To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still require exhaustive calculations for large-scale graph matching. This work utilizes CUR tensor decomposition and introduces a novel cascaded second and third-order hypergraph matching framework (CURSOR) for efficient hypergraph matching. A CUR-based second-order graph matching algorithm is used to provide a rough match, and then the core of CURSOR, a fiber-CUR-based tensor generation method, directly calculates entries of the compatibility tensor by leveraging the initial second-order match result. This significantly decreases the time complexity and tensor density. A probability relaxation labeling (PRL)-based matching algorithm, especially suitable for sparse tensors, is developed. Experiment results on large-scale synthetic datasets and widely-adopted benchmark sets demonstrate the superiority of CURSOR over existing methods. The tensor generation method in CURSOR can be integrated seamlessly into existing hypergraph matching methods to improve their performance and lower their computational costs.
Coronary artery disease (CAD) stands as the leading cause of death worldwide, and invasive coronary angiography (ICA) remains the gold standard for assessing vascular anatomical information. However, deep learning-based methods encounter challenges in generating semantic labels for arterial segments, primarily due to the morphological similarity between arterial branches and varying anatomy of arterial system between different projection view angles and patients. To address this challenge, we model the vascular tree as a graph and propose a multi-graph graph matching (MGM) algorithm for coronary artery semantic labeling. The MGM algorithm assesses the similarity between arterials in multiple vascular tree graphs, considering the cycle consistency between each pair of graphs. As a result, the unannotated arterial segments are appropriately labeled by matching them with annotated segments. Through the incorporation of anatomical graph structure, radiomics features, and semantic mapping, the proposed MGM model achieves an impressive accuracy of 0.9471 for coronary artery semantic labeling using our multi-site dataset with 718 ICAs. With the semantic labeled arteries, an overall accuracy of 0.9155 was achieved for stenosis detection. The proposed MGM presents a novel tool for coronary artery analysis using multiple ICA-derived graphs, offering valuable insights into vascular health and pathology.
We study the graph matching problem in the presence of vertex feature information using shallow graph neural networks. Specifically, given two graphs that are independent perturbations of a single random geometric graph with sparse binary features, the task is to recover an unknown one-to-one mapping between the vertices of the two graphs. We show under certain conditions on the sparsity and noise level of the feature vectors, a carefully designed two-layer graph neural network can, with high probability, recover the correct mapping between the vertices with the help of the graph structure. Additionally, we prove that our condition on the noise parameter is tight up to logarithmic factors. Finally, we compare the performance of the graph neural network to directly solving an assignment problem using the noisy vertex features and demonstrate that when the noise level is at least constant, this direct matching fails to achieve perfect recovery, whereas the graph neural network can tolerate noise levels growing as fast as a power of the size of the graph. Our theoretical findings are further supported by numerical studies as well as real-world data experiments.
Aligned text-image encoders such as CLIP have become the de facto model for vision-language tasks. Furthermore, modality-specific encoders achieve impressive performances in their respective domains. This raises a central question: does an alignment exist between uni-modal vision and language encoders since they fundamentally represent the same physical world? Analyzing the latent spaces structure of vision and language models on image-caption benchmarks using the Centered Kernel Alignment (CKA), we find that the representation spaces of unaligned and aligned encoders are semantically similar. In the absence of statistical similarity in aligned encoders like CLIP, we show that a possible matching of unaligned encoders exists without any training. We frame this as a seeded graph-matching problem exploiting the semantic similarity between graphs and propose two methods - a Fast Quadratic Assignment Problem optimization, and a novel localized CKA metric-based matching/retrieval. We demonstrate the effectiveness of this on several downstream tasks including cross-lingual, cross-domain caption matching and image classification. Code available at github.com/mayug/0-shot-llm-vision.
Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset.
State-of-the-art 3D point cloud registration methods rely on labeled 3D datasets for training, which limits their practical applications in real-world scenarios and often hinders generalization to unseen scenes. Leveraging the zero-shot capabilities of foundation models offers a promising solution to these challenges. In this paper, we introduce ZeroReg, a zero-shot registration approach that utilizes 2D foundation models to predict 3D correspondences. Specifically, ZeroReg adopts an object-to-point matching strategy, starting with object localization and semantic feature extraction from multi-view images using foundation models. In the object matching stage, semantic features help identify correspondences between objects across views. However, relying solely on semantic features can lead to ambiguity, especially in scenes with multiple instances of the same category. To address this, we construct scene graphs to capture spatial relationships among objects and apply a graph matching algorithm to these graphs to accurately identify matched objects. Finally, computing fine-grained point-level correspondences within matched object regions using algorithms like SuperGlue and LoFTR achieves robust point cloud registration. Evaluations on benchmarks such as 3DMatch, 3DLoMatch, and ScanNet demonstrate ZeroReg's competitive performance, highlighting its potential to advance point-cloud registration by integrating semantic features from foundation models.
Person search aims to find specific persons from visual scenes, including two subtasks, pedestrian detection, and person reidentification. The dominant fashion in this area is end-to-end networks that focus on analyzing the foreground (i.e., pedestrian) while ignoring the background (i.e., scene) information. However, the scene information often offers useful clues for person search. For example, pedestrians normally appear on the road rather than the top of a tree, and pedestrians appearing at the same location are likely to have similar occlusions. The interplay between the pedestrians and scenes can potentially improve the performance. In this article, a novel scene-pedestrian graph (SPG) is proposed, which can explicitly model the interplay between the pedestrians and scenes. To polish the quality of pedestrian bounding boxes, we pioneer a strategy of using the high-quality pedestrian bounding box to guide the low-quality one in the same scene. In addition, we design a contextual and temporal graph matching algorithm to effectively utilize the contextual and temporal information present in the constructed SPG to improve the performance of pedestrian matching. Benefiting from the robustness on complex scenes, our model achieves promising performance over the state-of-the-art methods on two popular person search benchmarks, CUHK-SYSU and PRW.
Subgraph matching is a challenging problem with a wide range of applications in database systems, biochemistry, and cognitive science. It involves determining whether a given query graph is present within a larger target graph. Traditional graph-matching algorithms provide precise results but face challenges in large graph instances due to the NP-complete problem, limiting their practical applicability. In contrast, recent neural network-based approximations offer more scalable solutions, but often lack interpretable node correspondences. To address these limitations, this article presents xNeuSM: Explainable Neural Subgraph Matching which introduces Graph Learnable Multi-hop Attention Networks (GLeMA) that adaptively learns the parameters governing the attention factor decay for each node across hops rather than relying on fixed hyperparameters. We provide a theoretical analysis establishing error bounds for GLeMA's approximation of multi-hop attention as a function of the number of hops. Additionally, we prove that learning distinct attention decay factors for each node leads to a correct approximation of multi-hop attention. Empirical evaluation on real-world datasets shows that xNeuSM achieves substantial improvements in prediction accuracy of up to 34% compared to approximate baselines and, notably, at least a seven-fold faster query time than exact algorithms. The source code of our implementation is available at https://github.com/martinakaduc/xNeuSM.
Obtaining large pre-trained models that can be fine-tuned to new tasks with limited annotated samples has remained an open challenge for medical imaging data. While pre-trained deep networks on ImageNet and vision-language foundation models trained on web-scale data are prevailing approaches, their effectiveness on medical tasks is limited due to the significant domain shift between natural and medical images. To bridge this gap, we introduce LVM-Med, the first family of deep networks trained on large-scale medical datasets. We have collected approximately 1.3 million medical images from 55 publicly available datasets, covering a large number of organs and modalities such as CT, MRI, X-ray, and Ultrasound. We benchmark several state-of-the-art self-supervised algorithms on this dataset and propose a novel self-supervised contrastive learning algorithm using a graph-matching formulation. The proposed approach makes three contributions: (i) it integrates prior pair-wise image similarity metrics based on local and global information; (ii) it captures the structural constraints of feature embeddings through a loss function constructed via a combinatorial graph-matching objective; and (iii) it can be trained efficiently end-to-end using modern gradient-estimation techniques for black-box solvers. We thoroughly evaluate the proposed LVM-Med on 15 downstream medical tasks ranging from segmentation and classification to object detection, and both for the in and out-of-distribution settings. LVM-Med empirically outperforms a number of state-of-the-art supervised, self-supervised, and foundation models. For challenging tasks such as Brain Tumor Classification or Diabetic Retinopathy Grading, LVM-Med improves previous vision-language models trained on 1 billion masks by 6-7% while using only a ResNet-50.
The high computational and memory requirements of generative large language models (LLMs) make it challenging to serve them cheaply. This paper aims to reduce the monetary cost for serving LLMs by leveraging preemptible GPU instances on modern clouds, which offer accesses to spare GPUs at a much cheaper price than regular instances but may be preempted by the cloud at any time. Serving LLMs on preemptible instances requires addressing challenges induced by frequent instance preemptions and the necessity of migrating instances to handle these preemptions. This paper presents SpotServe, the first distributed LLM serving system on preemptible instances. Several key techniques in SpotServe realize fast and reliable serving of generative LLMs on cheap preemptible instances. First, SpotServe dynamically adapts the LLM parallelization configuration for dynamic instance availability and fluctuating workload, while balancing the trade-off among the overall throughput, inference latency and monetary costs. Second, to minimize the cost of migrating instances for dynamic reparallelization, the task of migrating instances is formulated as a bipartite graph matching problem, which uses the Kuhn-Munkres algorithm to identify an optimal migration plan that minimizes communications. Finally, to take advantage of the grace period offered by modern clouds, we introduce stateful inference recovery, a new inference mechanism that commits inference progress at a much finer granularity and allows SpotServe to cheaply resume inference upon preemption. We evaluate on real spot instance preemption traces and various popular LLMs and show that SpotServe can reduce the P99 tail latency by 2.4 - 9.1x compared with the best existing LLM serving systems. We also show that SpotServe can leverage the price advantage of preemptive instances, saving 54% monetary cost compared with only using on-demand instances.
Vision transformers (ViTs) have recently been used for visual matching beyond object detection and segmentation. However, the original grid dividing strategy of ViTs neglects the spatial information of the keypoints, limiting the sensitivity to local information. Therefore, we propose QueryTrans (Query Transformer), which adopts a cross-attention module and keypoints-based center crop strategy for better spatial information extraction. We further integrate the graph attention module and devise a transformer-based graph matching approach GMTR (Graph Matching TRansformers) whereby the combinatorial nature of GM is addressed by a graph transformer neural GM solver. On standard GM benchmarks, GMTR shows competitive performance against the SOTA frameworks. Specifically, on Pascal VOC, GMTR achieves $\mathbf{83.6\%}$ accuracy, $\mathbf{0.9\%}$ higher than the SOTA framework. On Spair-71k, GMTR shows great potential and outperforms most of the previous works. Meanwhile, on Pascal VOC, QueryTrans improves the accuracy of NGMv2 from $80.1\%$ to $\mathbf{83.3\%}$, and BBGM from $79.0\%$ to $\mathbf{84.5\%}$. On Spair-71k, QueryTrans improves NGMv2 from $80.6\%$ to $\mathbf{82.5\%}$, and BBGM from $82.1\%$ to $\mathbf{83.9\%}$. Source code will be made publicly available.
Predictive combinatorial optimization, where the parameters of combinatorial optimization (CO) are unknown at the decision-making time, is the precise modeling of many real-world applications, including energy cost-aware scheduling and budget allocation on advertising. Tackling such a problem usually involves a prediction model and a CO solver. These two modules are integrated into the predictive CO pipeline following two design principles: "Predict-then-Optimize (PtO)", which learns predictions by supervised training and subsequently solves CO using predicted coefficients, while the other, named "Predict-and-Optimize (PnO)", directly optimizes towards the ultimate decision quality and claims to yield better decisions than traditional PtO approaches. However, there lacks a systematic benchmark of both approaches, including the specific design choices at the module level, as well as an evaluation dataset that covers representative real-world scenarios. To this end, we develop a modular framework to benchmark 11 existing PtO/PnO methods on 8 problems, including a new industrial dataset for combinatorial advertising that will be released. Our study shows that PnO approaches are better than PtO on 7 out of 8 benchmarks, but there is no silver bullet found for the specific design choices of PnO. A comprehensive categorization of current approaches and integration of typical scenarios are provided under a unified benchmark. Therefore, this paper could serve as a comprehensive benchmark for future PnO approach development and also offer fast prototyping for application-focused development. The code is available at https://github.com/Thinklab-SJTU/PredictiveCO-Benchmark.
Ontology (and more generally: Knowledge Graph) Matching is a challenging task where information in natural language is one of the most important signals to process. With the rise of Large Language Models, it is possible to incorporate this knowledge in a better way into the matching pipeline. A number of decisions still need to be taken, e.g., how to generate a prompt that is useful to the model, how information in the KG can be formulated in prompts, which Large Language Model to choose, how to provide existing correspondences to the model, how to generate candidates, etc. In this paper, we present a prototype that explores these questions by applying zero-shot and few-shot prompting with multiple open Large Language Models to different tasks of the Ontology Alignment Evaluation Initiative (OAEI). We show that with only a handful of examples and a well-designed prompt, it is possible to achieve results that are en par with supervised matching systems which use a much larger portion of the ground truth.
Model fusion is becoming a crucial component in the context of model-as-a-service scenarios, enabling the delivery of high-quality model services to local users. However, this approach introduces privacy risks and imposes certain limitations on its applications. Ensuring secure model exchange and knowledge fusion among users becomes a significant challenge in this setting. To tackle this issue, we propose PrivFusion, a novel architecture that preserves privacy while facilitating model fusion under the constraints of local differential privacy. PrivFusion leverages a graph-based structure, enabling the fusion of models from multiple parties without necessitating retraining. By employing randomized mechanisms, PrivFusion ensures privacy guarantees throughout the fusion process. To enhance model privacy, our approach incorporates a hybrid local differentially private mechanism and decentralized federated graph matching, effectively protecting both activation values and weights. Additionally, we introduce a perturbation filter adapter to alleviate the impact of randomized noise, thereby preserving the utility of the fused model. Through extensive experiments conducted on diverse image datasets and real-world healthcare applications, we provide empirical evidence showcasing the effectiveness of PrivFusion in maintaining model performance while preserving privacy. Our contributions offer valuable insights and practical solutions for secure and collaborative data analysis within the domain of privacy-preserving model fusion.
This paper addresses the Graph Matching problem, which consists of finding the best possible alignment between two input graphs, and has many applications in computer vision, network deanonymization and protein alignment. A common approach to tackle this problem is through convex relaxations of the NP-hard \emph{Quadratic Assignment Problem} (QAP). Here, we introduce a new convex relaxation onto the unit simplex and develop an efficient mirror descent scheme with closed-form iterations for solving this problem. Under the correlated Gaussian Wigner model, we show that the simplex relaxation admits a unique solution with high probability. In the noiseless case, this is shown to imply exact recovery of the ground truth permutation. Additionally, we establish a novel sufficiency condition for the input matrix in standard greedy rounding methods, which is less restrictive than the commonly used `diagonal dominance' condition. We use this condition to show exact one-step recovery of the ground truth (holding almost surely) via the mirror descent scheme, in the noiseless setting. We also use this condition to obtain significantly improved conditions for the GRAMPA algorithm [Fan et al. 2019] in the noiseless setting.
Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.
Molecular representation learning is fundamental for many drug related applications. Most existing molecular pre-training models are limited in using single molecular modality, either SMILES or graph representation. To effectively leverage both modalities, we argue that it is critical to capture the fine-grained 'semantics' between SMILES and graph, because subtle sequence/graph differences may lead to contrary molecular properties. In this paper, we propose a universal SMILE-graph representation learning model, namely UniMAP. Firstly, an embedding layer is employed to obtain the token and node/edge representation in SMILES and graph, respectively. A multi-layer Transformer is then utilized to conduct deep cross-modality fusion. Specially, four kinds of pre-training tasks are designed for UniMAP, including Multi-Level Cross-Modality Masking (CMM), SMILES-Graph Matching (SGM), Fragment-Level Alignment (FLA), and Domain Knowledge Learning (DKL). In this way, both global (i.e. SGM and DKL) and local (i.e. CMM and FLA) alignments are integrated to achieve comprehensive cross-modality fusion. We evaluate UniMAP on various downstream tasks, i.e. molecular property prediction, drug-target affinity prediction and drug-drug interaction. Experimental results show that UniMAP outperforms current state-of-the-art pre-training methods.We also visualize the learned representations to demonstrate the effect of multi-modality integration.
Graph matching is one of the most significant graph analytic tasks, which aims to find the node correspondence across different graphs. Most existing graph matching approaches mainly rely on topological information, whose performances are often sub-optimal and sensitive to data noise because of not fully leveraging the multi-modal information hidden in graphs, such as node attributes, subgraph structures, etc. In this study, we propose a novel and robust graph matching method based on an unbalanced hierarchical optimal transport (UHOT) framework, which, to our knowledge, makes the first attempt to exploit cross-modal alignment in graph matching. In principle, applying multi-layer message passing, we represent each graph as layer-wise node embeddings corresponding to different modalities. Given two graphs, we align their node embeddings within the same modality and across different modalities, respectively. Then, we infer the node correspondence by the weighted average of all the alignment results. This method is implemented as computing the UHOT distance between the two graphs -- each alignment is achieved by a node-level optimal transport plan between two sets of node embeddings, and the weights of all alignment results correspond to an unbalanced modality-level optimal transport plan. Experiments on various graph matching tasks demonstrate the superiority and robustness of our method compared to state-of-the-art approaches. Our implementation is available at https://github.com/Dixin-Lab/UHOT-GM.
LiDAR and cameras are complementary sensors for 3D object detection in autonomous driving. However, it is challenging to explore the unnatural interaction between point clouds and images, and the critical factor is how to conduct feature alignment of heterogeneous modalities. Currently, many methods achieve feature alignment by projection calibration only, without considering the problem of coordinate conversion accuracy errors between sensors, leading to sub-optimal performance. In this paper, we present GraphAlign, a more accurate feature alignment strategy for 3D object detection by graph matching. Specifically, we fuse image features from a semantic segmentation encoder in the image branch and point cloud features from a 3D Sparse CNN in the LiDAR branch. To save computation, we construct the nearest neighbor relationship by calculating Euclidean distance within the subspaces that are divided into the point cloud features. Through the projection calibration between the image and point cloud, we project the nearest neighbors of point cloud features onto the image features. Then by matching the nearest neighbors with a single point cloud to multiple images, we search for a more appropriate feature alignment. In addition, we provide a self-attention module to enhance the weights of significant relations to fine-tune the feature alignment between heterogeneous modalities. Extensive experiments on nuScenes benchmark demonstrate the effectiveness and efficiency of our GraphAlign.
Learning domain-invariant visual representations is important to train a model that can generalize well to unseen target task domains. Recent works demonstrate that text descriptions contain high-level class-discriminative information and such auxiliary semantic cues can be used as effective pivot embedding for domain generalization problems. However, they use pivot embedding in a global manner (i.e., aligning an image embedding with sentence-level text embedding), which does not fully utilize the semantic cues of given text description. In this work, we advocate for the use of local alignment between image regions and corresponding textual descriptions to get domain-invariant features. To this end, we first represent image and text inputs as graphs. We then cluster nodes within these graphs and match the graph-based image node features to the nodes of textual graphs. This matching process is conducted both globally and locally, tightly aligning visual and textual semantic sub-structures. We experiment with large-scale public datasets, such as CUB-DG and DomainBed, and our model achieves matched or better state-of-the-art performance on these datasets. The code is available at: https://github.com/noparkee/Graph-Clustering-based-DG