability is to provide fidelity measures that evaluate the performance of these explanation functions. This paper studies this foundational challenge, spotlighting the inherent limitations of prevailing fidelity metrics, including Fid_+, Fid_-, and Fid_Delta. Specifically, a formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios. The reason is due to potential distribution shifts when subgraphs are removed in computing these fidelity measures. Subsequently, a robust class of fidelity measures are introduced, and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios. Extensive empirical analysis on both synthetic and real datasets are provided to illustrate that the proposed metrics are more coherent with gold standard metrics. The source code is available at https://trustai4s-lab.github.io/fidelity.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Given a massive graph, how can we exploit its hierarchical structure for concisely but exactly summarizing the graph? By exploiting the structure, can we achieve better compression rates than state-of-the-art graph summarization methods? The explosive proliferation of the Web has accelerated the emergence of large graphs, such as online social networks and hyperlink networks. Consequently, graph compression has become increasingly important to process such large graphs without expensive I/O over the network or to disk. Among a number of approaches, graph summarization, which in essence combines similar nodes into a supernode and describe their connectivity concisely, protrudes with several advantages. However, we note that it fails to exploit pervasive hierarchical structures of real-world graphs as its underlying representation model enforces supernodes to be disjoint. In this work, we propose the hierarchical graph summarization model, which is an expressive graph representation model that includes the previous one proposed by Navlakha et al. as a special case. The new model represents an unweighted graph using positive and negative edges between hierarchical supernodes, each of which can contain others. Then, we propose Slugger, a scalable heuristic for concisely and exactly representing a given graph under our new model. Slugger greedily merges nodes into supernodes while maintaining and exploiting their hierarchy, which is later pruned. Slugger significantly accelerates this process by sampling, approximation, and memoization. Our experiments on 16 real-world graphs show that Slugger is (a) Effective: yielding up to 29.6% more concise summary than state-of-the-art lossless summarization methods, (b) Fast: summarizing a graph with 0.8 billion edges in a few hours, and (c) Scalable: scaling linearly with the number of edges in the input graph.

We study the problem of adversarially robust self-supervised learning on graphs. In the contrastive learning framework, we introduce a new method that increases the adversarial robustness of the learned representations through i) adversarial transformations and ii) transformations that not only remove but also insert edges. We evaluate the learned representations in a preliminary set of experiments, obtaining promising results. We believe this work takes an important step towards incorporating robustness as a viable auxiliary task in graph contrastive learning.

We introduce EvoGit, a decentralized multi-agent framework for collaborative software development driven by autonomous code evolution. EvoGit deploys a population of independent coding agents, each proposing edits to a shared codebase without centralized coordination, explicit message passing, or shared memory. Instead, all coordination emerges through a Git-based phylogenetic graph that tracks the full version lineage and enables agents to asynchronously read from and write to the evolving code repository. This graph-based structure supports fine-grained branching, implicit concurrency, and scalable agent interaction while preserving a consistent historical record. Human involvement is minimal but strategic: users define high-level goals, periodically review the graph, and provide lightweight feedback to promote promising directions or prune unproductive ones. Experiments demonstrate EvoGit's ability to autonomously produce functional and modular software artifacts across two real-world tasks: (1) building a web application from scratch using modern frameworks, and (2) constructing a meta-level system that evolves its own language-model-guided solver for the bin-packing optimization problem. Our results underscore EvoGit's potential to establish a new paradigm for decentralized, automated, and continual software development. EvoGit is open-sourced at https://github.com/BillHuang2001/evogit.

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel K-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

Machine learning on graphs has been extensively studied in both academic and industry. However, as the literature on graph learning booms with a vast number of emerging methods and techniques, it becomes increasingly difficult to manually design the optimal machine learning algorithm for different graph-related tasks. To solve this critical challenge, automated machine learning (AutoML) on graphs which combines the strength of graph machine learning and AutoML together, is gaining attention from the research community. Therefore, we comprehensively survey AutoML on graphs in this paper, primarily focusing on hyper-parameter optimization (HPO) and neural architecture search (NAS) for graph machine learning. We further overview libraries related to automated graph machine learning and in-depth discuss AutoGL, the first dedicated open-source library for AutoML on graphs. In the end, we share our insights on future research directions for automated graph machine learning. This paper is the first systematic and comprehensive review of automated machine learning on graphs to the best of our knowledge.

Heterogeneous graph learning aims to capture complex relationships and diverse relational semantics among entities in a heterogeneous graph to obtain meaningful representations for nodes and edges. Recent advancements in heterogeneous graph neural networks (HGNNs) have achieved state-of-the-art performance by considering relation heterogeneity and using specialized message functions and aggregation rules. However, existing frameworks for heterogeneous graph learning have limitations in generalizing across diverse heterogeneous graph datasets. Most of these frameworks follow the "pre-train" and "fine-tune" paradigm on the same dataset, which restricts their capacity to adapt to new and unseen data. This raises the question: "Can we generalize heterogeneous graph models to be well-adapted to diverse downstream learning tasks with distribution shifts in both node token sets and relation type heterogeneity?'' To tackle those challenges, we propose HiGPT, a general large graph model with Heterogeneous graph instruction-tuning paradigm. Our framework enables learning from arbitrary heterogeneous graphs without the need for any fine-tuning process from downstream datasets. To handle distribution shifts in heterogeneity, we introduce an in-context heterogeneous graph tokenizer that captures semantic relationships in different heterogeneous graphs, facilitating model adaptation. We incorporate a large corpus of heterogeneity-aware graph instructions into our HiGPT, enabling the model to effectively comprehend complex relation heterogeneity and distinguish between various types of graph tokens. Furthermore, we introduce the Mixture-of-Thought (MoT) instruction augmentation paradigm to mitigate data scarcity by generating diverse and informative instructions. Through comprehensive evaluations, our proposed framework demonstrates exceptional performance in terms of generalization performance.

Let G be a graph with adjacency matrix A(G). We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where n^+(G) and n^-(G) denote the number of positive and negative eigenvalues of A(G), respectively. This conjecture generalizes to all graphs the well-known absolute bound for strongly regular graphs. The conjecture also relates to a question posed by Torgasev. We prove the conjecture for special graph families, including line graphs and planar graphs, and provide examples where the conjecture is exact. We also conjecture that for any connected graph G, its line graph L(G) satisfies n^+(L(G)) le n^-(L(G)) + 1 and obtain partial results.

Graph Structure Learning (GSL) focuses on capturing intrinsic dependencies and interactions among nodes in graph-structured data by generating novel graph structures. Graph Neural Networks (GNNs) have emerged as promising GSL solutions, utilizing recursive message passing to encode node-wise inter-dependencies. However, many existing GSL methods heavily depend on explicit graph structural information as supervision signals, leaving them susceptible to challenges such as data noise and sparsity. In this work, we propose GraphEdit, an approach that leverages large language models (LLMs) to learn complex node relationships in graph-structured data. By enhancing the reasoning capabilities of LLMs through instruction-tuning over graph structures, we aim to overcome the limitations associated with explicit graph structural information and enhance the reliability of graph structure learning. Our approach not only effectively denoises noisy connections but also identifies node-wise dependencies from a global perspective, providing a comprehensive understanding of the graph structure. We conduct extensive experiments on multiple benchmark datasets to demonstrate the effectiveness and robustness of GraphEdit across various settings. We have made our model implementation available at: https://github.com/HKUDS/GraphEdit.

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs and successively generates the graph sub-structures in a coarse-to-fine fashion. At each level of hierarchy, this model generates communities in parallel, followed by the prediction of cross-edges between communities using separate neural networks. This modular approach enables scalable graph generation for large and complex graphs. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution. This enables us to generate community graphs with integer-valued edge weights in an autoregressive manner. Empirical studies demonstrate the effectiveness and scalability of our proposed generative model, achieving state-of-the-art performance in terms of graph quality across various benchmark datasets. The code is available at https://github.com/Karami-m/HiGen_main.

Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges, which exceeds the capability of existing embedding systems. We present PyTorch-BigGraph (PBG), an embedding system that incorporates several modifications to traditional multi-relation embedding systems that allow it to scale to graphs with billions of nodes and trillions of edges. PBG uses graph partitioning to train arbitrarily large embeddings on either a single machine or in a distributed environment. We demonstrate comparable performance with existing embedding systems on common benchmarks, while allowing for scaling to arbitrarily large graphs and parallelization on multiple machines. We train and evaluate embeddings on several large social network graphs as well as the full Freebase dataset, which contains over 100 million nodes and 2 billion edges.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Learning graph generative models over latent spaces has received less attention compared to models that operate on the original data space and has so far demonstrated lacklustre performance. We present GLAD a latent space graph generative model. Unlike most previous latent space graph generative models, GLAD operates on a discrete latent space that preserves to a significant extent the discrete nature of the graph structures making no unnatural assumptions such as latent space continuity. We learn the prior of our discrete latent space by adapting diffusion bridges to its structure. By operating over an appropriately constructed latent space we avoid relying on decompositions that are often used in models that operate in the original data space. We present experiments on a series of graph benchmark datasets which clearly show the superiority of the discrete latent space and obtain state of the art graph generative performance, making GLAD the first latent space graph generative model with competitive performance. Our source code is published at: https://github.com/v18nguye/GLAD.

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://github.com/GSL-Benchmark/GSLB.

In recent years, graph pre-training has gained significant attention, focusing on acquiring transferable knowledge from unlabeled graph data to improve downstream performance. Despite these recent endeavors, the problem of negative transfer remains a major concern when utilizing graph pre-trained models to downstream tasks. Previous studies made great efforts on the issue of what to pre-train and how to pre-train by designing a variety of graph pre-training and fine-tuning strategies. However, there are cases where even the most advanced "pre-train and fine-tune" paradigms fail to yield distinct benefits. This paper introduces a generic framework W2PGNN to answer the crucial question of when to pre-train (i.e., in what situations could we take advantage of graph pre-training) before performing effortful pre-training or fine-tuning. We start from a new perspective to explore the complex generative mechanisms from the pre-training data to downstream data. In particular, W2PGNN first fits the pre-training data into graphon bases, each element of graphon basis (i.e., a graphon) identifies a fundamental transferable pattern shared by a collection of pre-training graphs. All convex combinations of graphon bases give rise to a generator space, from which graphs generated form the solution space for those downstream data that can benefit from pre-training. In this manner, the feasibility of pre-training can be quantified as the generation probability of the downstream data from any generator in the generator space. W2PGNN offers three broad applications: providing the application scope of graph pre-trained models, quantifying the feasibility of pre-training, and assistance in selecting pre-training data to enhance downstream performance. We provide a theoretically sound solution for the first application and extensive empirical justifications for the latter two applications.

Enabling effective and efficient machine learning (ML) over large-scale graph data (e.g., graphs with billions of edges) can have a great impact on both industrial and scientific applications. However, existing efforts to advance large-scale graph ML have been largely limited by the lack of a suitable public benchmark. Here we present OGB Large-Scale Challenge (OGB-LSC), a collection of three real-world datasets for facilitating the advancements in large-scale graph ML. The OGB-LSC datasets are orders of magnitude larger than existing ones, covering three core graph learning tasks -- link prediction, graph regression, and node classification. Furthermore, we provide dedicated baseline experiments, scaling up expressive graph ML models to the massive datasets. We show that expressive models significantly outperform simple scalable baselines, indicating an opportunity for dedicated efforts to further improve graph ML at scale. Moreover, OGB-LSC datasets were deployed at ACM KDD Cup 2021 and attracted more than 500 team registrations globally, during which significant performance improvements were made by a variety of innovative techniques. We summarize the common techniques used by the winning solutions and highlight the current best practices in large-scale graph ML. Finally, we describe how we have updated the datasets after the KDD Cup to further facilitate research advances. The OGB-LSC datasets, baseline code, and all the information about the KDD Cup are available at https://ogb.stanford.edu/docs/lsc/ .

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Graph Neural Networks (GNNs) have achieved remarkable performance on graph-based tasks. The key idea for GNNs is to obtain informative representation through aggregating information from local neighborhoods. However, it remains an open question whether the neighborhood information is adequately aggregated for learning representations of nodes with few neighbors. To address this, we propose a simple and efficient data augmentation strategy, local augmentation, to learn the distribution of the node features of the neighbors conditioned on the central node's feature and enhance GNN's expressive power with generated features. Local augmentation is a general framework that can be applied to any GNN model in a plug-and-play manner. It samples feature vectors associated with each node from the learned conditional distribution as additional input for the backbone model at each training iteration. Extensive experiments and analyses show that local augmentation consistently yields performance improvement when applied to various GNN architectures across a diverse set of benchmarks. For example, experiments show that plugging in local augmentation to GCN and GAT improves by an average of 3.4\% and 1.6\% in terms of test accuracy on Cora, Citeseer, and Pubmed. Besides, our experimental results on large graphs (OGB) show that our model consistently improves performance over backbones. Code is available at https://github.com/SongtaoLiu0823/LAGNN.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Graph neural architecture search has sparked much attention as Graph Neural Networks (GNNs) have shown powerful reasoning capability in many relational tasks. However, the currently used graph search space overemphasizes learning node features and neglects mining hierarchical relational information. Moreover, due to diverse mechanisms in the message passing, the graph search space is much larger than that of CNNs. This hinders the straightforward application of classical search strategies for exploring complicated graph search space. We propose Automatic Relation-aware Graph Network Proliferation (ARGNP) for efficiently searching GNNs with a relation-guided message passing mechanism. Specifically, we first devise a novel dual relation-aware graph search space that comprises both node and relation learning operations. These operations can extract hierarchical node/relational information and provide anisotropic guidance for message passing on a graph. Second, analogous to cell proliferation, we design a network proliferation search paradigm to progressively determine the GNN architectures by iteratively performing network division and differentiation. The experiments on six datasets for four graph learning tasks demonstrate that GNNs produced by our method are superior to the current state-of-the-art hand-crafted and search-based GNNs. Codes are available at https://github.com/phython96/ARGNP.

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or cannot sufficiently model the complex dependency between nodes and edges, which is crucial for generating real-world graphs such as molecules. To overcome such limitations, we propose a novel score-based generative model for graphs with a continuous-time framework. Specifically, we propose a new graph diffusion process that models the joint distribution of the nodes and edges through a system of stochastic differential equations (SDEs). Then, we derive novel score matching objectives tailored for the proposed diffusion process to estimate the gradient of the joint log-density with respect to each component, and introduce a new solver for the system of SDEs to efficiently sample from the reverse diffusion process. We validate our graph generation method on diverse datasets, on which it either achieves significantly superior or competitive performance to the baselines. Further analysis shows that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule, demonstrating the effectiveness of the system of SDEs in modeling the node-edge relationships. Our code is available at https://github.com/harryjo97/GDSS.

Multi-view graph clustering (MGC) methods are increasingly being studied due to the explosion of multi-view data with graph structural information. The critical point of MGC is to better utilize view-specific and view-common information in features and graphs of multiple views. However, existing works have an inherent limitation that they are unable to concurrently utilize the consensus graph information across multiple graphs and the view-specific feature information. To address this issue, we propose Variational Graph Generator for Multi-View Graph Clustering (VGMGC). Specifically, a novel variational graph generator is proposed to extract common information among multiple graphs. This generator infers a reliable variational consensus graph based on a priori assumption over multiple graphs. Then a simple yet effective graph encoder in conjunction with the multi-view clustering objective is presented to learn the desired graph embeddings for clustering, which embeds the inferred view-common graph and view-specific graphs together with features. Finally, theoretical results illustrate the rationality of the VGMGC by analyzing the uncertainty of the inferred consensus graph with the information bottleneck principle.Extensive experiments demonstrate the superior performance of our VGMGC over SOTAs. The source code is publicly available at https://github.com/cjpcool/VGMGC.

Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

The success of deep learning notoriously requires larger amounts of costly annotated data. This has led to the development of self-supervised learning (SSL) that aims to alleviate this limitation by creating domain specific pretext tasks on unlabeled data. Simultaneously, there are increasing interests in generalizing deep learning to the graph domain in the form of graph neural networks (GNNs). GNNs can naturally utilize unlabeled nodes through the simple neighborhood aggregation that is unable to thoroughly make use of unlabeled nodes. Thus, we seek to harness SSL for GNNs to fully exploit the unlabeled data. Different from data instances in the image and text domains, nodes in graphs present unique structure information and they are inherently linked indicating not independent and identically distributed (or i.i.d.). Such complexity is a double-edged sword for SSL on graphs. On the one hand, it determines that it is challenging to adopt solutions from the image and text domains to graphs and dedicated efforts are desired. On the other hand, it provides rich information that enables us to build SSL from a variety of perspectives. Thus, in this paper, we first deepen our understandings on when, why, and which strategies of SSL work with GNNs by empirically studying numerous basic SSL pretext tasks on graphs. Inspired by deep insights from the empirical studies, we propose a new direction SelfTask to build advanced pretext tasks that are able to achieve state-of-the-art performance on various real-world datasets. The specific experimental settings to reproduce our results can be found in https://github.com/ChandlerBang/SelfTask-GNN.

We introduce a randomized topological augmentor based on Schur complements for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the technique generates unbiased approximations of its Schur complements and treats the corresponding graphs as augmented views. We discuss the benefits of our approach, provide theoretical justifications and present connections with graph diffusion. Unlike previous efforts, we study the empirical effectiveness of the augmentor in a controlled fashion by varying the design choices for subsequent GCL phases, such as encoding and contrasting. Extensive experiments on node and graph classification benchmarks demonstrate that our technique consistently outperforms pre-defined and adaptive augmentation approaches to achieve state-of-the-art results.

Although Large Language Models (LLMs) have demonstrated remarkable progress, their proficiency in graph-related tasks remains notably limited, hindering the development of truly general-purpose models. Previous attempts, including pretraining graph foundation models or employing supervised fine-tuning, often face challenges such as the scarcity of large-scale, universally represented graph data. We introduce G1, a simple yet effective approach demonstrating that Reinforcement Learning (RL) on synthetic graph-theoretic tasks can significantly scale LLMs' graph reasoning abilities. To enable RL training, we curate Erd\~os, the largest graph reasoning dataset to date comprising 50 diverse graph-theoretic tasks of varying difficulty levels, 100k training data and 5k test data, all drived from real-world graphs. With RL on Erd\~os, G1 obtains substantial improvements in graph reasoning, where our finetuned 3B model even outperforms Qwen2.5-72B-Instruct (24x size). RL-trained models also show strong zero-shot generalization to unseen tasks, domains, and graph encoding schemes, including other graph-theoretic benchmarks as well as real-world node classification and link prediction tasks, without compromising general reasoning abilities. Our findings offer an efficient, scalable path for building strong graph reasoners by finetuning LLMs with RL on graph-theoretic tasks, which combines the strengths of pretrained LLM capabilities with abundant, automatically generated synthetic data, suggesting that LLMs possess graph understanding abilities that RL can elicit successfully.

Self-supervised learning (SSL) for graph neural networks (GNNs) has attracted increasing attention from the graph machine learning community in recent years, owing to its capability to learn performant node embeddings without costly label information. One weakness of conventional SSL frameworks for GNNs is that they learn through a single philosophy, such as mutual information maximization or generative reconstruction. When applied to various downstream tasks, these frameworks rarely perform equally well for every task, because one philosophy may not span the extensive knowledge required for all tasks. To enhance the task generalization across tasks, as an important first step forward in exploring fundamental graph models, we introduce PARETOGNN, a multi-task SSL framework for node representation learning over graphs. Specifically, PARETOGNN is self-supervised by manifold pretext tasks observing multiple philosophies. To reconcile different philosophies, we explore a multiple-gradient descent algorithm, such that PARETOGNN actively learns from every pretext task while minimizing potential conflicts. We conduct comprehensive experiments over four downstream tasks (i.e., node classification, node clustering, link prediction, and partition prediction), and our proposal achieves the best overall performance across tasks on 11 widely adopted benchmark datasets. Besides, we observe that learning from multiple philosophies enhances not only the task generalization but also the single task performances, demonstrating that PARETOGNN achieves better task generalization via the disjoint yet complementary knowledge learned from different philosophies. Our code is publicly available at https://github.com/jumxglhf/ParetoGNN.

For supervised learning with tabular data, decision tree ensembles produced via boosting techniques generally dominate real-world applications involving iid training/test sets. However for graph data where the iid assumption is violated due to structured relations between samples, it remains unclear how to best incorporate this structure within existing boosting pipelines. To this end, we propose a generalized framework for iterating boosting with graph propagation steps that share node/sample information across edges connecting related samples. Unlike previous efforts to integrate graph-based models with boosting, our approach is anchored in a principled meta loss function such that provable convergence can be guaranteed under relatively mild assumptions. Across a variety of non-iid graph datasets with tabular node features, our method achieves comparable or superior performance than both tabular and graph neural network models, as well as existing hybrid strategies that combine the two. Beyond producing better predictive performance than recently proposed graph models, our proposed techniques are easy to implement, computationally more efficient, and enjoy stronger theoretical guarantees (which make our results more reproducible).

Hypergraphs offer a powerful framework for modeling higher-order interactions that traditional pairwise graphs cannot fully capture. However, practical constraints often lead to their simplification into projected graphs, resulting in substantial information loss and ambiguity in representing higher-order relationships. In this work, we propose MARIOH, a supervised approach for reconstructing the original hypergraph from its projected graph by leveraging edge multiplicity. To overcome the difficulties posed by the large search space, MARIOH integrates several key ideas: (a) identifying provable size-2 hyperedges, which reduces the candidate search space, (b) predicting the likelihood of candidates being hyperedges by utilizing both structural and multiplicity-related features, and (c) not only targeting promising hyperedge candidates but also examining less confident ones to explore alternative possibilities. Together, these ideas enable MARIOH to efficiently and effectively explore the search space. In our experiments using 10 real-world datasets, MARIOH achieves up to 74.51% higher reconstruction accuracy compared to state-of-the-art methods.

We introduceGraphGPT, a novel self-supervised generative pre-trained model for graph learning based on the Graph Eulerian Transformer (GET). First, we propose GET, which combines a standard transformer encoder or decoder architecture with an innovative graph-to-sequence transformation method. This method converts graphs or sampled subgraphs into sequences of tokens representing nodes, edges, and attributes in a reversible manner using Eulerian paths. We pre-train GET using either of the two self-supervised tasks: next-token prediction (NTP) and scheduled masked-token prediction (SMTP). The pre-trained model is then fine-tuned for downstream tasks such as graph-, edge-, and node-level prediction. Despite its simplicity, GraphGPT achieves performance comparable to or surpassing state-of-the-art methods on multiple large-scale Open Graph Benchmark (OGB) datasets. It demonstrates exceptional results on the molecular property prediction dataset PCQM4Mv2 and the protein-protein interaction dataset ogbl-ppa. Notably, generative pre-training enables scaling GraphGPT to 2 billion parameters while maintaining performance gains - a breakthrough that overcomes the scalability limitations of traditional Graph Neural Networks (GNNs) and prior graph transformers (GTs). To advance research in graph foundation models and facilitate scientific discovery in chemistry, materials science, and related fields, we will release the source code (https://github.com/alibaba/graph-gpt) and pre-trained checkpoints.

Transformers for graph data are increasingly widely studied and successful in numerous learning tasks. Graph inductive biases are crucial for Graph Transformers, and previous works incorporate them using message-passing modules and/or positional encodings. However, Graph Transformers that use message-passing inherit known issues of message-passing, and differ significantly from Transformers used in other domains, thus making transfer of research advances more difficult. On the other hand, Graph Transformers without message-passing often perform poorly on smaller datasets, where inductive biases are more crucial. To bridge this gap, we propose the Graph Inductive bias Transformer (GRIT) -- a new Graph Transformer that incorporates graph inductive biases without using message passing. GRIT is based on several architectural changes that are each theoretically and empirically justified, including: learned relative positional encodings initialized with random walk probabilities, a flexible attention mechanism that updates node and node-pair representations, and injection of degree information in each layer. We prove that GRIT is expressive -- it can express shortest path distances and various graph propagation matrices. GRIT achieves state-of-the-art empirical performance across a variety of graph datasets, thus showing the power that Graph Transformers without message-passing can deliver.

Community detection on attributed graphs with rich semantic and topological information offers great potential for real-world network analysis, especially user matching in online games. Graph Neural Networks (GNNs) have recently enabled Deep Graph Clustering (DGC) methods to learn cluster assignments from semantic and topological information. However, their success depends on the prior knowledge related to the number of communities K, which is unrealistic due to the high costs and privacy issues of acquisition.In this paper, we investigate the community detection problem without prior K, referred to as K-Free Community Detection problem. To address this problem, we propose a novel Deep Adaptive and Generative model~(DAG) for community detection without specifying the prior K. DAG consists of three key components, i.e., a node representation learning module with masked attribute reconstruction, a community affiliation readout module, and a community number search module with group sparsity. These components enable DAG to convert the process of non-differentiable grid search for the community number, i.e., a discrete hyperparameter in existing DGC methods, into a differentiable learning process. In such a way, DAG can simultaneously perform community detection and community number search end-to-end. To alleviate the cost of acquiring community labels in real-world applications, we design a new metric, EDGE, to evaluate community detection methods even when the labels are not feasible. Extensive offline experiments on five public datasets and a real-world online mobile game dataset demonstrate the superiority of our DAG over the existing state-of-the-art (SOTA) methods. DAG has a relative increase of 7.35\% in teams in a Tencent online game compared with the best competitor.

Federated learning is an active research topic since it enables several participants to jointly train a model without sharing local data. Currently, cross-silo federated learning is a popular training setting that utilizes a few hundred reliable data silos with high-speed access links to training a model. While this approach has been widely applied in real-world scenarios, designing a robust topology to reduce the training time remains an open problem. In this paper, we present a new multigraph topology for cross-silo federated learning. We first construct the multigraph using the overlay graph. We then parse this multigraph into different simple graphs with isolated nodes. The existence of isolated nodes allows us to perform model aggregation without waiting for other nodes, hence effectively reducing the training time. Intensive experiments on three public datasets show that our proposed method significantly reduces the training time compared with recent state-of-the-art topologies while maintaining the accuracy of the learned model. Our code can be found at https://github.com/aioz-ai/MultigraphFL

Contrastive learning is an effective unsupervised method in graph representation learning, and the key component of contrastive learning lies in the construction of positive and negative samples. Previous methods usually utilize the proximity of nodes in the graph as the principle. Recently, the data-augmentation-based contrastive learning method has advanced to show great power in the visual domain, and some works extended this method from images to graphs. However, unlike the data augmentation on images, the data augmentation on graphs is far less intuitive and much harder to provide high-quality contrastive samples, which leaves much space for improvement. In this work, by introducing an adversarial graph view for data augmentation, we propose a simple but effective method, Adversarial Graph Contrastive Learning (ARIEL), to extract informative contrastive samples within reasonable constraints. We develop a new technique called information regularization for stable training and use subgraph sampling for scalability. We generalize our method from node-level contrastive learning to the graph level by treating each graph instance as a super-node. ARIEL consistently outperforms the current graph contrastive learning methods for both node-level and graph-level classification tasks on real-world datasets. We further demonstrate that ARIEL is more robust in the face of adversarial attacks.

Graph neural networks achieve high accuracy in link prediction by jointly leveraging graph topology and node attributes. Topology, however, is represented indirectly; state-of-the-art methods based on subgraph classification label nodes with distance to the target link, so that, although topological information is present, it is tempered by pooling. This makes it challenging to leverage features like loops and motifs associated with network formation mechanisms. We propose a link prediction algorithm based on a new pooling scheme called WalkPool. WalkPool combines the expressivity of topological heuristics with the feature-learning ability of neural networks. It summarizes a putative link by random walk probabilities of adjacent paths. Instead of extracting transition probabilities from the original graph, it computes the transition matrix of a "predictive" latent graph by applying attention to learned features; this may be interpreted as feature-sensitive topology fingerprinting. WalkPool can leverage unsupervised node features or be combined with GNNs and trained end-to-end. It outperforms state-of-the-art methods on all common link prediction benchmarks, both homophilic and heterophilic, with and without node attributes. Applying WalkPool to a set of unsupervised GNNs significantly improves prediction accuracy, suggesting that it may be used as a general-purpose graph pooling scheme.

Generalized Tur\'an problems ask for the maximum number of copies of a graph H in an n-vertex, F-free graph, denoted by ex(n,H,F). We show how to extend the new, localized approach of Bradac, Malec, and Tompkins to generalized Tur\'{a}n problems. We weight the copies of H (typically taking H=K_t), instead of the edges, based on the size of the largest clique, path, or star containing the vertices of the copy of H, and in each case prove a tight upper bound on the sum of the weights. A consequence of our new localized theorems is an asymptotic determination of ex(n,H,K_{1,r}) for every H having at least one dominating vertex and mex(m,H,K_{1,r}) for every H having at least two dominating vertices.

Attributed bipartite graphs (ABGs) are an expressive data model for describing the interactions between two sets of heterogeneous nodes that are associated with rich attributes, such as customer-product purchase networks and author-paper authorship graphs. Partitioning the target node set in such graphs into k disjoint clusters (referred to as k-ABGC) finds widespread use in various domains, including social network analysis, recommendation systems, information retrieval, and bioinformatics. However, the majority of existing solutions towards k-ABGC either overlook attribute information or fail to capture bipartite graph structures accurately, engendering severely compromised result quality. The severity of these issues is accentuated in real ABGs, which often encompass millions of nodes and a sheer volume of attribute data, rendering effective k-ABGC over such graphs highly challenging. In this paper, we propose TPO, an effective and efficient approach to k-ABGC that achieves superb clustering performance on multiple real datasets. TPO obtains high clustering quality through two major contributions: (i) a novel formulation and transformation of the k-ABGC problem based on multi-scale attribute affinity specialized for capturing attribute affinities between nodes with the consideration of their multi-hop connections in ABGs, and (ii) a highly efficient solver that includes a suite of carefully-crafted optimizations for sidestepping explicit affinity matrix construction and facilitating faster convergence. Extensive experiments, comparing TPO against 19 baselines over 5 real ABGs, showcase the superior clustering quality of TPO measured against ground-truth labels. Moreover, compared to the state of the arts, TPO is often more than 40x faster over both small and large ABGs.

This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding or removing edges and changing the categories. A graph transformer network is trained to revert this process, simplifying the problem of distribution learning over graphs into a sequence of node and edge classification tasks. We further improve sample quality by introducing a Markovian noise model that preserves the marginal distribution of node and edge types during diffusion, and by incorporating auxiliary graph-theoretic features. A procedure for conditioning the generation on graph-level features is also proposed. DiGress achieves state-of-the-art performance on molecular and non-molecular datasets, with up to 3x validity improvement on a planar graph dataset. It is also the first model to scale to the large GuacaMol dataset containing 1.3M drug-like molecules without the use of molecule-specific representations.

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

A spanning tree T of graph G is a rho-approximate universal Steiner tree (UST) for root vertex r if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting S is within a rho factor of the minimum cost tree connecting S in G. Busch et al. (FOCS 2012) showed that every graph admits 2^{O(log n)}-approximate USTs by showing that USTs are equivalent to strong sparse partition hierarchies (up to poly-logs). Further, they posed poly-logarithmic USTs and strong sparse partition hierarchies as open questions. We settle these open questions by giving polynomial-time algorithms for computing both O(log ^ 7 n)-approximate USTs and poly-logarithmic strong sparse partition hierarchies. For graphs with constant doubling dimension or constant pathwidth we improve this to O(log n)-approximate USTs and O(1) strong sparse partition hierarchies. Our doubling dimension result is tight up to second order terms. We reduce the existence of these objects to the previously studied cluster aggregation problem and what we call dangling nets.

Graph Neural Networks (GNNs) are increasingly important given their popularity and the diversity of applications. Yet, existing studies of their vulnerability to adversarial attacks rely on relatively small graphs. We address this gap and study how to attack and defend GNNs at scale. We propose two sparsity-aware first-order optimization attacks that maintain an efficient representation despite optimizing over a number of parameters which is quadratic in the number of nodes. We show that common surrogate losses are not well-suited for global attacks on GNNs. Our alternatives can double the attack strength. Moreover, to improve GNNs' reliability we design a robust aggregation function, Soft Median, resulting in an effective defense at all scales. We evaluate our attacks and defense with standard GNNs on graphs more than 100 times larger compared to previous work. We even scale one order of magnitude further by extending our techniques to a scalable GNN.

Graph generation is integral to various engineering and scientific disciplines. Nevertheless, existing methodologies tend to overlook the generation of edge attributes. However, we identify critical applications where edge attributes are essential, making prior methods potentially unsuitable in such contexts. Moreover, while trivial adaptations are available, empirical investigations reveal their limited efficacy as they do not properly model the interplay among graph components. To address this, we propose a joint score-based model of nodes and edges for graph generation that considers all graph components. Our approach offers two key novelties: (i) node and edge attributes are combined in an attention module that generates samples based on the two ingredients; and (ii) node, edge and adjacency information are mutually dependent during the graph diffusion process. We evaluate our method on challenging benchmarks involving real-world and synthetic datasets in which edge features are crucial. Additionally, we introduce a new synthetic dataset that incorporates edge values. Furthermore, we propose a novel application that greatly benefits from the method due to its nature: the generation of traffic scenes represented as graphs. Our method outperforms other graph generation methods, demonstrating a significant advantage in edge-related measures.

We present a novel edge-level ego-network encoding for learning on graphs that can boost Message Passing Graph Neural Networks (MP-GNNs) by providing additional node and edge features or extending message-passing formats. The proposed encoding is sufficient to distinguish Strongly Regular Graphs, a family of challenging 3-WL equivalent graphs. We show theoretically that such encoding is more expressive than node-based sub-graph MP-GNNs. In an empirical evaluation on four benchmarks with 10 graph datasets, our results match or improve previous baselines on expressivity, graph classification, graph regression, and proximity tasks -- while reducing memory usage by 18.1x in certain real-world settings.

Graph representation learning is crucial for many real-world applications (e.g. social relation analysis). A fundamental problem for graph representation learning is how to effectively learn representations without human labeling, which is usually costly and time-consuming. Graph contrastive learning (GCL) addresses this problem by pulling the positive node pairs (or similar nodes) closer while pushing the negative node pairs (or dissimilar nodes) apart in the representation space. Despite the success of the existing GCL methods, they primarily sample node pairs based on the node-level proximity yet the community structures have rarely been taken into consideration. As a result, two nodes from the same community might be sampled as a negative pair. We argue that the community information should be considered to identify node pairs in the same communities, where the nodes insides are semantically similar. To address this issue, we propose a novel Graph Communal Contrastive Learning (gCooL) framework to jointly learn the community partition and learn node representations in an end-to-end fashion. Specifically, the proposed gCooL consists of two components: a Dense Community Aggregation (DeCA) algorithm for community detection and a Reweighted Self-supervised Cross-contrastive (ReSC) training scheme to utilize the community information. Additionally, the real-world graphs are complex and often consist of multiple views. In this paper, we demonstrate that the proposed gCooL can also be naturally adapted to multiplex graphs. Finally, we comprehensively evaluate the proposed gCooL on a variety of real-world graphs. The experimental results show that the gCooL outperforms the state-of-the-art methods.

Graph Neural Networks (GNNs) show promising results for graph tasks. However, existing GNNs' generalization ability will degrade when there exist distribution shifts between testing and training graph data. The cardinal impetus underlying the severe degeneration is that the GNNs are architected predicated upon the I.I.D assumptions. In such a setting, GNNs are inclined to leverage imperceptible statistical correlations subsisting in the training set to predict, albeit it is a spurious correlation. In this paper, we study the problem of the generalization ability of GNNs in Out-Of-Distribution (OOD) settings. To solve this problem, we propose the Learning to Reweight for Generalizable Graph Neural Network (L2R-GNN) to enhance the generalization ability for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. We propose a novel nonlinear graph decorrelation method, which can substantially improve the out-of-distribution generalization ability and compares favorably to previous methods in restraining the over-reduced sample size. The variables of the graph representation are clustered based on the stability of the correlation, and the graph decorrelation method learns weights to remove correlations between the variables of different clusters rather than any two variables. Besides, we interpose an efficacious stochastic algorithm upon bi-level optimization for the L2R-GNN framework, which facilitates simultaneously learning the optimal weights and GNN parameters, and avoids the overfitting problem. Experimental results show that L2R-GNN greatly outperforms baselines on various graph prediction benchmarks under distribution shifts.

Following the success of Word2Vec embeddings, graph embeddings (GEs) have gained substantial traction. GEs are commonly generated and evaluated extrinsically on downstream applications, but intrinsic evaluations of the original graph properties in terms of topological structure and semantic information have been lacking. Understanding these will help identify the deficiency of the various families of GE methods when vectorizing graphs in terms of preserving the relevant knowledge or learning incorrect knowledge. To address this, we propose RESTORE, a framework for intrinsic GEs assessment through graph reconstruction. We show that reconstructing the original graph from the underlying GEs yields insights into the relative amount of information preserved in a given vector form. We first introduce the graph reconstruction task. We generate GEs from three GE families based on factorization methods, random walks, and deep learning (with representative algorithms from each family) on the CommonSense Knowledge Graph (CSKG). We analyze their effectiveness in preserving the (a) topological structure of node-level graph reconstruction with an increasing number of hops and (b) semantic information on various word semantic and analogy tests. Our evaluations show deep learning-based GE algorithm (SDNE) is overall better at preserving (a) with a mean average precision (mAP) of 0.54 and 0.35 for 2 and 3-hop reconstruction respectively, while the factorization-based algorithm (HOPE) is better at encapsulating (b) with an average Euclidean distance of 0.14, 0.17, and 0.11 for 1, 2, and 3-hop reconstruction respectively. The modest performance of these GEs leaves room for further research avenues on better graph representation learning.

Subgraph GNNs are provably expressive neural architectures that learn graph representations from sets of subgraphs. Unfortunately, their applicability is hampered by the computational complexity associated with performing message passing on many subgraphs. In this paper, we consider the problem of learning to select a small subset of the large set of possible subgraphs in a data-driven fashion. We first motivate the problem by proving that there are families of WL-indistinguishable graphs for which there exist efficient subgraph selection policies: small subsets of subgraphs that can already identify all the graphs within the family. We then propose a new approach, called Policy-Learn, that learns how to select subgraphs in an iterative manner. We prove that, unlike popular random policies and prior work addressing the same problem, our architecture is able to learn the efficient policies mentioned above. Our experimental results demonstrate that Policy-Learn outperforms existing baselines across a wide range of datasets.

Simulating physics using Graph Neural Networks (GNNs) is predominantly driven by message-passing architectures, which face challenges in scaling and efficiency, particularly in handling large, complex meshes. These architectures have inspired numerous enhancements, including multigrid approaches and K-hop aggregation (using neighbours of distance K), yet they often introduce significant complexity and suffer from limited in-depth investigations. In response to these challenges, we propose a novel Graph Transformer architecture that leverages the adjacency matrix as an attention mask. The proposed approach incorporates innovative augmentations, including Dilated Sliding Windows and Global Attention, to extend receptive fields without sacrificing computational efficiency. Through extensive experimentation, we evaluate model size, adjacency matrix augmentations, positional encoding and K-hop configurations using challenging 3D computational fluid dynamics (CFD) datasets. We also train over 60 models to find a scaling law between training FLOPs and parameters. The introduced models demonstrate remarkable scalability, performing on meshes with up to 300k nodes and 3 million edges. Notably, the smallest model achieves parity with MeshGraphNet while being 7times faster and 6times smaller. The largest model surpasses the previous state-of-the-art by 38.8\% on average and outperforms MeshGraphNet by 52\% on the all-rollout RMSE, while having a similar training speed. Code and datasets are available at https://github.com/DonsetPG/graph-physics.

Graph In-Context Learning, with the ability to adapt pre-trained graph models to novel and diverse downstream graphs without updating any parameters, has gained much attention in the community. The key to graph in-context learning is to perform downstream graphs conditioned on chosen prompt examples. Existing methods randomly select subgraphs or edges as prompts, leading to noisy graph prompts and inferior model performance. Additionally, due to the gap between pre-training and testing graphs, when the number of classes in the testing graphs is much greater than that in the training, the in-context learning ability will also significantly deteriorate. To tackle the aforementioned challenges, we develop a multi-stage adaptive prompt optimization method GraphPrompter, which optimizes the entire process of generating, selecting, and using graph prompts for better in-context learning capabilities. Firstly, Prompt Generator introduces a reconstruction layer to highlight the most informative edges and reduce irrelevant noise for graph prompt construction. Furthermore, in the selection stage, Prompt Selector employs the k-nearest neighbors algorithm and pre-trained selection layers to dynamically choose appropriate samples and minimize the influence of irrelevant prompts. Finally, we leverage a Prompt Augmenter with a cache replacement strategy to enhance the generalization capability of the pre-trained model on new datasets. Extensive experiments show that GraphPrompter effectively enhances the in-context learning ability of graph models. On average across all the settings, our approach surpasses the state-of-the-art baselines by over 8%. Our code is released at https://github.com/karin0018/GraphPrompter.

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the 1-dimensional Weisfeiler--Leman algorithm (1-WL). Here, the 1-WL is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik--Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the 1-WL. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the 1-WL and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.