Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of the classic Sinkhorn algorithm for jointly encoding multiple sets of marginal distributions. We further theoretically characterize the convergence property of the Sinkhorn algorithm for multiple marginals. In contrast to the sequential decision e.g.\ reinforcement learning-based solvers, we showcase our technique in solving constrained (specifically satisfiability) problems by one-shot neural networks, including i) a neural routing solver learned without supervision of optimal solutions; ii) a partial graph matching network handling graphs with unmatchable outliers on both sides; iii) a predictive network for financial portfolios with continuous constraints. To our knowledge, there exists no one-shot neural solver for these scenarios when they are formulated as satisfiability problems. Source code is available at https://github.com/Thinklab-SJTU/LinSATNet
Graph matching has important applications in pattern recognition and beyond. Current approaches predominantly adopt supervised learning, demanding extensive labeled data which can be limited or costly. Meanwhile, self-supervised learning methods for graph matching often require additional side information such as extra categorical information and input features, limiting their application to the general case. Moreover, designing the optimal graph augmentations for self-supervised graph matching presents another challenge to ensure robustness and efficacy. To address these issues, we introduce a novel Graph-centric Contrastive framework for Graph Matching (GCGM), capitalizing on a vast pool of graph augmentations for contrastive learning, yet without needing any side information. Given the variety of augmentation choices, we further introduce a Boosting-inspired Adaptive Augmentation Sampler (BiAS), which adaptively selects more challenging augmentations tailored for graph matching. Through various experiments, our GCGM surpasses state-of-the-art self-supervised methods across various datasets, marking a significant step toward more effective, efficient and general graph matching.
This paper presents a spectral framework for assessing the generalization and stability of Graph Neural Networks (GNNs) by introducing a Graph Geodesic Distance (GGD) metric. For two different graphs with the same number of nodes, our framework leverages a spectral graph matching procedure to find node correspondence so that the geodesic distance between them can be subsequently computed by solving a generalized eigenvalue problem associated with their Laplacian matrices. For graphs with different sizes, a resistance-based spectral graph coarsening scheme is introduced to reduce the size of the bigger graph while preserving the original spectral properties. We show that the proposed GGD metric can effectively quantify dissimilarities between two graphs by encapsulating their differences in key structural (spectral) properties, such as effective resistances between nodes, cuts, the mixing time of random walks, etc. Through extensive experiments comparing with the state-of-the-art metrics, such as the latest Tree-Mover's Distance (TMD) metric, the proposed GGD metric shows significantly improved performance for stability evaluation of GNNs especially when only partial node features are available.
Graph theory has been a powerful tool in solving difficult and complex problems arising in all disciplines. In particular, graph matching is a classical problem in pattern analysis with enormous applications. Many graph problems have been formulated as a mathematical program and then solved using exact, heuristic, and/or approximated-guaranteed procedures. On the other hand, graph theory has been a powerful tool in visualizing and understanding complex mathematical programming problems, especially integer programs. Formulating a graph problem as a natural integer program (IP) is often a challenging task. However, an IP formulation of the problem has many advantages. Several researchers have noted the need for natural IP formulation of graph theoretic problems. The present study aims to provide a unified framework for IP formulation of graph-matching problems. Although there are many surveys on graph matching problems, none is concerned with IP formulation. This paper is the first to provide a comprehensive IP formulation for such problems. The framework includes a variety of graph optimization problems in the literature. While these problems have been studied by different research communities, however, the framework presented here helps to bring efforts from different disciplines to tackle such diverse and complex problems. We hope the present study can significantly help to simplify some of the difficult problems arising in practice, especially in pattern analysis.
We consider the two-sample testing problem for networks, where the goal is to determine whether two sets of networks originated from the same stochastic model. Assuming no vertex correspondence and allowing for different numbers of nodes, we address a fundamental network testing problem that goes beyond simple adjacency matrix comparisons. We adopt the stochastic block model (SBM) for network distributions, due to their interpretability and the potential to approximate more general models. The lack of meaningful node labels and vertex correspondence translate to a graph matching challenge when developing a test for SBMs. We introduce an efficient algorithm to match estimated network parameters, allowing us to properly combine and contrast information within and across samples, leading to a powerful test. We show that the matching algorithm, and the overall test are consistent, under mild conditions on the sparsity of the networks and the sample sizes, and derive a chi-squared asymptotic null distribution for the test. Through a mixture of theoretical insights and empirical validations, including experiments with both synthetic and real-world data, this study advances robust statistical inference for complex network data.
Semantic communication, as a revolutionary communication architecture, is considered a promising novel communication paradigm. Unlike traditional symbol-based error-free communication systems, semantic-based visual communication systems extract, compress, transmit, and reconstruct images at the semantic level. However, widely used image similarity evaluation metrics, whether pixel-based MSE or PSNR or structure-based MS-SSIM, struggle to accurately measure the loss of semantic-level information of the source during system transmission. This presents challenges in evaluating the performance of visual semantic communication systems, especially when comparing them with traditional communication systems. To address this, we propose a semantic evaluation metric -- SeSS (Semantic Similarity Score), based on Scene Graph Generation and graph matching, which shifts the similarity scores between images into semantic-level graph matching scores. Meanwhile, semantic similarity scores for tens of thousands of image pairs are manually annotated to fine-tune the hyperparameters in the graph matching algorithm, aligning the metric more closely with human semantic perception. The performance of the SeSS is tested on different datasets, including (1)images transmitted by traditional and semantic communication systems at different compression rates, (2)images transmitted by traditional and semantic communication systems at different signal-to-noise ratios, (3)images generated by large-scale model with different noise levels introduced, and (4)cases of images subjected to certain special transformations. The experiments demonstrate the effectiveness of SeSS, indicating that the metric can measure the semantic-level differences in semantic-level information of images and can be used for evaluation in visual semantic communication systems.
The success of existing cross-modal retrieval (CMR) methods heavily rely on the assumption that the annotated cross-modal correspondence is faultless. In practice, however, the correspondence of some pairs would be inevitably contaminated during data collection or annotation, thus leading to the so-called Noisy Correspondence (NC) problem. To alleviate the influence of NC, we propose a novel method termed Consistency REfining And Mining (CREAM) by revealing and exploiting the difference between correspondence and consistency. Specifically, the correspondence and the consistency only be coincident for true positive and true negative pairs, while being distinct for false positive and false negative pairs. Based on the observation, CREAM employs a collaborative learning paradigm to detect and rectify the correspondence of positives, and a negative mining approach to explore and utilize the consistency. Thanks to the consistency refining and mining strategy of CREAM, the overfitting on the false positives could be prevented and the consistency rooted in the false negatives could be exploited, thus leading to a robust CMR method. Extensive experiments verify the effectiveness of our method on three image-text benchmarks including Flickr30K, MS-COCO, and Conceptual Captions. Furthermore, we adopt our method into the graph matching task and the results demonstrate the robustness of our method against fine-grained NC problem. The code is available on https://github.com/XLearning-SCU/2024-TIP-CREAM .
In the field of 3D object detection tasks, fusing heterogeneous features from LiDAR and camera sensors into a unified Bird's Eye View (BEV) representation is a widely adopted paradigm. However, existing methods are often compromised by imprecise sensor calibration, resulting in feature misalignment in LiDAR-camera BEV fusion. Moreover, such inaccuracies result in errors in depth estimation for the camera branch, ultimately causing misalignment between LiDAR and camera BEV features. In this work, we propose a novel ContrastAlign approach that utilizes contrastive learning to enhance the alignment of heterogeneous modalities, thereby improving the robustness of the fusion process. Specifically, our approach includes the L-Instance module, which directly outputs LiDAR instance features within LiDAR BEV features. Then, we introduce the C-Instance module, which predicts camera instance features through RoI (Region of Interest) pooling on the camera BEV features. We propose the InstanceFusion module, which utilizes contrastive learning to generate similar instance features across heterogeneous modalities. We then use graph matching to calculate the similarity between the neighboring camera instance features and the similarity instance features to complete the alignment of instance features. Our method achieves state-of-the-art performance, with an mAP of 70.3%, surpassing BEVFusion by 1.8% on the nuScenes validation set. Importantly, our method outperforms BEVFusion by 7.3% under conditions with misalignment noise.
Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM). Specifically, we relax and decompose the quadratic assignment problem for the graph matching into a sequence of convex optimization problems. The whole algorithm can be considered as a differentiable map from the graph affinity matrix to the prediction of node correspondence. Therefore, the proposed method can be organically integrated into an end-to-end deep learning framework to jointly learn both the deep feature representation and the graph affinity matrix. In addition, we provide a theoretical guarantee to ensure the proposed method converges to a stable point with a reasonable number of iterations. Numerical experiments show that PGM outperforms existing graph matching algorithms on diverse datasets such as synthetic data, and CMU House. Meanwhile, PGM can fully harness the capability of deep feature extractors and achieve state-of-art performance on PASCAL VOC keypoints.
Network interdiction problems are combinatorial optimization problems involving two players: one aims to solve an optimization problem on a network, while the other seeks to modify the network to thwart the first player's objectives. Such problems typically emerge in an attacker-defender context, encompassing areas such as military operations, disease spread analysis, and communication network management. The primary bottleneck in network interdiction arises from the high time complexity of using conventional exact solvers and the challenges associated with devising efficient heuristic solvers. GNNs, recognized as a cutting-edge methodology, have shown significant effectiveness in addressing single-level CO problems on graphs, such as the traveling salesman problem, graph matching, and graph edit distance. Nevertheless, network interdiction presents a bi-level optimization challenge, which current GNNs find difficult to manage. To address this gap, we represent network interdiction problems as Mixed-Integer Linear Programming (MILP) instances, then apply a multipartite GNN with sufficient representational capacity to learn these formulations. This approach ensures that our neural network is more compatible with the mathematical algorithms designed to solve network interdiction problems, resulting in improved generalization. Through two distinct tasks, we demonstrate that our proposed method outperforms theoretical baseline models and provides advantages over traditional exact solvers.
Multi Object Tracking (MOT) in ice hockey pursues the combined task of localizing and associating players across a given sequence to maintain their identities. Tracking players from monocular broadcast feeds is an important computer vision problem offering various downstream analytics and enhanced viewership experience. However, existing trackers encounter significant difficulties in dealing with occlusions, blurs, and agile player movements prevalent in telecast feeds. In this work, we propose a novel tracking approach by formulating MOT as a bipartite graph matching problem infused with homography. We disentangle the positional representations of occluded and overlapping players in broadcast view, by mapping their foot keypoints to an overhead rink template, and encode these projected positions into the graph network. This ensures reliable spatial context for consistent player tracking and unfragmented tracklet prediction. Our results show considerable improvements in both the IDsw and IDF1 metrics on the two available broadcast ice hockey datasets.
Ontology and knowledge graph matching systems are evaluated annually by the Ontology Alignment Evaluation Initiative (OAEI). More and more systems use machine learning-based approaches, including large language models. The training and validation datasets are usually determined by the system developer and often a subset of the reference alignments are used. This sampling is against the OAEI rules and makes a fair comparison impossible. Furthermore, those models are trained offline (a trained and optimized model is packaged into the matcher) and therefore the systems are specifically trained for those tasks. In this paper, we introduce a dataset that contains training, validation, and test sets for most of the OAEI tracks. Thus, online model learning (the systems must adapt to the given input alignment without human intervention) is made possible to enable a fair comparison for ML-based systems. We showcase the usefulness of the dataset by fine-tuning the confidence thresholds of popular systems.
Knowledge graphs play a pivotal role in various applications, such as question-answering and fact-checking. Abstract Meaning Representation (AMR) represents text as knowledge graphs. Evaluating the quality of these graphs involves matching them structurally to each other and semantically to the source text. Existing AMR metrics are inefficient and struggle to capture semantic similarity. We also lack a systematic evaluation benchmark for assessing structural similarity between AMR graphs. To overcome these limitations, we introduce a novel AMR similarity metric, rematch, alongside a new evaluation for structural similarity called RARE. Among state-of-the-art metrics, rematch ranks second in structural similarity; and first in semantic similarity by 1--5 percentage points on the STS-B and SICK-R benchmarks. Rematch is also five times faster than the next most efficient metric.
Scene graphs have been recently introduced into 3D spatial understanding as a comprehensive representation of the scene. The alignment between 3D scene graphs is the first step of many downstream tasks such as scene graph aided point cloud registration, mosaicking, overlap checking, and robot navigation. In this work, we treat 3D scene graph alignment as a partial graph-matching problem and propose to solve it with a graph neural network. We reuse the geometric features learned by a point cloud registration method and associate the clustered point-level geometric features with the node-level semantic feature via our designed feature fusion module. Partial matching is enabled by using a learnable method to select the top-k similar node pairs. Subsequent downstream tasks such as point cloud registration are achieved by running a pre-trained registration network within the matched regions. We further propose a point-matching rescoring method, that uses the node-wise alignment of the 3D scene graph to reweight the matching candidates from a pre-trained point cloud registration method. It reduces the false point correspondences estimated especially in low-overlapping cases. Experiments show that our method improves the alignment accuracy by 10~20% in low-overlap and random transformation scenarios and outperforms the existing work in multiple downstream tasks.
Image captioning can automatically generate captions for the given images, and the key challenge is to learn a mapping function from visual features to natural language features. Existing approaches are mostly supervised ones, i.e., each image has a corresponding sentence in the training set. However, considering that describing images always requires a huge of manpower, we usually have limited amount of described images (i.e., image-text pairs) and a large number of undescribed images in real-world applications. Thereby, a dilemma is the "Semi-Supervised Image Captioning". To solve this problem, we propose a novel Semi-Supervised Image Captioning method considering Wasserstein Graph Matching (SSIC-WGM), which turns to adopt the raw image inputs to supervise the generated sentences. Different from traditional single modal semi-supervised methods, the difficulty of semi-supervised cross-modal learning lies in constructing intermediately comparable information among heterogeneous modalities. In this paper, SSIC-WGM adopts the successful scene graphs as intermediate information, and constrains the generated sentences from two aspects: 1) inter-modal consistency. SSIC-WGM constructs the scene graphs of the raw image and generated sentence respectively, then employs the wasserstein distance to better measure the similarity between region embeddings of different graphs. 2) intra-modal consistency. SSIC-WGM takes the data augmentation techniques for the raw images, then constrains the consistency among augmented images and generated sentences. Consequently, SSIC-WGM combines the cross-modal pseudo supervision and structure invariant measure for efficiently using the undescribed images, and learns more reasonable mapping function.
Scene graph generation aims to capture detailed spatial and semantic relationships between objects in an image, which is challenging due to incomplete labelling, long-tailed relationship categories, and relational semantic overlap. Existing Transformer-based methods either employ distinct queries for objects and predicates or utilize holistic queries for relation triplets and hence often suffer from limited capacity in learning low-frequency relationships. In this paper, we present a new Transformer-based method, called DSGG, that views scene graph detection as a direct graph prediction problem based on a unique set of graph-aware queries. In particular, each graph-aware query encodes a compact representation of both the node and all of its relations in the graph, acquired through the utilization of a relaxed sub-graph matching during the training process. Moreover, to address the problem of relational semantic overlap, we utilize a strategy for relation distillation, aiming to efficiently learn multiple instances of semantic relationships. Extensive experiments on the VG and the PSG datasets show that our model achieves state-of-the-art results, showing a significant improvement of 3.5\% and 6.7\% in mR@50 and mR@100 for the scene-graph generation task and achieves an even more substantial improvement of 8.5\% and 10.3\% in mR@50 and mR@100 for the panoptic scene graph generation task. Code is available at \url{https://github.com/zeeshanhayder/DSGG}.
Integrating LiDAR and camera information into Bird's-Eye-View (BEV) representation has emerged as a crucial aspect of 3D object detection in autonomous driving. However, existing methods are susceptible to the inaccurate calibration relationship between LiDAR and the camera sensor. Such inaccuracies result in errors in depth estimation for the camera branch, ultimately causing misalignment between LiDAR and camera BEV features. In this work, we propose a robust fusion framework called Graph BEV. Addressing errors caused by inaccurate point cloud projection, we introduce a Local Align module that employs neighbor-aware depth features via Graph matching. Additionally, we propose a Global Align module to rectify the misalignment between LiDAR and camera BEV features. Our Graph BEV framework achieves state-of-the-art performance, with an mAP of 70.1\%, surpassing BEV Fusion by 1.6\% on the nuscenes validation set. Importantly, our Graph BEV outperforms BEV Fusion by 8.3\% under conditions with misalignment noise.
In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization results. In this second part of the study, we continue our error bound analysis for the cases of partial permutation matrices, size-constrained assignment matrices and non-negative semi-orthogonal matrices. We develop new error bounds and penalized formulations for these three cases, and the new formulations possess good structures for building computationally efficient algorithms. Moreover, we provide numerical results to demonstrate our framework in a variety of applications such as the densest k-subgraph problem, graph matching, size-constrained clustering, non-negative orthogonal matrix factorization and sparse fair principal component analysis.
Most real-world Multi-Robot Task Allocation (MRTA) problems require fast and efficient decision-making, which is often achieved using heuristics-aided methods such as genetic algorithms, auction-based methods, and bipartite graph matching methods. These methods often assume a form that lends better explainability compared to an end-to-end (learnt) neural network based policy for MRTA. However, deriving suitable heuristics can be tedious, risky and in some cases impractical if problems are too complex. This raises the question: can these heuristics be learned? To this end, this paper particularly develops a Graph Reinforcement Learning (GRL) framework to learn the heuristics or incentives for a bipartite graph matching approach to MRTA. Specifically a Capsule Attention policy model is used to learn how to weight task/robot pairings (edges) in the bipartite graph that connects the set of tasks to the set of robots. The original capsule attention network architecture is fundamentally modified by adding encoding of robots' state graph, and two Multihead Attention based decoders whose output are used to construct a LogNormal distribution matrix from which positive bigraph weights can be drawn. The performance of this new bigraph matching approach augmented with a GRL-derived incentive is found to be at par with the original bigraph matching approach that used expert-specified heuristics, with the former offering notable robustness benefits. During training, the learned incentive policy is found to get initially closer to the expert-specified incentive and then slightly deviate from its trend.
Graph matching is a commonly used technique in computer vision and pattern recognition. Recent data-driven approaches have improved the graph matching accuracy remarkably, whereas some traditional algorithm-based methods are more robust to feature noises, outlier nodes, and global transformation (e.g.~rotation). In this paper, we propose a graph neural network (GNN) based approach to combine the advantages of data-driven and traditional methods. In the GNN framework, we transform traditional graph-matching solvers as single-channel GNNs on the association graph and extend the single-channel architecture to the multi-channel network. The proposed model can be seen as an ensemble method that fuses multiple algorithms at every iteration. Instead of averaging the estimates at the end of the ensemble, in our approach, the independent iterations of the ensembled algorithms exchange their information after each iteration via a 1x1 channel-wise convolution layer. Experiments show that our model improves the performance of traditional algorithms significantly. In addition, we propose a random sampling strategy to reduce the computational complexity and GPU memory usage, so the model applies to matching graphs with thousands of nodes. We evaluate the performance of our method on three tasks: geometric graph matching, semantic feature matching, and few-shot 3D shape classification. The proposed model performs comparably or outperforms the best existing GNN-based methods.