HyperGCT: A Dynamic Hyper-GNN-Learned Geometric Constraint for 3D Registration

Geometric constraints between feature matches are critical in 3D point cloud registration problems. Existing approaches typically model unordered matches as a consistency graph and sample consistent matches to generate hypotheses. However, explicit graph construction introduces noise, posing great challenges for handcrafted geometric constraints to render consistency among matches. To overcome this, we propose HyperGCT, a flexible dynamic Hyper-GNN-learned geometric constraint that leverages high-order consistency among 3D correspondences. To our knowledge, HyperGCT is the first method that mines robust geometric constraints from dynamic hypergraphs for 3D registration. By dynamically optimizing the hypergraph through vertex and edge feature aggregation, HyperGCT effectively captures the correlations among correspondences, leading to accurate hypothesis generation. Extensive experiments on 3DMatch, 3DLoMatch, KITTI-LC, and ETH show that HyperGCT achieves state-of-the-art performance. Furthermore, our method is robust to graph noise, demonstrating a significant advantage in terms of generalization. The code will be released.

Edge-Colored Clustering in Hypergraphs: Beyond Minimizing Unsatisfied Edges

We consider a framework for clustering edge-colored hypergraphs, where the goal is to cluster (equivalently, to color) objects based on the primary type of multiway interactions they participate in. One well-studied objective is to color nodes to minimize the number of unsatisfied hyperedges -- those containing one or more nodes whose color does not match the hyperedge color. We motivate and present advances for several directions that extend beyond this minimization problem. We first provide new algorithms for maximizing satisfied edges, which is the same at optimality but is much more challenging to approximate, with all prior work restricted to graphs. We develop the first approximation algorithm for hypergraphs, and then refine it to improve the best-known approximation factor for graphs. We then introduce new objective functions that incorporate notions of balance and fairness, and provide new hardness results, approximations, and fixed-parameter tractability results.

DAMPER: A Dual-Stage Medical Report Generation Framework with Coarse-Grained MeSH Alignment and Fine-Grained Hypergraph Matching

Medical report generation is crucial for clinical diagnosis and patient management, summarizing diagnoses and recommendations based on medical imaging. However, existing work often overlook the clinical pipeline involved in report writing, where physicians typically conduct an initial quick review followed by a detailed examination. Moreover, current alignment methods may lead to misaligned relationships. To address these issues, we propose DAMPER, a dual-stage framework for medical report generation that mimics the clinical pipeline of report writing in two stages. In the first stage, a MeSH-Guided Coarse-Grained Alignment (MCG) stage that aligns chest X-ray (CXR) image features with medical subject headings (MeSH) features to generate a rough keyphrase representation of the overall impression. In the second stage, a Hypergraph-Enhanced Fine-Grained Alignment (HFG) stage that constructs hypergraphs for image patches and report annotations, modeling high-order relationships within each modality and performing hypergraph matching to capture semantic correlations between image regions and textual phrases. Finally,the coarse-grained visual features, generated MeSH representations, and visual hypergraph features are fed into a report decoder to produce the final medical report. Extensive experiments on public datasets demonstrate the effectiveness of DAMPER in generating comprehensive and accurate medical reports, outperforming state-of-the-art methods across various evaluation metrics.

Low coordinate degree algorithms II: Categorical signals and generalized stochastic block models

We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can test for the presence of categorical structure, including community structure and generalizations thereof, in high-dimensional data. This complements the first paper of this series, which studied the power of LCDF in testing for continuous structure like real-valued signals perturbed by additive noise. We apply the tools developed there to a general form of stochastic block model (SBM), where a population is assigned random labels and every $p$-tuple of the population generates an observation according to an arbitrary probability measure associated to the $p$ labels of its members. We show that the performance of LCDF admits a unified analysis for this class of models. As applications, we prove tight lower bounds against LCDF (and therefore also against low degree polynomials) for nearly arbitrary graph and regular hypergraph SBMs, always matching suitable generalizations of the Kesten-Stigum threshold. We also prove tight lower bounds for group synchronization and abelian group sumset problems under the "truth-or-Haar" noise model, and use our technical results to give an improved analysis of Gaussian multi-frequency group synchronization. In most of these models, for some parameter settings our lower bounds give new evidence for conjectural statistical-to-computational gaps. Finally, interpreting some of our findings, we propose a precise analogy between categorical and continuous signals: a general SBM as above behaves, in terms of the tradeoff between subexponential runtime cost of testing algorithms and the signal strength needed for a testing algorithm to succeed, like a spiked $p_*$-tensor model of a certain order $p_*$ that may be computed from the parameters of the SBM.

Fair Computation Offloading for RSMA-Assisted Mobile Edge Computing Networks

Rate splitting multiple access (RSMA) provides a flexible transmission framework that can be applied in mobile edge computing (MEC) systems. However, the research work on RSMA-assisted MEC systems is still at the infancy and many design issues remain unsolved, such as the MEC server and channel allocation problem in general multi-server and multi-channel scenarios as well as the user fairness issues. In this regard, we study an RSMA-assisted MEC system with multiple MEC servers, channels and devices, and consider the fairness among devices. A max-min fairness computation offloading problem to maximize the minimum computation offloading rate is investigated. Since the problem is difficult to solve optimally, we develop an efficient algorithm to obtain a suboptimal solution. Particularly, the time allocation and the computing frequency allocation are derived as closed-form functions of the transmit power allocation and the successive interference cancellation (SIC) decoding order, while the SIC decoding order is obtained heuristically, and the bisection search and the successive convex approximation methods are employed to optimize the transmit power allocation. For the MEC server and channel allocation problem, we transform it into a hypergraph matching problem and solve it by matching theory. Simulation results demonstrate that the proposed RSMA-assisted MEC system outperforms current MEC systems under various system setups.

Adapting Job Recommendations to User Preference Drift with Behavioral-Semantic Fusion Learning

Job recommender systems are crucial for aligning job opportunities with job-seekers in online job-seeking. However, users tend to adjust their job preferences to secure employment opportunities continually, which limits the performance of job recommendations. The inherent frequency of preference drift poses a challenge to promptly and precisely capture user preferences. To address this issue, we propose a novel session-based framework, BISTRO, to timely model user preference through fusion learning of semantic and behavioral information. Specifically, BISTRO is composed of three stages: 1) coarse-grained semantic clustering, 2) fine-grained job preference extraction, and 3) personalized top-$k$ job recommendation. Initially, BISTRO segments the user interaction sequence into sessions and leverages session-based semantic clustering to achieve broad identification of person-job matching. Subsequently, we design a hypergraph wavelet learning method to capture the nuanced job preference drift. To mitigate the effect of noise in interactions caused by frequent preference drift, we innovatively propose an adaptive wavelet filtering technique to remove noisy interaction. Finally, a recurrent neural network is utilized to analyze session-based interaction for inferring personalized preferences. Extensive experiments on three real-world offline recruitment datasets demonstrate the significant performances of our framework. Significantly, BISTRO also excels in online experiments, affirming its effectiveness in live recruitment settings. This dual success underscores the robustness and adaptability of BISTRO. The source code is available at https://github.com/Applied-Machine-Learning-Lab/BISTRO.

CURSOR: Scalable Mixed-Order Hypergraph Matching with CUR Decomposition

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, specifically 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.

Combinatorial Complex Score-based Diffusion Modelling through Stochastic Differential Equations

Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have excelled in generating various objects, generating graphs remains challenging. This thesis explores the potential of score-based generative models in generating such objects through a modelization as combinatorial complexes, which are powerful topological structures that encompass higher-order relationships. In this thesis, we propose a unified framework by employing stochastic differential equations. We not only generalize the generation of complex objects such as graphs and hypergraphs, but we also unify existing generative modelling approaches such as Score Matching with Langevin dynamics and Denoising Diffusion Probabilistic Models. This innovation overcomes limitations in existing frameworks that focus solely on graph generation, opening up new possibilities in generative AI. The experiment results showed that our framework could generate these complex objects, and could also compete against state-of-the-art approaches for mere graph and molecule generation tasks.

Text-Video Retrieval via Variational Multi-Modal Hypergraph Networks

Text-video retrieval is a challenging task that aims to identify relevant videos given textual queries. Compared to conventional textual retrieval, the main obstacle for text-video retrieval is the semantic gap between the textual nature of queries and the visual richness of video content. Previous works primarily focus on aligning the query and the video by finely aggregating word-frame matching signals. Inspired by the human cognitive process of modularly judging the relevance between text and video, the judgment needs high-order matching signal due to the consecutive and complex nature of video contents. In this paper, we propose chunk-level text-video matching, where the query chunks are extracted to describe a specific retrieval unit, and the video chunks are segmented into distinct clips from videos. We formulate the chunk-level matching as n-ary correlations modeling between words of the query and frames of the video and introduce a multi-modal hypergraph for n-ary correlation modeling. By representing textual units and video frames as nodes and using hyperedges to depict their relationships, a multi-modal hypergraph is constructed. In this way, the query and the video can be aligned in a high-order semantic space. In addition, to enhance the model's generalization ability, the extracted features are fed into a variational inference component for computation, obtaining the variational representation under the Gaussian distribution. The incorporation of hypergraphs and variational inference allows our model to capture complex, n-ary interactions among textual and visual contents. Experimental results demonstrate that our proposed method achieves state-of-the-art performance on the text-video retrieval task.

Fast Algorithms for Directed Graph Partitioning Using Flows and Reweighted Eigenvalues

We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation. Applying the matrix multiplicative weight update method to this relaxation, we derive almost linear-time algorithms to achieve $O(\sqrt{\log{n}})$-approximation and Cheeger-type guarantee for directed edge expansion, as well as an improved cut-matching game for directed graphs. This provides a primal-dual flow-based framework to obtain the best known algorithms for directed graph partitioning. The same approach also works for vertex expansion and for hypergraphs, providing a simple and unified approach to achieve the best known results for different expansion problems and different algorithmic techniques.