NeurIPS 2024 Papers

Node centralities play a pivotal role in network science, social network analysis, and recommender systems. In temporal data, static path-based centralities like closeness or betweenness can give misleading results about the true importance of nodes in a temporal graph. To address this issue, temporal generalizations of betweenness and closeness have been defined that are based on the shortest time-respecting paths between pairs of nodes. However, a major issue of those generalizations is that the calculation of such paths is computationally expensive. Addressing this issue, we study the application of De Bruijn Graph Neural Networks (DBGNN), a time-aware graph neural network architecture, to predict temporal path-based centralities in time series data. We experimentally evaluate our approach in 13 temporal graphs from biological and social systems and show that it considerably improves the prediction of betweenness and closeness centrality compared to (i) a static Graph Convolutional Neural Network, (ii) an efficient sampling-based approximation technique for temporal betweenness, and (iii) two state-of-the-art time-aware graph learning techniques for dynamic graphs.

Graph neural networks (GNNs) provide state-of-the-art results in a wide variety of tasks which typically involve predicting features at the vertices of a graph. They are built from layers of graph convolutions which serve as a powerful inductive bias for describing the flow of information among the vertices. Often, more than one data modality is available. This work considers a setting in which several graphs have the same vertex set and a common vertex-level learning task. This generalizes standard GNN models to GNNs with several graph operators that do not commute. We may call this model graph-tuple neural networks (GtNN). In this work, we develop the mathematical theory to address the stability and transferability of GtNNs using properties of non-commuting non-expansive operators. We develop a limit theory of graphon-tuple neural networks and use it to prove a universal transferability theorem that guarantees that all graph-tuple neural networks are transferable on convergent graph-tuple sequences. In particular, there is no non-transferable energy under the convergence we consider here. Our theoretical results extend well-known transferability theorems for GNNs to the case of several simultaneous graphs (GtNNs) and provide a strict improvement on what is currently known even in the GNN case. We illustrate our theoretical results with simple experiments on synthetic and real-world data. To this end, we derive a training procedure that provably enforces the stability of the resulting model.

Neural algorithmic reasoning is an emerging area of machine learning that focuses on building neural networks capable of solving complex algorithmic tasks. Recent advancements predominantly follow the standard supervised learning paradigm -- feeding an individual problem instance into the network each time and training it to approximate the execution steps of a classical algorithm. We challenge this mode and propose a novel open-book learning framework. In this framework, whether during training or testing, the network can access and utilize all instances in the training dataset when reasoning for a given instance. Empirical evaluation is conducted on the challenging CLRS Algorithmic Reasoning Benchmark, which consists of 30 diverse algorithmic tasks. Our open-book learning framework exhibits a significant enhancement in neural reasoning capabilities. Further, we notice that there is recent literature suggesting that multi-task training on CLRS can improve the reasoning accuracy of certain tasks, implying intrinsic connections between different algorithmic tasks. We delve into this direction via the open-book framework. When the network reasons for a specific task, we enable it to aggregate information from training instances of other tasks in an attention-based manner. We show that this open-book attention mechanism offers insights into the inherent relationships among various tasks in the benchmark and provides a robust tool for interpretable multi-task training.

Message passing plays a vital role in graph neural networks (GNNs) for effective feature learning. However, the over-reliance on input topology diminishes the efficacy of message passing and restricts the ability of GNNs. Despite efforts to mitigate the reliance, existing study encounters message-passing bottlenecks or high computational expense problems, which invokes the demands for flexible message passing with low complexity. In this paper, we propose a novel dynamic message-passing mechanism for GNNs. It projects graph nodes and learnable pseudo nodes into a common space with measurable spatial relations between them. With nodes moving in the space, their evolving relations facilitate flexible pathway construction for a dynamic message-passing process. Associating pseudo nodes to input graphs with their measured relations, graph nodes can communicate with each other intermediately through pseudo nodes under linear complexity. We further develop a GNN model named $\mathtt{N^2}$ based on our dynamic message-passing mechanism. $\mathtt{N^2}$ employs a single recurrent layer to recursively generate the displacements of nodes and construct optimal dynamic pathways. Evaluation on eighteen benchmarks demonstrates the superior performance of $\mathtt{N^2}$ over popular GNNs. $\mathtt{N^2}$ successfully scales to large-scale benchmarks and requires significantly fewer parameters for graph classification with the shared recurrent layer.

In the realm of graph learning, there is a category of methods that conceptualize graphs as hierarchical structures, utilizing node clustering to capture broader structural information. While generally effective, these methods often rely on a fixed graph coarsening routine, leading to overly homogeneous cluster representations and loss of node-level information. In this paper, we envision the graph as a network of interconnected node sets without compressing each cluster into a single embedding. To enable effective information transfer among these node sets, we propose the Node-to-Cluster Attention (N2C-Attn) mechanism. N2C-Attn incorporates techniques from Multiple Kernel Learning into the kernelized attention framework, effectively capturing information at both node and cluster levels. We then devise an efficient form for N2C-Attn using the cluster-wise message-passing framework, achieving linear time complexity. We further analyze how N2C-Attn combines bi-level feature maps of queries and keys, demonstrating its capability to merge dual-granularity information. The resulting architecture, Cluster-wise Graph Transformer (Cluster-GT), which uses node clusters as tokens and employs our proposed N2C-Attn module, shows superior performance on various graph-level tasks. Code is available at https://github.com/LUMIA-Group/Cluster-wise-Graph-Transformer.

Open-set Classification (OSC) is a critical requirement for safely deploying machine learning models in the open world, which aims to classify samples from known classes and reject samples from out-of-distribution (OOD). Existing methods exploit the feature space of trained network and attempt at estimating the uncertainty in the predictions. However, softmax-based neural networks are found to be overly confident in their predictions even on data they have never seen before and the immense diversity of the OOD examples also makes such methods fragile. To this end, we follow the idea of estimating the underlying density of the training data to decide whether a given input is close to the in-distribution (IND) data and adopt Energy-based models (EBMs) as density estimators. A novel energy-based generative open-set node classification method, \textit{EGonc}, is proposed to achieve open-set graph learning. Specifically, we generate substitute unknowns to mimic the distribution of real open-set samples firstly, based on the information of graph structures. Then, an additional energy logit representing the virtual OOD class is learned from the residual of the feature against the principal space, and matched with the original logits by a constant scaling. This virtual logit serves as the indicator of OOD-ness. EGonc has nice theoretical properties that guarantee an overall distinguishable margin between the detection scores for IND and OOD samples. Comprehensive experimental evaluations of EGonc also demonstrate its superiority.

Efficient computation of graph diffusion equations (GDEs), such as Personalized PageRank, Katz centrality, and the Heat kernel, is crucial for clustering, training neural networks, and many other graph-related problems. Standard iterative methods require accessing the whole graph per iteration, making them time-consuming for large-scale graphs. While existing local solvers approximate diffusion vectors through heuristic local updates, they often operate sequentially and are typically designed for specific diffusion types, limiting their applicability. Given that diffusion vectors are highly localizable, as measured by the participation ratio, this paper introduces a novel framework for approximately solving GDEs using a local diffusion process. This framework reveals the suboptimality of existing local solvers. Furthermore, our approach effectively localizes standard iterative solvers by designing simple and provably sublinear time algorithms. These new local solvers are highly parallelizable, making them well-suited for implementation on GPUs. We demonstrate the effectiveness of our framework in quickly obtaining approximate diffusion vectors, achieving up to a hundred-fold speed improvement, and its applicability to large-scale dynamic graphs. Our framework could also facilitate more efficient local message-passing mechanisms for GNNs.

Heterophily, or the tendency of connected nodes in networks to have different class labels or dissimilar features, has been identified as challenging for many Graph Neural Network (GNN) models. While the challenges of applying GNNs for node classification when class labels display strong heterophily are well understood, it is unclear how heterophily affects GNN performance in other important graph learning tasks where class labels are not available. In this work, we focus on the link prediction task and systematically analyze the impact of heterophily in node features on GNN performance. We first introduce formal definitions of homophilic and heterophilic link prediction tasks, and present a theoretical framework that highlights the different optimizations needed for the respective tasks. We then analyze how different link prediction encoders and decoders adapt to varying levels of feature homophily and introduce designs for improved performance. Based on our definitions, we identify and analyze six real-world benchmarks spanning from homophilic to heterophilic link prediction settings, with graphs containing up to 30M edges. Our empirical analysis on a variety of synthetic and real-world datasets confirms our theoretical insights and highlights the importance of adopting learnable decoders and GNN encoders with ego- and neighbor-embedding separation in message passing for link prediction tasks beyond homophily.

Detecting dependencies among variables is a fundamental task across scientific disciplines. We propose a novel neural network model for graph structure inference, which aims to learn a mapping from observational data to the corresponding underlying dependence structures. The model is trained with variably shaped and coupled simulated input data and requires only a single forward pass through the trained network for inference. Central to our approach is a novel bilinear attention mechanism (BAM) operating on covariance matrices of transformed data while respecting the geometry of the manifold of symmetric positive definite (SPD) matrices. Inspired by graphical lasso methods, our model optimizes over continuous graph representations in the SPD space, where inverse covariance matrices encode conditional independence relations. Empirical evaluations demonstrate the robustness of our method in detecting diverse dependencies, excelling in undirected graph estimation and showing competitive performance in completed partially directed acyclic graph estimation via a novel two-step approach. The trained model effectively detects causal relationships and generalizes well across different functional forms of nonlinear dependencies.

Recent research has underscored the efficacy of Graph Neural Networks (GNNs) in modeling diverse geometric structures within graph data. However, real-world graphs typically exhibit geometrically heterogeneous characteristics, rendering the confinement to a single geometric paradigm insufficient for capturing their intricate structural complexities. To address this limitation, we examine the performance of GNNs across various geometries through the lens of knowledge distillation (KD) and introduce a novel cross-geometric framework. This framework encodes graphs by integrating both Euclidean and hyperbolic geometries in a space-mixing fashion. Our approach employs multiple teacher models, each generating hint embeddings that encapsulate distinct geometric properties. We then implement a structure-wise knowledge transfer module that optimally leverages these embeddings within their respective geometric contexts, thereby enhancing the training efficacy of the student model. Additionally, our framework incorporates a geometric optimization network designed to bridge the distributional disparities among these embeddings. Experimental results demonstrate that our model-agnostic framework more effectively captures topological graph knowledge, resulting in superior performance of the student models when compared to traditional KD methodologies.

Zero-shot graph machine learning, especially with graph neural networks (GNNs), has garnered significant interest due to the challenge of scarce labeled data. While methods like self-supervised learning and graph prompt learning have been extensively explored, they often rely on fine-tuning with task-specific labels, limiting their effectiveness in zero-shot scenarios. Inspired by the zero-shot capabilities of instruction-fine-tuned large language models (LLMs), we introduce a novel framework named Token Embedding-Aligned Graph Language Model (TEA-GLM) that leverages LLMs as cross-dataset and cross-task zero-shot learners for graph machine learning. Concretely, we pretrain a GNN, aligning its representations with token embeddings of an LLM. We then train a linear projector that transforms the GNN's representations into a fixed number of graph token embeddings without tuning the LLM. A unified instruction is designed for various graph tasks at different levels, such as node classification (node-level) and link prediction (edge-level). These design choices collectively enhance our method's effectiveness in zero-shot learning, setting it apart from existing methods. Experiments show that our graph token embeddings help the LLM predictor achieve state-of-the-art performance on unseen datasets and tasks compared to other methods using LLMs as predictors. Our code is available at https://github.com/W-rudder/TEA-GLM.

Semi-supervised graph domain adaptation, as a branch of graph transfer learning, aims to annotate unlabeled target graph nodes by utilizing transferable knowledge learned from a label-scarce source graph. However, most existing studies primarily concentrate on aligning feature distributions directly to extract domain-invariant features, while ignoring the utilization of the intrinsic structure information in graphs. Inspired by the significance of data structure information in enhancing models' generalization performance, this paper aims to investigate how to leverage the structure information to assist graph transfer learning. To this end, we propose an innovative framework called TFGDA. Specially, TFGDA employs a structure alignment strategy named STSA to encode graphs' topological structure information into the latent space, greatly facilitating the learning of transferable features. To achieve a stable alignment of feature distributions, we also introduce a SDA strategy to mitigate domain discrepancy on the sphere. Moreover, to address the overfitting issue caused by label scarcity, a simple but effective RNC strategy is devised to guide the discriminative clustering of unlabeled nodes. Experiments on various benchmarks demonstrate the superiority of TFGDA over SOTA methods.

_Graph Neural Tangent Kernel_ (GNTK) fuses graph neural networks and graph kernels, simplifies the process of graph representation learning, interprets the training dynamics of graph neural networks, and serves various applications like protein identification, image segmentation, and social network analysis. In practice, graph data carries complex information among entities that inevitably evolves over time, and previous static graph neural tangent kernel methods may be stuck in the sub-optimal solution in terms of both effectiveness and efficiency. As a result, extending the advantage of GNTK to temporal graphs becomes a critical problem. To this end, we propose the temporal graph neural tangent kernel, which not only extends the simplicity and interpretation ability of GNTK to the temporal setting but also leads to rigorous temporal graph classification error bounds. Furthermore, we prove that when the input temporal graph grows over time in the number of nodes, our temporal graph neural tangent kernel will converge in the limit to the _graphon_ NTK value, which implies the transferability and robustness of the proposed kernel method, named **Temp**oral **G**raph **N**eural **T**angent **K**ernel with **G**raphon-**G**uaranteed or **Temp-G$^3$NTK**. In addition to the theoretical analysis, we also perform extensive experiments, not only demonstrating the superiority of Temp-G$^3$NTK in the temporal graph classification task, but also showing that Temp-G^3NTK can achieve very competitive performance in node-level tasks like node classification compared with various SOTA graph kernel and representation learning baselines. Our code is available at https://github.com/kthrn22/TempGNTK.

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs). Graph kernels often suffer from computational costs and manual feature engineering, while GNNs commonly utilize global pooling operations, risking the loss of structural or semantic information. This work introduces Graph Reference Distribution Learning (GRDL), an efficient and accurate graph classification method. GRDL treats each graph's latent node embeddings given by GNN layers as a discrete distribution, enabling direct classification without global pooling, based on maximum mean discrepancy to adaptively learned reference distributions. To fully understand this new model (the existing theories do not apply) and guide its configuration (e.g., network architecture, references' sizes, number, and regularization) for practical use, we derive generalization error bounds for GRDL and verify them numerically. More importantly, our theoretical and numerical results both show that GRDL has a stronger generalization ability than GNNs with global pooling operations. Experiments on moderate-scale and large-scale graph datasets show the superiority of GRDL over the state-of-the-art, emphasizing its remarkable efficiency, being at least 10 times faster than leading competitors in both training and inference stages.

Non-maximum suppression (NMS) is an indispensable post-processing step in object detection. With the continuous optimization of network models, NMS has become the ``last mile'' to enhance the efficiency of object detection. This paper systematically analyzes NMS from a graph theory perspective for the first time, revealing its intrinsic structure. Consequently, we propose two optimization methods, namely QSI-NMS and BOE-NMS. The former is a fast recursive divide-and-conquer algorithm with negligible mAP loss, and its extended version (eQSI-NMS) achieves optimal complexity of $\mathcal{O}(n\log n)$. The latter, concentrating on the locality of NMS, achieves an optimization at a constant level without an mAP loss penalty. Moreover, to facilitate rapid evaluation of NMS methods for researchers, we introduce NMS-Bench, the first benchmark designed to comprehensively assess various NMS methods. Taking the YOLOv8-N model on MS COCO 2017 as the benchmark setup, our method QSI-NMS provides $6.2\times$ speed of original NMS on the benchmark, with a $0.1\%$ decrease in mAP. The optimal eQSI-NMS, with only a $0.3\%$ mAP decrease, achieves $10.7\times$ speed. Meanwhile, BOE-NMS exhibits $5.1\times$ speed with no compromise in mAP.

We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the expressivity of GNNs using diverse activation functions and arithmetic circuits over real numbers. In our results the activation function of the network becomes a gate type in the circuit. Our result holds for families of constant depth circuits and networks, both uniformly and non-uniformly, for all common activation functions.

Graph Neural Networks (GNNs) have shown great performance in various tasks, with the core idea of learning from data labels and aggregating messages within the neighborhood of nodes. However, the common challenges in graphs are twofold: insufficient accurate (high-quality) labels and limited neighbors for nodes, resulting in weak GNNs. Existing graph augmentation methods typically address only one of these challenges, often adding training costs or relying on oversimplified or knowledge-intensive strategies, limiting their generalization. To simultaneously address both challenges faced by graphs in a generalized way, we propose an elegant method called IntraMix. Considering the incompatibility of vanilla Mixup with the complex topology of graphs, IntraMix innovatively employs Mixup among inaccurate labeled data of the same class, generating high-quality labeled data at minimal cost. Additionally, it finds data with high confidence of being clustered into the same group as the generated data to serve as their neighbors, thereby enriching the neighborhoods of graphs. IntraMix efficiently tackles both issues faced by graphs and challenges the prior notion of the limited effectiveness of Mixup in node classification. IntraMix is a theoretically grounded plug-in-play method that can be readily applied to all GNNs. Extensive experiments demonstrate the effectiveness of IntraMix across various GNNs and datasets. Our code is available at: [https://github.com/Zhengsh123/IntraMix](https://github.com/Zhengsh123/IntraMix).

Inspired by the success of foundation models in applications such as ChatGPT, as graph data has been ubiquitous, one can envision the far-reaching impacts that can be brought by Graph Foundation Models (GFMs) with broader applications in the areas such as scientific research, social network analysis, drug discovery, and e-commerce. Despite the significant progress of pre-trained graph neural networks, there haven’t been GFMs that can achieve desired performance on various graph-learning-related tasks. Building GFMs may rely on a vocabulary that encodes transferable patterns shared among different tasks and domains. Unlike image and text, defining such transferable patterns for graphs remains an open question. In this paper, we aim to bridge this gap by rethinking the transferable patterns on graphs as computation trees -- i.e., tree structures derived from the message-passing process. Based on this insight, we propose a cross-task, cross-domain graph foundation model named GFT, short for Graph Foundation model with transferable Tree vocabulary. By treating computation trees as tokens within the transferable vocabulary, GFT improves model generalization and reduces the risk of negative transfer. The theoretical analyses and extensive experimental studies have demonstrated the transferability of computation trees and shown the effectiveness of GFT across diverse tasks and domains in graph learning. The open source code and data are available at https://github.com/Zehong-Wang/GFT.

The emergence of large language models (LLMs) has revolutionized the way we interact with graphs, leading to a new paradigm called GraphLLM. Despite the rapid development of GraphLLM methods in recent years, the progress and understanding of this field remain unclear due to the lack of a benchmark with consistent experimental protocols. To bridge this gap, we introduce GLBench, the first comprehensive benchmark for evaluating GraphLLM methods in both supervised and zero-shot scenarios. GLBench provides a fair and thorough evaluation of different categories of GraphLLM methods, along with traditional baselines such as graph neural networks. Through extensive experiments on a collection of real-world datasets with consistent data processing and splitting strategies, we have uncovered several key findings. Firstly, GraphLLM methods outperform traditional baselines in supervised settings, with LLM-as-enhancers showing the most robust performance. However, using LLMs as predictors is less effective and often leads to uncontrollable output issues. We also notice that no clear scaling laws exist for current GraphLLM methods. In addition, both structures and semantics are crucial for effective zero-shot transfer, and our proposed simple baseline can even outperform several models tailored for zero-shot scenarios. The data and code of the benchmark can be found at https://github.com/NineAbyss/GLBench.