This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width Neural Networks are connecting Deep Learning to Gaussian Processes and Kernels, both Machine Learning Frameworks with long traditions and extensive theoretical foundations. Gaussian Processes and Kernels have much less hyperparameters then Neural Networks and can be used for uncertainty estimation, making them more user friendly for applications. This works extends the increasing amount of research connecting Gaussian Processes and Kernels to Neural Networks. The Kernel and Gaussian Process closed forms are derived for a variety of architectures, namely the standard Graph Neural Network, the Graph Neural Network with Skip-Concatenate Connections and the Graph Attention Neural Network. All architectures are evaluated on a variety of datasets on the task of transductive Node Regression and Classification. Additionally, a Spectral Sparsification method known as Effective Resistance is used to improve runtime and memory requirements. Extending the setting to inductive graph learning tasks (Graph Regression/ Classification) is straightforward and is briefly discussed in 3.5.
Multimodal learning combines multiple data modalities, broadening the types and complexity of data our models can utilize: for example, from plain text to image-caption pairs. Most multimodal learning algorithms focus on modeling simple one-to-one pairs of data from two modalities, such as image-caption pairs, or audio-text pairs. However, in most real-world settings, entities of different modalities interact with each other in more complex and multifaceted ways, going beyond one-to-one mappings. We propose to represent these complex relationships as graphs, allowing us to capture data with any number of modalities, and with complex relationships between modalities that can flexibly vary from one sample to another. Toward this goal, we propose Multimodal Graph Learning (MMGL), a general and systematic framework for capturing information from multiple multimodal neighbors with relational structures among them. In particular, we focus on MMGL for generative tasks, building upon pretrained Language Models (LMs), aiming to augment their text generation with multimodal neighbor contexts. We study three research questions raised by MMGL: (1) how can we infuse multiple neighbor information into the pretrained LMs, while avoiding scalability issues? (2) how can we infuse the graph structure information among multimodal neighbors into the LMs? and (3) how can we finetune the pretrained LMs to learn from the neighbor context in a parameter-efficient manner? We conduct extensive experiments to answer these three questions on MMGL and analyze the empirical results to pave the way for future MMGL research.
The advancement of Large Language Models (LLMs) has remarkably pushed the boundaries towards artificial general intelligence (AGI), with their exceptional ability on understanding diverse types of information, including but not limited to images and audio. Despite this progress, a critical gap remains in empowering LLMs to proficiently understand and reason on graph data. Recent studies underscore LLMs' underwhelming performance on fundamental graph reasoning tasks. In this paper, we endeavor to unearth the obstacles that impede LLMs in graph reasoning, pinpointing the common practice of converting graphs into natural language descriptions (Graph2Text) as a fundamental bottleneck. To overcome this impediment, we introduce GraphLLM, a pioneering end-to-end approach that synergistically integrates graph learning models with LLMs. This synergy equips LLMs with the ability to proficiently interpret and reason on graph data, harnessing the superior expressive power of graph learning models. Our empirical evaluations across four fundamental graph reasoning tasks validate the effectiveness of GraphLLM. The results exhibit a substantial average accuracy enhancement of 54.44%, alongside a noteworthy context reduction of 96.45% across various graph reasoning tasks.
Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.
Designing a single model to address multiple tasks has been a long-standing objective in artificial intelligence. Recently, large language models have demonstrated exceptional capability in solving different tasks within the language domain. However, a unified model for various graph tasks remains underexplored, primarily due to the challenges unique to the graph learning domain. First, graph data from different areas carry distinct attributes and follow different distributions. Such discrepancy makes it hard to represent graphs in a single representation space. Second, tasks on graphs diversify into node, link, and graph tasks, requiring distinct embedding strategies. Finally, an appropriate graph prompting paradigm for in-context learning is unclear. We propose \textbf{One for All (OFA)}, the first general framework that can use a single graph model to address the above challenges. Specifically, OFA proposes text-attributed graphs to unify different graph data by describing nodes and edges with natural language and uses language models to encode the diverse and possibly cross-domain text attributes to feature vectors in the same embedding space. Furthermore, OFA introduces the concept of nodes-of-interest to standardize different tasks with a single task representation. For in-context learning on graphs, OFA introduces a novel graph prompting paradigm that appends prompting substructures to the input graph, which enables it to address varied tasks without fine-tuning. We train the OFA model using graph data from multiple domains (including citation networks, molecular graphs, knowledge graphs, etc.) simultaneously and evaluate its ability in supervised, few-shot, and zero-shot learning scenarios. OFA performs well across different tasks, making it the first general-purpose across-domains classification model on graphs.
Pulmonary diseases rank prominently among the principal causes of death worldwide. Curing them will require, among other things, a better understanding of the complex 3D tree-shaped structures within the pulmonary system, such as airways, arteries, and veins. Traditional approaches using high-resolution image stacks and standard CNNs on dense voxel grids face challenges in computational efficiency, limited resolution, local context, and inadequate preservation of shape topology. Our method addresses these issues by shifting from dense voxel to sparse point representation, offering better memory efficiency and global context utilization. However, the inherent sparsity in point representation can lead to a loss of crucial connectivity in tree-shaped structures. To mitigate this, we introduce graph learning on skeletonized structures, incorporating differentiable feature fusion for improved topology and long-distance context capture. Furthermore, we employ an implicit function for efficient conversion of sparse representations into dense reconstructions end-to-end. The proposed method not only delivers state-of-the-art performance in labeling accuracy, both overall and at key locations, but also enables efficient inference and the generation of closed surface shapes. Addressing data scarcity in this field, we have also curated a comprehensive dataset to validate our approach. Data and code are available at \url{https://github.com/M3DV/pulmonary-tree-labeling}.
Large language models (LLMs) are gaining increasing attention for their capability to process graphs with rich text attributes, especially in a zero-shot fashion. Recent studies demonstrate that LLMs obtain decent text classification performance on common text-rich graph benchmarks, and the performance can be improved by appending encoded structural information as natural languages into prompts. We aim to understand why the incorporation of structural information inherent in graph data can improve the prediction performance of LLMs. First, we rule out the concern of data leakage by curating a novel leakage-free dataset and conducting a comparative analysis alongside a previously widely-used dataset. Second, as past work usually encodes the ego-graph by describing the graph structure in natural language, we ask the question: do LLMs understand the graph structure in accordance with the intent of the prompt designers? Third, we investigate why LLMs can improve their performance after incorporating structural information. Our exploration of these questions reveals that (i) there is no substantial evidence that the performance of LLMs is significantly attributed to data leakage; (ii) instead of understanding prompts as graph structures as intended by the prompt designers, LLMs tend to process prompts more as contextual paragraphs and (iii) the most efficient elements of the local neighborhood included in the prompt are phrases that are pertinent to the node label, rather than the graph structure.
Protein-protein interactions (PPIs) are critical for various biological processes, and understanding their dynamics is essential for decoding molecular mechanisms and advancing fields such as cancer research and drug discovery. Mutations in PPIs can disrupt protein binding affinity and lead to functional changes and disease. Predicting the impact of mutations on binding affinity is valuable but experimentally challenging. Computational methods, including physics-based and machine learning-based approaches, have been developed to address this challenge. Machine learning-based methods, fueled by extensive PPI datasets such as Ab-Bind, PINT, SKEMPI, and others, have shown promise in predicting binding affinity changes. However, accurate predictions and generalization of these models across different datasets remain challenging. Geometric graph learning has emerged as a powerful approach, combining graph theory and machine learning, to capture structural features of biomolecules. We present GGL-PPI, a novel method that integrates geometric graph learning and machine learning to predict mutation-induced binding free energy changes. GGL-PPI leverages atom-level graph coloring and multi-scale weighted colored geometric subgraphs to extract informative features, demonstrating superior performance on three validation datasets, namely AB-Bind, SKEMPI 1.0, and SKEMPI 2.0 datasets. Evaluation on a blind test set highlights the unbiased predictions of GGL-PPI for both direct and reverse mutations. The findings underscore the potential of GGL-PPI in accurately predicting binding free energy changes, contributing to our understanding of PPIs and aiding drug design efforts.
Audiovisual data is everywhere in this digital age, which raises higher requirements for the deep learning models developed on them. To well handle the information of the multi-modal data is the key to a better audiovisual modal. We observe that these audiovisual data naturally have temporal attributes, such as the time information for each frame in the video. More concretely, such data is inherently multi-modal according to both audio and visual cues, which proceed in a strict chronological order. It indicates that temporal information is important in multi-modal acoustic event modeling for both intra- and inter-modal. However, existing methods deal with each modal feature independently and simply fuse them together, which neglects the mining of temporal relation and thus leads to sub-optimal performance. With this motivation, we propose a Temporal Multi-modal graph learning method for Acoustic event Classification, called TMac, by modeling such temporal information via graph learning techniques. In particular, we construct a temporal graph for each acoustic event, dividing its audio data and video data into multiple segments. Each segment can be considered as a node, and the temporal relationships between nodes can be considered as timestamps on their edges. In this case, we can smoothly capture the dynamic information in intra-modal and inter-modal. Several experiments are conducted to demonstrate TMac outperforms other SOTA models in performance. Our code is available at https://github.com/MGitHubL/TMac.
Continual graph learning (CGL) is purposed to continuously update a graph model with graph data being fed in a streaming manner. Since the model easily forgets previously learned knowledge when training with new-coming data, the catastrophic forgetting problem has been the major focus in CGL. Recent replay-based methods intend to solve this problem by updating the model using both (1) the entire new-coming data and (2) a sampling-based memory bank that stores replayed graphs to approximate the distribution of historical data. After updating the model, a new replayed graph sampled from the incoming graph will be added to the existing memory bank. Despite these methods are intuitive and effective for the CGL, two issues are identified in this paper. Firstly, most sampling-based methods struggle to fully capture the historical distribution when the storage budget is tight. Secondly, a significant data imbalance exists in terms of the scales of the complex new-coming graph data and the lightweight memory bank, resulting in unbalanced training. To solve these issues, a Condense and Train (CaT) framework is proposed in this paper. Prior to each model update, the new-coming graph is condensed to a small yet informative synthesised replayed graph, which is then stored in a Condensed Graph Memory with historical replay graphs. In the continual learning phase, a Training in Memory scheme is used to update the model directly with the Condensed Graph Memory rather than the whole new-coming graph, which alleviates the data imbalance problem. Extensive experiments conducted on four benchmark datasets successfully demonstrate superior performances of the proposed CaT framework in terms of effectiveness and efficiency. The code has been released on https://github.com/superallen13/CaT-CGL.
Irregular data in real-world are usually organized as heterogeneous graphs (HGs) consisting of multiple types of nodes and edges. To explore useful knowledge from real-world data, both the large-scale encyclopedic HG datasets and corresponding effective learning methods are crucial, but haven't been well investigated. In this paper, we construct a large-scale HG benchmark dataset named UniKG from Wikidata to facilitate knowledge mining and heterogeneous graph representation learning. Overall, UniKG contains more than 77 million multi-attribute entities and 2000 diverse association types, which significantly surpasses the scale of existing HG datasets. To perform effective learning on the large-scale UniKG, two key measures are taken, including (i) the semantic alignment strategy for multi-attribute entities, which projects the feature description of multi-attribute nodes into a common embedding space to facilitate node aggregation in a large receptive field; (ii) proposing a novel plug-and-play anisotropy propagation module (APM) to learn effective multi-hop anisotropy propagation kernels, which extends methods of large-scale homogeneous graphs to heterogeneous graphs. These two strategies enable efficient information propagation among a tremendous number of multi-attribute entities and meantimes adaptively mine multi-attribute association through the multi-hop aggregation in large-scale HGs. We set up a node classification task on our UniKG dataset, and evaluate multiple baseline methods which are constructed by embedding our APM into large-scale homogenous graph learning methods. Our UniKG dataset and the baseline codes have been released at https://github.com/Yide-Qiu/UniKG.
The recent Long-Range Graph Benchmark (LRGB, Dwivedi et al. 2022) introduced a set of graph learning tasks strongly dependent on long-range interaction between vertices. Empirical evidence suggests that on these tasks Graph Transformers significantly outperform Message Passing GNNs (MPGNNs). In this paper, we carefully reevaluate multiple MPGNN baselines as well as the Graph Transformer GPS (Ramp\'a\v{s}ek et al. 2022) on LRGB. Through a rigorous empirical analysis, we demonstrate that the reported performance gap is overestimated due to suboptimal hyperparameter choices. It is noteworthy that across multiple datasets the performance gap completely vanishes after basic hyperparameter optimization. In addition, we discuss the impact of lacking feature normalization for LRGB's vision datasets and highlight a spurious implementation of LRGB's link prediction metric. The principal aim of our paper is to establish a higher standard of empirical rigor within the graph machine learning community.
Anchor-based multi-view graph clustering (AMVGC) has received abundant attention owing to its high efficiency and the capability to capture complementary structural information across multiple views. Intuitively, a high-quality anchor graph plays an essential role in the success of AMVGC. However, the existing AMVGC methods only consider single-structure information, i.e., local or global structure, which provides insufficient information for the learning task. To be specific, the over-scattered global structure leads to learned anchors failing to depict the cluster partition well. In contrast, the local structure with an improper similarity measure results in potentially inaccurate anchor assignment, ultimately leading to sub-optimal clustering performance. To tackle the issue, we propose a novel anchor-based multi-view graph clustering framework termed Efficient Multi-View Graph Clustering with Local and Global Structure Preservation (EMVGC-LG). Specifically, a unified framework with a theoretical guarantee is designed to capture local and global information. Besides, EMVGC-LG jointly optimizes anchor construction and graph learning to enhance the clustering quality. In addition, EMVGC-LG inherits the linear complexity of existing AMVGC methods respecting the sample number, which is time-economical and scales well with the data size. Extensive experiments demonstrate the effectiveness and efficiency of our proposed method.
The success of existing multi-view clustering (MVC) relies on the assumption that all views are complete. However, samples are usually partially available due to data corruption or sensor malfunction, which raises the research of incomplete multi-view clustering (IMVC). Although several anchor-based IMVC methods have been proposed to process the large-scale incomplete data, they still suffer from the following drawbacks: i) Most existing approaches neglect the inter-view discrepancy and enforce cross-view representation to be consistent, which would corrupt the representation capability of the model; ii) Due to the samples disparity between different views, the learned anchor might be misaligned, which we referred as the Anchor-Unaligned Problem for Incomplete data (AUP-ID). Such the AUP-ID would cause inaccurate graph fusion and degrades clustering performance. To tackle these issues, we propose a novel incomplete anchor graph learning framework termed Scalable Incomplete Multi-View Clustering with Structure Alignment (SIMVC-SA). Specially, we construct the view-specific anchor graph to capture the complementary information from different views. In order to solve the AUP-ID, we propose a novel structure alignment module to refine the cross-view anchor correspondence. Meanwhile, the anchor graph construction and alignment are jointly optimized in our unified framework to enhance clustering quality. Through anchor graph construction instead of full graphs, the time and space complexity of the proposed SIMVC-SA is proven to be linearly correlated with the number of samples. Extensive experiments on seven incomplete benchmark datasets demonstrate the effectiveness and efficiency of our proposed method. Our code is publicly available at https://github.com/wy1019/SIMVC-SA.
The electronic design automation of analog circuits has been a longstanding challenge in the integrated circuit field due to the huge design space and complex design trade-offs among circuit specifications. In the past decades, intensive research efforts have mostly been paid to automate the transistor sizing with a given circuit topology. By recognizing the graph nature of circuits, this paper presents a Circuit Graph Neural Network (CktGNN) that simultaneously automates the circuit topology generation and device sizing based on the encoder-dependent optimization subroutines. Particularly, CktGNN encodes circuit graphs using a two-level GNN framework (of nested GNN) where circuits are represented as combinations of subgraphs in a known subgraph basis. In this way, it significantly improves design efficiency by reducing the number of subgraphs to perform message passing. Nonetheless, another critical roadblock to advancing learning-assisted circuit design automation is a lack of public benchmarks to perform canonical assessment and reproducible research. To tackle the challenge, we introduce Open Circuit Benchmark (OCB), an open-sourced dataset that contains $10$K distinct operational amplifiers with carefully-extracted circuit specifications. OCB is also equipped with communicative circuit generation and evaluation capabilities such that it can help to generalize CktGNN to design various analog circuits by producing corresponding datasets. Experiments on OCB show the extraordinary advantages of CktGNN through representation-based optimization frameworks over other recent powerful GNN baselines and human experts' manual designs. Our work paves the way toward a learning-based open-sourced design automation for analog circuits. Our source code is available at \url{https://github.com/zehao-dong/CktGNN}.
Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks including node classification and link prediction. However, these methods often suffer from data imbalance, a common issue in graph data where certain segments possess abundant data while others are scarce, thereby leading to biased learning outcomes. This necessitates the emerging field of imbalanced learning on graphs, which aims to correct these data distribution skews for more accurate and representative learning outcomes. In this survey, we embark on a comprehensive review of the literature on imbalanced learning on graphs. We begin by providing a definitive understanding of the concept and related terminologies, establishing a strong foundational understanding for readers. Following this, we propose two comprehensive taxonomies: (1) the problem taxonomy, which describes the forms of imbalance we consider, the associated tasks, and potential solutions; (2) the technique taxonomy, which details key strategies for addressing these imbalances, and aids readers in their method selection process. Finally, we suggest prospective future directions for both problems and techniques within the sphere of imbalanced learning on graphs, fostering further innovation in this critical area.
Class imbalance is prevalent in real-world node classification tasks and poses great challenges for graph learning models. Most existing studies are rooted in a class-rebalancing (CR) perspective and address class imbalance with class-wise reweighting or resampling. In this work, we approach the root cause of class-imbalance bias from an topological paradigm. Specifically, we theoretically reveal two fundamental phenomena in the graph topology that greatly exacerbate the predictive bias stemming from class imbalance. On this basis, we devise a lightweight topological augmentation framework BAT to mitigate the class-imbalance bias without class rebalancing. Being orthogonal to CR, BAT can function as an efficient plug-and-play module that can be seamlessly combined with and significantly boost existing CR techniques. Systematic experiments on real-world imbalanced graph learning tasks show that BAT can deliver up to 46.27% performance gain and up to 72.74% bias reduction over existing techniques. Code, examples, and documentations are available at https://github.com/ZhiningLiu1998/BAT.
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.
Accurate prediction of what types of patents that companies will apply for in the next period of time can figure out their development strategies and help them discover potential partners or competitors in advance. Although important, this problem has been rarely studied in previous research due to the challenges in modelling companies' continuously evolving preferences and capturing the semantic correlations of classification codes. To fill in this gap, we propose an event-based dynamic graph learning framework for patent application trend prediction. In particular, our method is founded on the memorable representations of both companies and patent classification codes. When a new patent is observed, the representations of the related companies and classification codes are updated according to the historical memories and the currently encoded messages. Moreover, a hierarchical message passing mechanism is provided to capture the semantic proximities of patent classification codes by updating their representations along the hierarchical taxonomy. Finally, the patent application trend is predicted by aggregating the representations of the target company and classification codes from static, dynamic, and hierarchical perspectives. Experiments on real-world data demonstrate the effectiveness of our approach under various experimental conditions, and also reveal the abilities of our method in learning semantics of classification codes and tracking technology developing trajectories of companies.
Contrastive graph node clustering via learnable data augmentation is a hot research spot in the field of unsupervised graph learning. The existing methods learn the sampling distribution of a pre-defined augmentation to generate data-driven augmentations automatically. Although promising clustering performance has been achieved, we observe that these strategies still rely on pre-defined augmentations, the semantics of the augmented graph can easily drift. The reliability of the augmented view semantics for contrastive learning can not be guaranteed, thus limiting the model performance. To address these problems, we propose a novel CONtrastiVe Graph ClustEring network with Reliable AugmenTation (CONVERT). Specifically, in our method, the data augmentations are processed by the proposed reversible perturb-recover network. It distills reliable semantic information by recovering the perturbed latent embeddings. Moreover, to further guarantee the reliability of semantics, a novel semantic loss is presented to constrain the network via quantifying the perturbation and recovery. Lastly, a label-matching mechanism is designed to guide the model by clustering information through aligning the semantic labels and the selected high-confidence clustering pseudo labels. Extensive experimental results on seven datasets demonstrate the effectiveness of the proposed method. We release the code and appendix of CONVERT at https://github.com/xihongyang1999/CONVERT on GitHub.