factor-graph structure learning

This study addresses the long-standing reliance of Boolean factor model identifiability on the pure node assumption, which severely restricts the applicability of interpretable models. By leveraging Hasse diagrams to reformulate the identifiability problem as a graph isomorphism task and integrating Boolean satisfiability (SAT) algorithms, this work establishes necessary and sufficient conditions for identifiability without requiring pure nodes, further extending these results to probabilistic settings. The proposed framework transcends traditional pure node constraints by introducing novel graphical and algebraic identifiability theories alongside efficient verification tools. Ultimately, this research substantially broadens the class of interpretable Boolean factor models and equips practitioners with concrete methodologies for assessing identifiability in practice.

This work addresses the quantification and optimization of consistency repair in graph models, moving beyond traditional binary consistency paradigms by modeling consistency as a gradable, quantitative property. Methodologically, it establishes a theoretical theorem that characterizes constraint violation changes via application condition differences, enabling the first predictable and rankable assessment of repair gains induced by graph transformation rules. It further designs a constraint-driven rule derivation and look-ahead ranking algorithm, yielding a formally verifiable framework for evaluating repair gains. Experimental results demonstrate significant improvements in both accuracy and efficiency of graph repair, establishing a novel paradigm for error detection and automated correction in graph-based systems.

该文提出一个统一框架，将图拓扑学习和图生成视为共同生成过程的逆问题，以解决从数据中学习图结构的问题。

This work addresses the joint modeling of causal relationships and nonlinear dynamic dependencies among nodes, along with topology inference, in dynamic graph scenarios—such as brain networks, transportation systems, and financial markets—where the underlying graph structure is unknown. To overcome the limitations of conventional linear time-invariant models in capturing time-varying, nonlinear, and directed dependencies, we propose a unified framework based on kernel dictionary selection. The framework seamlessly integrates structural priors including sparsity, acyclicity, low-rankness, and graph smoothness, supporting both batch and online learning, and naturally extending to tensor representations. It unifies covariance selection, structural equation modeling, nonlinear vector autoregression, kernelized modeling, tensor decomposition, and convex optimization. Theoretically guaranteed convergence is established. Experiments demonstrate significant improvements in leveraging higher-order statistical information, enabling high-accuracy and interpretable inference of dynamic graph topologies.

Existing graph analysis systems struggle to effectively integrate topological structure with node attributes, limiting the discovery of patterns driven by their interaction. This work proposes ZipLine, a novel system that, for the first time, unifies predicate logic to express topology, node attributes, and neighborhood relationships within a single formalism. ZipLine introduces an interaction-driven predicate learning algorithm that enables cross-space collaborative reasoning and iterative analysis. By integrating coordinated views, subgraph selection, and attribute brushing techniques, the system facilitates expressive and efficient exploration of complex patterns in multivariate graphs. Empirical evaluation across three real-world domains—energy infrastructure, cybersecurity, and drug discovery—demonstrates ZipLine’s effectiveness in significantly enhancing the expressiveness and discoverability of intricate graph patterns.

This study addresses the challenge of unified modeling of source/sink dynamics, cyclic behavior, and topology-constrained transport in complex dynamical systems. By integrating the continuous theory of Helmholtz–Hodge decomposition with discrete data-driven approaches, the authors propose a structured flow modeling paradigm based on graph vector fields (GVFs) and gradient–curl–harmonic decompositions over simplicial complexes. They develop a multi-level modeling strategy that spans from high expressivity to low computational cost through parameterized conditional models and a simplified Hodge representation. A cross-domain validation and diagnosis–simplification iterative pipeline is further designed to ensure model interpretability while achieving computational efficiency. The framework systematically elucidates the trade-offs among model complexity, interpretability, and predictive performance.

This work addresses the tendency of generative models to produce statistically plausible yet structurally infeasible dynamic graph trajectories. To explicitly enforce structural admissibility, we propose integrating a conditional diffusion model with an external symbolic constraint layer, employing three mechanisms: hard filtering, soft weighting, and projection-based repair. We formally distinguish statistical plausibility from structural admissibility as two independent reliability attributes and demonstrate that symbolic constraints become especially critical in high-complexity graph systems. Experimental results show that in compact graphs, the proportion of invalid trajectories drops to as low as 0.002996; under moderate complexity, hard filtering retains 84.4% of valid samples while entirely eliminating infeasible outputs, confirming that constraint violations are the primary source of structural unacceptability.

This study addresses the challenge of generating power grid feeders that satisfy electrical compatibility and radial topology constraints when detailed parameters are unavailable. To this end, we propose PG-DiGress, a model that pioneers the integration of domain-specific physical rules into a discrete denoising diffusion process. The method combines graph neural networks with soft-mask injection to guide sampling, and employs a topology projection algorithm for constraint reconstruction, thereby overcoming the limitation of conventional generative models that merely match statistical properties. Experimental results demonstrate that the strict rule compliance rate of generated feeders increases from 13.7% to 96.8%. Furthermore, the generated topologies can be directly applied to downstream power system analysis, achieving highly compliant and practically deployable topology generation.

This work addresses the limited generality of traditional large neighborhood search methods, which rely on manually designed variable selection strategies. The authors propose a problem-agnostic automated pipeline that leverages large language models (LLMs) to generate unified weighted graphs from semantic prompts—where nodes represent decision variables and edges encode constraint relationships—to guide variable selection within the Structured Local Improvement Method (SLIM) framework. This approach requires no domain-specific knowledge and automatically extracts structural features to configure optimization algorithms for any MiniZinc problem. Evaluated on 20 MiniZinc Challenge instances, the method achieves an average win rate of 39.5%, substantially outperforming the best single algorithm configuration (19.3%); further ablation-based refinements improve this to 44.0%.

Piping and Instrumentation Diagrams (P&IDs) are the authoritative maps of process plants: isolation, maintenance, and HAZOP decisions depend on what connects to what. Vision-language models describe these sheets fluently, yet they often invent or miss process connections---and an invented or missed link can reverse an isolation or reachability call, so a plant decision cannot trust a fluent answer that was never checked against the linework. We instead recover an explicit graph of the drawing---its symbols, the process connections between them, and the tags that name them---and then require the model to answer only by querying that graph through seven read-only operators, so a topology claim is returned only when it cites the query results that support it. On TopoPID-VQA, a new suite of 3000 topology questions over these sheets, Graph-Grounded Harness (Ours) raises exact match accuracy from 36.7--41.3% under image-only prompting to 74.3--76.0% for Qwen3-VL-4B, Qwen3-VL-8B, and Gemma-4-E4B. It does so on an imperfect substrate: on Digitize-PID dataset the recovered graph scores F1 0.742 on exact process connections, and 0.801 once symbols and tags are pooled in. The residual errors track that gap---grounding pays off where the recovered graph is right, and perception error still breaks topology questions where it is not.