The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.
In this paper, we propose the Graph-Learning-Dual Graph Convolutional Neural Network called GLDGCN based on the classic Graph Convolutional Neural Network(GCN) by introducing dual convolutional layer and graph learning layer. We apply GLDGCN to the semi-supervised node classification task. Compared with the baseline methods, we achieve higher classification accuracy on three citation networks Citeseer, Cora and Pubmed, and we also analyze and discussabout selection of the hyperparameters and network depth. GLDGCN also perform well on the classic social network KarateClub and the new Wiki-CS dataset. For the insufficient ability of our algorithm to process large graphs during the experiment, we also introduce subgraph clustering and stochastic gradient descent methods into GCN and design a semi-supervised node classification algorithm based on the CLustering Graph Convolutional neural Network, which enables GCN to process large graph and improves its application value. We complete semi-supervised node classification experiments on two classic large graph which are PPI dataset (more than 50,000 nodes) and Reddit dataset (more than 200,000 nodes), and also perform well.
Pursuit-evasion games (PEGs) model interactions between a team of pursuers and an evader in graph-based environments such as urban street networks. Recent advancements have demonstrated the effectiveness of the pre-training and fine-tuning paradigm in PSRO to improve scalability in solving large-scale PEGs. However, these methods primarily focus on specific PEGs with fixed initial conditions that may vary substantially in real-world scenarios, which significantly hinders the applicability of the traditional methods. To address this issue, we introduce Grasper, a GeneRAlist purSuer for Pursuit-Evasion pRoblems, capable of efficiently generating pursuer policies tailored to specific PEGs. Our contributions are threefold: First, we present a novel architecture that offers high-quality solutions for diverse PEGs, comprising critical components such as (i) a graph neural network (GNN) to encode PEGs into hidden vectors, and (ii) a hypernetwork to generate pursuer policies based on these hidden vectors. As a second contribution, we develop an efficient three-stage training method involving (i) a pre-pretraining stage for learning robust PEG representations through self-supervised graph learning techniques like GraphMAE, (ii) a pre-training stage utilizing heuristic-guided multi-task pre-training (HMP) where heuristic-derived reference policies (e.g., through Dijkstra's algorithm) regularize pursuer policies, and (iii) a fine-tuning stage that employs PSRO to generate pursuer policies on designated PEGs. Finally, we perform extensive experiments on synthetic and real-world maps, showcasing Grasper's significant superiority over baselines in terms of solution quality and generalizability. We demonstrate that Grasper provides a versatile approach for solving pursuit-evasion problems across a broad range of scenarios, enabling practical deployment in real-world situations.
Random Projections have been widely used to generate embeddings for various graph learning tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper, we take a step further and investigate how well dot product and cosine similarity are preserved by random projections when these are applied over the rows of the graph matrix. Our analysis provides new asymptotic and finite-sample results, identifies pathological cases, and tests them with numerical experiments. We specialize our fundamental results to a ranking application by computing the probability of random projections flipping the node ordering induced by their embeddings. We find that, depending on the degree distribution, the method produces especially unreliable embeddings for the dot product, regardless of whether the adjacency or the normalized transition matrix is used. With respect to the statistical noise introduced by random projections, we show that cosine similarity produces remarkably more precise approximations.
The diagnosis and prognosis of cancer are typically based on multi-modal clinical data, including histology images and genomic data, due to the complex pathogenesis and high heterogeneity. Despite the advancements in digital pathology and high-throughput genome sequencing, establishing effective multi-modal fusion models for survival prediction and revealing the potential association between histopathology and transcriptomics remains challenging. In this paper, we propose Pathology-Genome Heterogeneous Graph (PGHG) that integrates whole slide images (WSI) and bulk RNA-Seq expression data with heterogeneous graph neural network for cancer survival analysis. The PGHG consists of biological knowledge-guided representation learning network and pathology-genome heterogeneous graph. The representation learning network utilizes the biological prior knowledge of intra-modal and inter-modal data associations to guide the feature extraction. The node features of each modality are updated through attention-based graph learning strategy. Unimodal features and bi-modal fused features are extracted via attention pooling module and then used for survival prediction. We evaluate the model on low-grade gliomas, glioblastoma, and kidney renal papillary cell carcinoma datasets from the Cancer Genome Atlas (TCGA) and the First Affiliated Hospital of Zhengzhou University (FAHZU). Extensive experimental results demonstrate that the proposed method outperforms both unimodal and other multi-modal fusion models. For demonstrating the model interpretability, we also visualize the attention heatmap of pathological images and utilize integrated gradient algorithm to identify important tissue structure, biological pathways and key genes.
This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By incorporating this assumption that the graph lies in a polytopic set into two established graph learning frameworks, we find that our approach yields better results with less computation.
Contemporary automatic first break (FB) picking methods typically analyze 1D signals, 2D source gathers, or 3D source-receiver gathers. Utilizing higher-dimensional data, such as 2D or 3D, incorporates global features, improving the stability of local picking. Despite the benefits, high-dimensional data requires structured input and increases computational demands. Addressing this, we propose a novel approach using deep graph learning called DGL-FB, constructing a large graph to efficiently extract information. In this graph, each seismic trace is represented as a node, connected by edges that reflect similarities. To manage the size of the graph, we develop a subgraph sampling technique to streamline model training and inference. Our proposed framework, DGL-FB, leverages deep graph learning for FB picking. It encodes subgraphs into global features using a deep graph encoder. Subsequently, the encoded global features are combined with local node signals and fed into a ResUNet-based 1D segmentation network for FB detection. Field survey evaluations of DGL-FB show superior accuracy and stability compared to a 2D U-Net-based benchmark method.
Graph neural networks (GNN) have achieved remarkable success in a wide range of tasks by encoding features combined with topology to create effective representations. However, the fundamental problem of understanding and analyzing how graph topology influences the performance of learning models on downstream tasks has not yet been well understood. In this paper, we propose a metric, TopoInf, which characterizes the influence of graph topology by measuring the level of compatibility between the topological information of graph data and downstream task objectives. We provide analysis based on the decoupled GNNs on the contextual stochastic block model to demonstrate the effectiveness of the metric. Through extensive experiments, we demonstrate that TopoInf is an effective metric for measuring topological influence on corresponding tasks and can be further leveraged to enhance graph learning.
Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is known to be highly sensitive to outliers, which can result in large inaccuracies if the outliers are given the same weight as other samples in the objective function. To mitigate this issue, we introduce a new and robust version of the GW distance called RGW. RGW features optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set. To make the benefits of RGW more accessible in practice, we develop a computationally efficient and theoretically provable procedure using Bregman proximal alternating linearized minimization algorithm. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of RGW on real-world graph learning tasks, such as subgraph matching and partial shape correspondence.
Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph learning. As an essential part of spectral GNNs, spectral graph convolution extracts crucial frequency information in graph data, leading to superior performance of spectral GNNs in downstream tasks. However, in this paper, we show that existing spectral GNNs remain critical drawbacks in performing the spectral graph convolution. Specifically, considering the spectral graph convolution as a construction operation towards target output, we prove that existing popular convolution paradigms cannot construct the target output with mild conditions on input graph signals, causing spectral GNNs to fall into suboptimal solutions. To address the issues, we rethink the spectral graph convolution from a more general two-dimensional (2-D) signal convolution perspective and propose a new convolution paradigm, named 2-D graph convolution. We prove that 2-D graph convolution unifies existing graph convolution paradigms, and is capable to construct arbitrary target output. Based on the proposed 2-D graph convolution, we further propose ChebNet2D, an efficient and effective GNN implementation of 2-D graph convolution through applying Chebyshev interpolation. Extensive experiments on benchmark datasets demonstrate both effectiveness and efficiency of the ChebNet2D.
Pre-trained deep learning (DL) models are increasingly accessible in public repositories, i.e., model zoos. Given a new prediction task, finding the best model to fine-tune can be computationally intensive and costly, especially when the number of pre-trained models is large. Selecting the right pre-trained models is crucial, yet complicated by the diversity of models from various model families (like ResNet, Vit, Swin) and the hidden relationships between models and datasets. Existing methods, which utilize basic information from models and datasets to compute scores indicating model performance on target datasets, overlook the intrinsic relationships, limiting their effectiveness in model selection. In this study, we introduce TransferGraph, a novel framework that reformulates model selection as a graph learning problem. TransferGraph constructs a graph using extensive metadata extracted from models and datasets, while capturing their inherent relationships. Through comprehensive experiments across 16 real datasets, both images and texts, we demonstrate TransferGraph's effectiveness in capturing essential model-dataset relationships, yielding up to a 32% improvement in correlation between predicted performance and the actual fine-tuning results compared to the state-of-the-art methods.
Graph transformers have recently received significant attention in graph learning, partly due to their ability to capture more global interaction via self-attention. Nevertheless, while higher-order graph neural networks have been reasonably well studied, the exploration of extending graph transformers to higher-order variants is just starting. Both theoretical understanding and empirical results are limited. In this paper, we provide a systematic study of the theoretical expressive power of order-$k$ graph transformers and sparse variants. We first show that, an order-$k$ graph transformer without additional structural information is less expressive than the $k$-Weisfeiler Lehman ($k$-WL) test despite its high computational cost. We then explore strategies to both sparsify and enhance the higher-order graph transformers, aiming to improve both their efficiency and expressiveness. Indeed, sparsification based on neighborhood information can enhance the expressive power, as it provides additional information about input graph structures. In particular, we show that a natural neighborhood-based sparse order-$k$ transformer model is not only computationally efficient, but also expressive -- as expressive as $k$-WL test. We further study several other sparse graph attention models that are computationally efficient and provide their expressiveness analysis. Finally, we provide experimental results to show the effectiveness of the different sparsification strategies.
This paper introduces Polynomial Graphical Lasso (PGL), a new approach to learning graph structures from nodal signals. Our key contribution lies in modeling the signals as Gaussian and stationary on the graph, enabling the development of a graph-learning formulation that combines the strengths of graphical lasso with a more encompassing model. Specifically, we assume that the precision matrix can take any polynomial form of the sought graph, allowing for increased flexibility in modeling nodal relationships. Given the resulting complexity and nonconvexity of the resulting optimization problem, we (i) propose a low-complexity algorithm that alternates between estimating the graph and precision matrices, and (ii) characterize its convergence. We evaluate the performance of PGL through comprehensive numerical simulations using both synthetic and real data, demonstrating its superiority over several alternatives. Overall, this approach presents a significant advancement in graph learning and holds promise for various applications in graph-aware signal analysis and beyond.
Product bundling has been a prevailing marketing strategy that is beneficial in the online shopping scenario. Effective product bundling methods depend on high-quality item representations, which need to capture both the individual items' semantics and cross-item relations. However, previous item representation learning methods, either feature fusion or graph learning, suffer from inadequate cross-modal alignment and struggle to capture the cross-item relations for cold-start items. Multimodal pre-train models could be the potential solutions given their promising performance on various multimodal downstream tasks. However, the cross-item relations have been under-explored in the current multimodal pre-train models. To bridge this gap, we propose a novel and simple framework Cross-Item Relational Pre-training (CIRP) for item representation learning in product bundling. Specifically, we employ a multimodal encoder to generate image and text representations. Then we leverage both the cross-item contrastive loss (CIC) and individual item's image-text contrastive loss (ITC) as the pre-train objectives. Our method seeks to integrate cross-item relation modeling capability into the multimodal encoder, while preserving the in-depth aligned multimodal semantics. Therefore, even for cold-start items that have no relations, their representations are still relation-aware. Furthermore, to eliminate the potential noise and reduce the computational cost, we harness a relation pruning module to remove the noisy and redundant relations. We apply the item representations extracted by CIRP to the product bundling model ItemKNN, and experiments on three e-commerce datasets demonstrate that CIRP outperforms various leading representation learning methods.
The run-time for optimization tools used in chip design has grown with the complexity of designs to the point where it can take several days to go through one design cycle which has become a bottleneck. Designers want fast tools that can quickly give feedback on a design. Using the input and output data of the tools from past designs, one can attempt to build a machine learning model that predicts the outcome of a design in significantly shorter time than running the tool. The accuracy of such models is affected by the representation of the design data, which is usually a netlist that describes the elements of the digital circuit and how they are connected. Graph representations for the netlist together with graph neural networks have been investigated for such models. However, the characteristics of netlists pose several challenges for existing graph learning frameworks, due to the large number of nodes and the importance of long-range interactions between nodes. To address these challenges, we represent the netlist as a directed hypergraph and propose a Directional Equivariant Hypergraph Neural Network (DE-HNN) for the effective learning of (directed) hypergraphs. Theoretically, we show that our DE-HNN can universally approximate any node or hyperedge based function that satisfies certain permutation equivariant and invariant properties natural for directed hypergraphs. We compare the proposed DE-HNN with several State-of-the-art (SOTA) machine learning models for (hyper)graphs and netlists, and show that the DE-HNN significantly outperforms them in predicting the outcome of optimized place-and-route tools directly from the input netlists. Our source code and the netlists data used are publicly available at https://github.com/YusuLab/chips.git
The choice of a graph learning (GL) model (i.e., a GL algorithm and its hyperparameter settings) has a significant impact on the performance of downstream tasks. However, selecting the right GL model becomes increasingly difficult and time consuming as more and more GL models are developed. Accordingly, it is of great significance and practical value to equip users of GL with the ability to perform a near-instantaneous selection of an effective GL model without manual intervention. Despite the recent attempts to tackle this important problem, there has been no comprehensive benchmark environment to evaluate the performance of GL model selection methods. To bridge this gap, we present GLEMOS in this work, a comprehensive benchmark for instantaneous GL model selection that makes the following contributions. (i) GLEMOS provides extensive benchmark data for fundamental GL tasks, i.e., link prediction and node classification, including the performances of 366 models on 457 graphs on these tasks. (ii) GLEMOS designs multiple evaluation settings, and assesses how effectively representative model selection techniques perform in these different settings. (iii) GLEMOS is designed to be easily extended with new models, new graphs, and new performance records. (iv) Based on the experimental results, we discuss the limitations of existing approaches and highlight future research directions. To promote research on this significant problem, we make the benchmark data and code publicly available at https://github.com/facebookresearch/glemos.
With the digitization of modern cities, large data volumes and powerful computational resources facilitate the rapid update of intelligent models deployed in smart cities. Continual learning (CL) is a novel machine learning paradigm that constantly updates models to adapt to changing environments, where the learning tasks, data, and distributions can vary over time. Our survey provides a comprehensive review of continual learning methods that are widely used in smart city development. The content consists of three parts: 1) Methodology-wise. We categorize a large number of basic CL methods and advanced CL frameworks in combination with other learning paradigms including graph learning, spatial-temporal learning, multi-modal learning, and federated learning. 2) Application-wise. We present numerous CL applications covering transportation, environment, public health, safety, networks, and associated datasets related to urban computing. 3) Challenges. We discuss current problems and challenges and envision several promising research directions. We believe this survey can help relevant researchers quickly familiarize themselves with the current state of continual learning research used in smart city development and direct them to future research trends.
Node classification on graphs is of great importance in many applications. Due to the limited labeling capability and evolution in real-world open scenarios, novel classes can emerge on unlabeled testing nodes. However, little attention has been paid to novel class discovery on graphs. Discovering novel classes is challenging as novel and known class nodes are correlated by edges, which makes their representations indistinguishable when applying message passing GNNs. Furthermore, the novel classes lack labeling information to guide the learning process. In this paper, we propose a novel method Open-world gRAph neuraL network (ORAL) to tackle these challenges. ORAL first detects correlations between classes through semi-supervised prototypical learning. Inter-class correlations are subsequently eliminated by the prototypical attention network, leading to distinctive representations for different classes. Furthermore, to fully explore multi-scale graph features for alleviating label deficiencies, ORAL generates pseudo-labels by aligning and ensembling label estimations from multiple stacked prototypical attention networks. Extensive experiments on several benchmark datasets show the effectiveness of our proposed method.
Effective collaboration among heterogeneous clients in a decentralized setting is a rather unexplored avenue in the literature. To structurally address this, we introduce Model Agnostic Peer-to-peer Learning (coined as MAPL) a novel approach to simultaneously learn heterogeneous personalized models as well as a collaboration graph through peer-to-peer communication among neighboring clients. MAPL is comprised of two main modules: (i) local-level Personalized Model Learning (PML), leveraging a combination of intra- and inter-client contrastive losses; (ii) network-wide decentralized Collaborative Graph Learning (CGL) dynamically refining collaboration weights in a privacy-preserving manner based on local task similarities. Our extensive experimentation demonstrates the efficacy of MAPL and its competitive (or, in most cases, superior) performance compared to its centralized model-agnostic counterparts, without relying on any central server. Our code is available and can be accessed here: https://github.com/SayakMukherjee/MAPL
In the evolving field of psychopathology, the accurate assessment and forecasting of data derived from Ecological Momentary Assessment (EMA) is crucial. EMA offers contextually-rich psychopathological measurements over time, that practically lead to Multivariate Time Series (MTS) data. Thus, many challenges arise in analysis from the temporal complexities inherent in emotional, behavioral, and contextual EMA data as well as their inter-dependencies. To address both of these aspects, this research investigates the performance of Recurrent and Temporal Graph Neural Networks (GNNs). Overall, GNNs, by incorporating additional information from graphs reflecting the inner relationships between the variables, notably enhance the results by decreasing the Mean Squared Error (MSE) to 0.84 compared to the baseline LSTM model at 1.02. Therefore, the effect of constructing graphs with different characteristics on GNN performance is also explored. Additionally, GNN-learned graphs, which are dynamically refined during the training process, were evaluated. Using such graphs showed a similarly good performance. Thus, graph learning proved also promising for other GNN methods, potentially refining the pre-defined graphs.