Accurate graph similarity is critical for knowledge transfer in VLSI design, enabling the reuse of prior solutions to reduce engineering effort and turnaround time. We propose Pieceformer, a scalable, self-supervised similarity assessment framework, equipped with a hybrid message-passing and graph transformer encoder. To address transformer scalability, we incorporate a linear transformer backbone and introduce a partitioned training pipeline for efficient memory and parallelism management. Evaluations on synthetic and real-world CircuitNet datasets show that Pieceformer reduces mean absolute error (MAE) by 24.9% over the baseline and is the only method to correctly cluster all real-world design groups. We further demonstrate the practical usage of our model through a case study on a partitioning task, achieving up to 89% runtime reduction. These results validate the framework's effectiveness for scalable, unbiased design reuse in modern VLSI systems.
Despite the dominance of convolutional and transformer-based architectures in image-to-image retrieval, these models are prone to biases arising from low-level visual features, such as color. Recognizing the lack of semantic understanding as a key limitation, we propose a novel scene graph-based retrieval framework that emphasizes semantic content over superficial image characteristics. Prior approaches to scene graph retrieval predominantly rely on supervised Graph Neural Networks (GNNs), which require ground truth graph pairs driven from image captions. However, the inconsistency of caption-based supervision stemming from variable text encodings undermine retrieval reliability. To address these, we present SCENIR, a Graph Autoencoder-based unsupervised retrieval framework, which eliminates the dependence on labeled training data. Our model demonstrates superior performance across metrics and runtime efficiency, outperforming existing vision-based, multimodal, and supervised GNN approaches. We further advocate for Graph Edit Distance (GED) as a deterministic and robust ground truth measure for scene graph similarity, replacing the inconsistent caption-based alternatives for the first time in image-to-image retrieval evaluation. Finally, we validate the generalizability of our method by applying it to unannotated datasets via automated scene graph generation, while substantially contributing in advancing state-of-the-art in counterfactual image retrieval.
The Maximum Common Edge Subgraph (MCES) problem is a crucial challenge with significant implications in domains such as biology and chemistry. Traditional approaches, which include transformations into max-clique and search-based algorithms, suffer from scalability issues when dealing with larger instances. This paper introduces ``Neural Graduated Assignment'' (NGA), a simple, scalable, unsupervised-training-based method that addresses these limitations by drawing inspiration from the classical Graduated Assignment (GA) technique. Central to NGA is stacking of neural components that closely resemble the GA process, but with the reparameterization of learnable temperature into higher dimension. We further theoretically analyze the learning dynamics of NGA, showing its design leads to fast convergence, better exploration-exploitation tradeoff, and ability to escape local optima. Extensive experiments across MCES computation, graph similarity estimation, and graph retrieval tasks reveal that NGA not only significantly improves computation time and scalability on large instances but also enhances performance compared to existing methodologies. The introduction of NGA marks a significant advancement in the computation of MCES and offers insights into other assignment problems.
LiDAR loop closure detection (LCD) is crucial for consistent Simultaneous Localization and Mapping (SLAM) but faces challenges in robustness and accuracy. Existing methods, including semantic graph approaches, often suffer from coarse geometric representations and lack temporal robustness against noise, dynamics, and viewpoint changes. We introduce PNE-SGAN, a Probabilistic NDT-Enhanced Semantic Graph Attention Network, to overcome these limitations. PNE-SGAN enhances semantic graphs by using Normal Distributions Transform (NDT) covariance matrices as rich, discriminative geometric node features, processed via a Graph Attention Network (GAT). Crucially, it integrates graph similarity scores into a probabilistic temporal filtering framework (modeled as an HMM/Bayes filter), incorporating uncertain odometry for motion modeling and utilizing forward-backward smoothing to effectively handle ambiguities. Evaluations on challenging KITTI sequences (00 and 08) demonstrate state-of-the-art performance, achieving Average Precision of 96.2\% and 95.1\%, respectively. PNE-SGAN significantly outperforms existing methods, particularly in difficult bidirectional loop scenarios where others falter. By synergizing detailed NDT geometry with principled probabilistic temporal reasoning, PNE-SGAN offers a highly accurate and robust solution for LiDAR LCD, enhancing SLAM reliability in complex, large-scale environments.
Graph Edit Distance (GED) offers a principled and flexible measure of graph similarity, as it quantifies the minimum cost needed to transform one graph into another with customizable edit operation costs. Despite recent learning-based efforts to approximate GED via vector space representations, existing methods struggle with adapting to varying operation costs. Furthermore, they suffer from inefficient, reactive mapping refinements due to reliance on isolated node-level distance as guidance. To address these issues, we propose GEN, a novel learning-based approach for flexible GED approximation. GEN addresses the varying costs adaptation by integrating operation costs prior to match establishment, enabling mappings to dynamically adapt to cost variations. Furthermore, GEN introduces a proactive guidance optimization strategy that captures graph-level dependencies between matches, allowing informed matching decisions in a single step without costly iterative refinements. Extensive evaluations on real-world and synthetic datasets demonstrate that GEN achieves up to 37.8% reduction in GED approximation error and 72.7% reduction in inference time compared with state-of-the-art methods, while consistently maintaining robustness under diverse cost settings and graph sizes.
Full-reference point cloud objective metrics are currently providing very accurate representations of perceptual quality. These metrics are usually composed of a set of features that are somehow combined, resulting in a final quality value. In this study, the different features of the best-performing metrics are analyzed. For that, different objective quality metrics are compared between them, and the differences in their quality representation are studied. This provided a selection of the set of metrics used in this study, namely the point-to-plane, point-to-attribute, Point Cloud Structural Similarity, Point Cloud Quality Metric and Multiscale Graph Similarity. The features defined in those metrics are examined based on their contribution to the objective estimation using recursive feature elimination. To employ the recursive feature selection algorithm, both the support vector regression and the ridge regression algorithms were employed. For this study, the Broad Quality Assessment of Static Point Clouds in Compression Scenario database was used for both training and validation of the models. According to the recursive feature elimination, several features were selected and then combined using the regression method used to select those features. The best combination models were then evaluated across five different publicly available subjective quality assessment datasets, targeting different point cloud characteristics and distortions. It was concluded that a combination of features selected from the Point Cloud Quality Metric, Multiscale Graph Similarity and PSNR MSE D2, combined with Ridge Regression, results in the best performance. This model leads to the definition of the Feature Selection Model.
Graph-level clustering is a fundamental task of data mining, aiming at dividing unlabeled graphs into distinct groups. However, existing deep methods that are limited by pooling have difficulty extracting diverse and complex graph structure features, while traditional graph kernel methods rely on exhaustive substructure search, unable to adaptive handle multi-relational data. This limitation hampers producing robust and representative graph-level embeddings. To address this issue, we propose a novel Multi-Relation Graph-Kernel Strengthen Network for Graph-Level Clustering (MGSN), which integrates multi-relation modeling with graph kernel techniques to fully leverage their respective advantages. Specifically, MGSN constructs multi-relation graphs to capture diverse semantic relationships between nodes and graphs, which employ graph kernel methods to extract graph similarity features, enriching the representation space. Moreover, a relation-aware representation refinement strategy is designed, which adaptively aligns multi-relation information across views while enhancing graph-level features through a progressive fusion process. Extensive experiments on multiple benchmark datasets demonstrate the superiority of MGSN over state-of-the-art methods. The results highlight its ability to leverage multi-relation structures and graph kernel features, establishing a new paradigm for robust graph-level clustering.
The recruitment process is undergoing a significant transformation with the increasing use of machine learning and natural language processing techniques. While previous studies have focused on automating candidate selection, the role of multiple vacancies in this process remains understudied. This paper addresses this gap by proposing a novel pipeline that leverages Large Language Models and graph similarity measures to suggest ideal candidates for specific job openings. Our approach represents candidate profiles as multimodal embeddings, enabling the capture of nuanced relationships between job requirements and candidate attributes. The proposed approach has significant implications for the recruitment industry, enabling companies to streamline their hiring processes and identify top talent more efficiently. Our work contributes to the growing body of research on the application of machine learning in human resources, highlighting the potential of LLMs and graph-based methods in revolutionizing the recruitment landscape.
In the domain of analog circuit design, the retrieval of circuit diagrams has drawn a great interest, primarily due to its vital role in the consultation of legacy designs and the detection of design plagiarism. Existing image retrieval techniques are adept at handling natural images, which converts images into feature vectors and retrieval similar images according to the closeness of these vectors. Nonetheless, these approaches exhibit limitations when applied to the more specialized and intricate domain of circuit diagrams. This paper presents a novel approach to circuit diagram retrieval by employing a graph representation of circuit diagrams, effectively reformulating the retrieval task as a graph retrieval problem. The proposed methodology consists of two principal components: a circuit diagram recognition algorithm designed to extract the circuit components and topological structure of the circuit using proposed GAM-YOLO model and a 2-step connected domain filtering algorithm, and a hierarchical retrieval strategy based on graph similarity and different graph representation methods for analog circuits. Our methodology pioneers the utilization of graph representation in the retrieval of circuit diagrams, incorporating topological features that are commonly overlooked by standard image retrieval methods. The results of our experiments substantiate the efficacy of our approach in retrieving circuit diagrams across of different types.
Graph similarity learning (GSL), also referred to as graph matching in many scenarios, is a fundamental problem in computer vision, pattern recognition, and graph learning. However, previous GSL methods assume that graphs are homogeneous and struggle to maintain their performance on heterogeneous graphs. To address this problem, this paper proposes a Heterogeneous Graph Matching Network (HeGMN), which is an end-to-end graph similarity learning framework composed of a two-tier matching mechanism. Firstly, a heterogeneous graph isomorphism network is proposed as the encoder, which reinvents graph isomorphism network for heterogeneous graphs by perceiving different semantic relationships during aggregation. Secondly, a graph-level and node-level matching modules are designed, both employing type-aligned matching principles. The former conducts graph-level matching by node type alignment, and the latter computes the interactions between the cross-graph nodes with the same type thus reducing noise interference and computational overhead. Finally, the graph-level and node-level matching features are combined and fed into fully connected layers for predicting graph similarity scores. In experiments, we propose a heterogeneous graph resampling method to construct heterogeneous graph pairs and define the corresponding heterogeneous graph edit distance, filling the gap in missing datasets. Extensive experiments demonstrate that HeGMN consistently achieves advanced performance on graph similarity prediction across all datasets.
Recent studies show that graph neural networks (GNNs) are vulnerable to backdoor attacks. Existing backdoor attacks against GNNs use fixed-pattern triggers and lack reasonable trigger constraints, overlooking individual graph characteristics and rendering insufficient evasiveness. To tackle the above issues, we propose ABARC, the first Adaptive Backdoor Attack with Reasonable Constraints, applying to both graph-level and node-level tasks in GNNs. For graph-level tasks, we propose a subgraph backdoor attack independent of the graph's topology. It dynamically selects trigger nodes for each target graph and modifies node features with constraints based on graph similarity, feature range, and feature type. For node-level tasks, our attack begins with an analysis of node features, followed by selecting and modifying trigger features, which are then constrained by node similarity, feature range, and feature type. Furthermore, an adaptive edge-pruning mechanism is designed to reduce the impact of neighbors on target nodes, ensuring a high attack success rate (ASR). Experimental results show that even with reasonable constraints for attack evasiveness, our attack achieves a high ASR while incurring a marginal clean accuracy drop (CAD). When combined with the state-of-the-art defense randomized smoothing (RS) method, our attack maintains an ASR over 94%, surpassing existing attacks by more than 7%.
Deep generative models have recently achieved significant success in modeling graph data, including dynamic graphs, where topology and features evolve over time. However, unlike in vision and natural language domains, evaluating generative models for dynamic graphs is challenging due to the difficulty of visualizing their output, making quantitative metrics essential. In this work, we develop a new quality metric for evaluating generative models of dynamic graphs. Current metrics for dynamic graphs typically involve discretizing the continuous-evolution of graphs into static snapshots and then applying conventional graph similarity measures. This approach has several limitations: (a) it models temporally related events as i.i.d. samples, failing to capture the non-uniform evolution of dynamic graphs; (b) it lacks a unified measure that is sensitive to both features and topology; (c) it fails to provide a scalar metric, requiring multiple metrics without clear superiority; and (d) it requires explicitly instantiating each static snapshot, leading to impractical runtime demands that hinder evaluation at scale. We propose a novel metric based on the \textit{Johnson-Lindenstrauss} lemma, applying random projections directly to dynamic graph data. This results in an expressive, scalar, and application-agnostic measure of dynamic graph similarity that overcomes the limitations of traditional methods. We also provide a comprehensive empirical evaluation of metrics for continuous-time dynamic graphs, demonstrating the effectiveness of our approach compared to existing methods. Our implementation is available at https://github.com/ryienh/jl-metric.
Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the interactions between graphs. Traditional methods often entail separate, redundant computations for each graph pair, leading to unnecessary complexity. This paper revolutionizes the approach by introducing a parallel graph interaction method called graph fusion. By merging the node sequences of graph pairs into a single large graph, our method leverages a global attention mechanism to facilitate interaction computations and to harvest cross-graph insights. We further assess the similarity between graph pairs at two distinct levels-graph-level and node-level-introducing two innovative, yet straightforward, similarity computation algorithms. Extensive testing across five public datasets shows that our model not only outperforms leading baseline models in graph-to-graph classification and regression tasks but also sets a new benchmark for performance and efficiency. The code for this paper is open-source and available at https://github.com/LLiRarry/GFM-code.git
Graph neural networks (GNNs) are powerful deep learning models for graph-structured data, demonstrating remarkable success across diverse domains. Recently, the database (DB) community has increasingly recognized the potentiality of GNNs, prompting a surge of researches focusing on improving database systems through GNN-based approaches. However, despite notable advances, There is a lack of a comprehensive review and understanding of how GNNs could improve DB systems. Therefore, this survey aims to bridge this gap by providing a structured and in-depth overview of GNNs for DB systems. Specifically, we propose a new taxonomy that classifies existing methods into two key categories: (1) Relational Databases, which includes tasks like performance prediction, query optimization, and text-to-SQL, and (2) Graph Databases, addressing challenges like efficient graph query processing and graph similarity computation. We systematically review key methods in each category, highlighting their contributions and practical implications. Finally, we suggest promising avenues for integrating GNNs into Database systems.
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints. The ``space-decoupling" is reflected in several ways. We show that the tangent cone of coupled constraints is the intersection of tangent cones of each constraint. Moreover, we decouple the intertwined bounded-rank and orthogonally invariant constraints into two spaces, leading to optimization on a smooth manifold. Implementing Riemannian algorithms on this manifold is painless as long as the geometry of additional constraints is known. In addition, we unveil the equivalence between the reformulated problem and the original problem. Numerical experiments on real-world applications -- spherical data fitting, graph similarity measuring, low-rank SDP, model reduction of Markov processes, reinforcement learning, and deep learning -- validate the superiority of the proposed framework.
Graph similarity computation (GSC) is to calculate the similarity between one pair of graphs, which is a fundamental problem with fruitful applications in the graph community. In GSC, graph edit distance (GED) and maximum common subgraph (MCS) are two important similarity metrics, both of which are NP-hard to compute. Instead of calculating the exact values, recent solutions resort to leveraging graph neural networks (GNNs) to learn data-driven models for the estimation of GED and MCS. Most of them are built on components involving node-level interactions crossing graphs, which engender vast computation overhead but are of little avail in effectiveness. In the paper, we present GraSP, a simple yet effective GSC approach for GED and MCS prediction. GraSP achieves high result efficacy through several key instruments: enhanced node features via positional encoding and a GNN model augmented by a gating mechanism, residual connections, as well as multi-scale pooling. Theoretically, GraSP can surpass the 1-WL test, indicating its high expressiveness. Empirically, extensive experiments comparing GraSP against 10 competitors on multiple widely adopted benchmark datasets showcase the superiority of GraSP over prior arts in terms of both effectiveness and efficiency. The code is available at https://github.com/HaoranZ99/GraSP.
The expressive power of message-passing graph neural networks (MPNNs) is reasonably well understood, primarily through combinatorial techniques from graph isomorphism testing. However, MPNNs' generalization abilities -- making meaningful predictions beyond the training set -- remain less explored. Current generalization analyses often overlook graph structure, limit the focus to specific aggregation functions, and assume the impractical, hard-to-optimize $0$-$1$ loss function. Here, we extend recent advances in graph similarity theory to assess the influence of graph structure, aggregation, and loss functions on MPNNs' generalization abilities. Our empirical study supports our theoretical insights, improving our understanding of MPNNs' generalization properties.
Graph similarity computation (GSC) aims to quantify the similarity score between two graphs. Although recent GSC methods based on graph neural networks (GNNs) take advantage of intra-graph structures in message passing, few of them fully utilize the structures presented by edges to boost the representation of their connected nodes. Moreover, previous cross-graph node embedding matching lacks the perception of the overall structure of the graph pair, due to the fact that the node representations from GNNs are confined to the intra-graph structure, causing the unreasonable similarity score. Intuitively, the cross-graph structure represented in the assignment graph is helpful to rectify the inappropriate matching. Therefore, we propose a structure-enhanced graph matching network (SEGMN). Equipped with a dual embedding learning module and a structure perception matching module, SEGMN achieves structure enhancement in both embedding learning and cross-graph matching. The dual embedding learning module incorporates adjacent edge representation into each node to achieve a structure-enhanced representation. The structure perception matching module achieves cross-graph structure enhancement through assignment graph convolution. The similarity score of each cross-graph node pair can be rectified by aggregating messages from structurally relevant node pairs. Experimental results on benchmark datasets demonstrate that SEGMN outperforms the state-of-the-art GSC methods in the GED regression task, and the structure perception matching module is plug-and-play, which can further improve the performance of the baselines by up to 25%.
We propose PieClam (Prior Inclusive Exclusive Cluster Affiliation Model): a probabilistic graph model for representing any graph as overlapping generalized communities. Our method can be interpreted as a graph autoencoder: nodes are embedded into a code space by an algorithm that maximizes the log-likelihood of the decoded graph, given the input graph. PieClam is a community affiliation model that extends well-known methods like BigClam in two main manners. First, instead of the decoder being defined via pairwise interactions between the nodes in the code space, we also incorporate a learned prior on the distribution of nodes in the code space, turning our method into a graph generative model. Secondly, we generalize the notion of communities by allowing not only sets of nodes with strong connectivity, which we call inclusive communities, but also sets of nodes with strong disconnection, which we call exclusive communities. To model both types of communities, we propose a new type of decoder based the Lorentz inner product, which we prove to be much more expressive than standard decoders based on standard inner products or norm distances. By introducing a new graph similarity measure, that we call the log cut distance, we show that PieClam is a universal autoencoder, able to uniformly approximately reconstruct any graph. Our method is shown to obtain competitive performance in graph anomaly detection benchmarks.
This report evaluates the efficiency of Graph Edit Distance (GED) computation for graph similarity search, comparing Cascading Metric Trees (CMT) with brute-force verification. Despite the anticipated advantages of CMT, our findings indicate it does not consistently outperform brute-force methods in speed. The study, based on graph data from PubChem, suggests that the computational complexity of GED-based GSS remains a challenge.