Primal-Dual Neural Algorithmic Reasoning

Neural Algorithmic Reasoning (NAR) trains neural networks to simulate classical algorithms, enabling structured and interpretable reasoning over complex data. While prior research has predominantly focused on learning exact algorithms for polynomial-time-solvable problems, extending NAR to harder problems remains an open challenge. In this work, we introduce a general NAR framework grounded in the primal-dual paradigm, a classical method for designing efficient approximation algorithms. By leveraging a bipartite representation between primal and dual variables, we establish an alignment between primal-dual algorithms and Graph Neural Networks. Furthermore, we incorporate optimal solutions from small instances to greatly enhance the model's reasoning capabilities. Our empirical results demonstrate that our model not only simulates but also outperforms approximation algorithms for multiple tasks, exhibiting robust generalization to larger and out-of-distribution graphs. Moreover, we highlight the framework's practical utility by integrating it with commercial solvers and applying it to real-world datasets.

LLM Enhancers for GNNs: An Analysis from the Perspective of Causal Mechanism Identification

The use of large language models (LLMs) as feature enhancers to optimize node representations, which are then used as inputs for graph neural networks (GNNs), has shown significant potential in graph representation learning. However, the fundamental properties of this approach remain underexplored. To address this issue, we propose conducting a more in-depth analysis of this issue based on the interchange intervention method. First, we construct a synthetic graph dataset with controllable causal relationships, enabling precise manipulation of semantic relationships and causal modeling to provide data for analysis. Using this dataset, we conduct interchange interventions to examine the deeper properties of LLM enhancers and GNNs, uncovering their underlying logic and internal mechanisms. Building on the analytical results, we design a plug-and-play optimization module to improve the information transfer between LLM enhancers and GNNs. Experiments across multiple datasets and models validate the proposed module.

LLM-CoT Enhanced Graph Neural Recommendation with Harmonized Group Policy Optimization

Graph neural networks (GNNs) have advanced recommender systems by modeling interaction relationships. However, existing graph-based recommenders rely on sparse ID features and do not fully exploit textual information, resulting in low information density within representations. Furthermore, graph contrastive learning faces challenges. Random negative sampling can introduce false negative samples, while fixed temperature coefficients cannot adapt to the heterogeneity of different nodes. In addition, current efforts to enhance recommendations with large language models (LLMs) have not fully utilized their Chain-of-Thought (CoT) reasoning capabilities to guide representation learning. To address these limitations, we introduces LGHRec (LLM-CoT Enhanced Graph Neural Recommendation with Harmonized Group Policy Optimization). This framework leverages the CoT reasoning ability of LLMs to generate semantic IDs, enriching reasoning processes and improving information density and semantic quality of representations. Moreover, we design a reinforcement learning algorithm, Harmonized Group Policy Optimization (HGPO), to optimize negative sampling strategies and temperature coefficients in contrastive learning. This approach enhances long-tail recommendation performance and ensures optimization consistency across different groups. Experimental results on three datasets demonstrate that LGHRec improves representation quality through semantic IDs generated by LLM's CoT reasoning and effectively boosts contrastive learning with HGPO. Our method outperforms several baseline models. The code is available at: https://anonymous.4open.science/r/LLM-Rec.

MolEditRL: Structure-Preserving Molecular Editing via Discrete Diffusion and Reinforcement Learning

Molecular editing aims to modify a given molecule to optimize desired chemical properties while preserving structural similarity. However, current approaches typically rely on string-based or continuous representations, which fail to adequately capture the discrete, graph-structured nature of molecules, resulting in limited structural fidelity and poor controllability. In this paper, we propose MolEditRL, a molecular editing framework that explicitly integrates structural constraints with precise property optimization. Specifically, MolEditRL consists of two stages: (1) a discrete graph diffusion model pretrained to reconstruct target molecules conditioned on source structures and natural language instructions; (2) an editing-aware reinforcement learning fine-tuning stage that further enhances property alignment and structural preservation by explicitly optimizing editing decisions under graph constraints. For comprehensive evaluation, we construct MolEdit-Instruct, the largest and most property-rich molecular editing dataset, comprising 3 million diverse examples spanning single- and multi-property tasks across 10 chemical attributes. Experimental results demonstrate that MolEditRL significantly outperforms state-of-the-art methods in both property optimization accuracy and structural fidelity, achieving a 74\% improvement in editing success rate while using 98\% fewer parameters.

PCDCNet: A Surrogate Model for Air Quality Forecasting with Physical-Chemical Dynamics and Constraints

Air quality forecasting (AQF) is critical for public health and environmental management, yet remains challenging due to the complex interplay of emissions, meteorology, and chemical transformations. Traditional numerical models, such as CMAQ and WRF-Chem, provide physically grounded simulations but are computationally expensive and rely on uncertain emission inventories. Deep learning models, while computationally efficient, often struggle with generalization due to their lack of physical constraints. To bridge this gap, we propose PCDCNet, a surrogate model that integrates numerical modeling principles with deep learning. PCDCNet explicitly incorporates emissions, meteorological influences, and domain-informed constraints to model pollutant formation, transport, and dissipation. By combining graph-based spatial transport modeling, recurrent structures for temporal accumulation, and representation enhancement for local interactions, PCDCNet achieves state-of-the-art (SOTA) performance in 72-hour station-level PM2.5 and O3 forecasting while significantly reducing computational costs. Furthermore, our model is deployed in an online platform, providing free, real-time air quality forecasts, demonstrating its scalability and societal impact. By aligning deep learning with physical consistency, PCDCNet offers a practical and interpretable solution for AQF, enabling informed decision-making for both personal and regulatory applications.

Graph-Supported Dynamic Algorithm Configuration for Multi-Objective Combinatorial Optimization

Deep reinforcement learning (DRL) has been widely used for dynamic algorithm configuration, particularly in evolutionary computation, which benefits from the adaptive update of parameters during the algorithmic execution. However, applying DRL to algorithm configuration for multi-objective combinatorial optimization (MOCO) problems remains relatively unexplored. This paper presents a novel graph neural network (GNN) based DRL to configure multi-objective evolutionary algorithms. We model the dynamic algorithm configuration as a Markov decision process, representing the convergence of solutions in the objective space by a graph, with their embeddings learned by a GNN to enhance the state representation. Experiments on diverse MOCO challenges indicate that our method outperforms traditional and DRL-based algorithm configuration methods in terms of efficacy and adaptability. It also exhibits advantageous generalizability across objective types and problem sizes, and applicability to different evolutionary computation methods.

The Correspondence Between Bounded Graph Neural Networks and Fragments of First-Order Logic

Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad applicability, understanding their expressive power remains an important question. In this paper, we show that bounded GNN architectures correspond to specific fragments of first-order logic (FO), including modal logic (ML), graded modal logic (GML), modal logic with the universal modality (ML(A)), the two-variable fragment (FO2) and its extension with counting quantifiers (C2). To establish these results, we apply methods and tools from finite model theory of first-order and modal logics to the domain of graph representation learning. This provides a unifying framework for understanding the logical expressiveness of GNNs within FO.

Rethinking Contrastive Learning in Graph Anomaly Detection: A Clean-View Perspective

Graph anomaly detection aims to identify unusual patterns in graph-based data, with wide applications in fields such as web security and financial fraud detection. Existing methods typically rely on contrastive learning, assuming that a lower similarity between a node and its local subgraph indicates abnormality. However, these approaches overlook a crucial limitation: the presence of interfering edges invalidates this assumption, since it introduces disruptive noise that compromises the contrastive learning process. Consequently, this limitation impairs the ability to effectively learn meaningful representations of normal patterns, leading to suboptimal detection performance. To address this issue, we propose a Clean-View Enhanced Graph Anomaly Detection framework (CVGAD), which includes a multi-scale anomaly awareness module to identify key sources of interference in the contrastive learning process. Moreover, to mitigate bias from the one-step edge removal process, we introduce a novel progressive purification module. This module incrementally refines the graph by iteratively identifying and removing interfering edges, thereby enhancing model performance. Extensive experiments on five benchmark datasets validate the effectiveness of our approach.

A Survey on Temporal Interaction Graph Representation Learning: Progress, Challenges, and Opportunities

Temporal interaction graphs (TIGs), defined by sequences of timestamped interaction events, have become ubiquitous in real-world applications due to their capability to model complex dynamic system behaviors. As a result, temporal interaction graph representation learning (TIGRL) has garnered significant attention in recent years. TIGRL aims to embed nodes in TIGs into low-dimensional representations that effectively preserve both structural and temporal information, thereby enhancing the performance of downstream tasks such as classification, prediction, and clustering within constantly evolving data environments. In this paper, we begin by introducing the foundational concepts of TIGs and emphasize the critical role of temporal dependencies. We then propose a comprehensive taxonomy of state-of-the-art TIGRL methods, systematically categorizing them based on the types of information utilized during the learning process to address the unique challenges inherent to TIGs. To facilitate further research and practical applications, we curate the source of datasets and benchmarks, providing valuable resources for empirical investigations. Finally, we examine key open challenges and explore promising research directions in TIGRL, laying the groundwork for future advancements that have the potential to shape the evolution of this field.

UQLegalAI@COLIEE2025: Advancing Legal Case Retrieval with Large Language Models and Graph Neural Networks

Legal case retrieval plays a pivotal role in the legal domain by facilitating the efficient identification of relevant cases, supporting legal professionals and researchers to propose legal arguments and make informed decision-making. To improve retrieval accuracy, the Competition on Legal Information Extraction and Entailment (COLIEE) is held annually, offering updated benchmark datasets for evaluation. This paper presents a detailed description of CaseLink, the method employed by UQLegalAI, the second highest team in Task 1 of COLIEE 2025. The CaseLink model utilises inductive graph learning and Global Case Graphs to capture the intrinsic case connectivity to improve the accuracy of legal case retrieval. Specifically, a large language model specialized in text embedding is employed to transform legal texts into embeddings, which serve as the feature representations of the nodes in the constructed case graph. A new contrastive objective, incorporating a regularization on the degree of case nodes, is proposed to leverage the information within the case reference relationship for model optimization. The main codebase used in our method is based on an open-sourced repo of CaseLink: https://github.com/yanran-tang/CaseLink.