Generating Graph-Like Logical Rules for Knowledge Graph Reasoning via Diffusion Models

Logical rules constitute a cornerstone of knowledge graph (KG) reasoning, valued for their interpretability and ability to model relational patterns. However, existing rule mining methods predominantly focus on simple chain-like rules and therefore neglect the richer relational information encoded in graph-like structures, such as cycles and branches. This limitation is further exacerbated by computational bottlenecks caused by the combinatorial explosion of the search space, which is especially challenging for graph-like rules. Meanwhile, generative approaches such as diffusion models, despite their success in other domains, cannot be directly applied to rule mining because their training objectives are not aligned with the goal of learning high-quality rules, and non-differentiable KG rule quality metrics cannot directly guide model optimization. To address these limitations, we propose GRiD, a framework that reformulates graph-like rule discovery as a discrete generative process conditioned on the target relation. GRiD employs a two-phase training strategy. First, supervised pre-training enables GRiD to capture structural priors from subgraphs sampled from the KG meta-graph. Subsequently, reinforcement learning is applied to fine-tune GRiD through policy gradient optimization guided directly by non-differentiable rule-quality metrics. Experiments on six benchmark datasets show that GRiD achieves competitive performance on KG completion tasks. Ablation studies confirm the efficiency and robustness of GRiD and further show that graph-like rules complement chain-like rules in KG completion. Our code and datasets are available in https://github.com/Haoxiang-Cheng/GRiD.

Generating Graph-like Rules for Knowledge Graph Reasoning via Diffusion Models

Logical rules constitute a cornerstone of knowledge graph (KG) reasoning, valued for their interpretability and ability to model relational patterns. However, existing rule mining methods predominantly focus on simple chain-like rules and therefore neglect the richer relational information encoded in graph-like structures, such as cycles and branches. This limitation is further exacerbated by computational bottlenecks caused by the combinatorial explosion of the search space, which is especially challenging for graph-like rules. Meanwhile, generative approaches such as diffusion models, despite their success in other domains, can not be directly applied to rule mining because their training objectives are not aligned with the goal of learning high-quality rules, and non-differentiable KG rule quality metrics cannot directly guide model optimization. To address these limitations, we propose GRiD, a framework that reformulates graph-like rule discovery as a discrete generative process conditioned on the target relation. GRiD employs a two-phase training strategy. First, supervised pre-training enables GRiD to capture structural priors from subgraphs sampled from the KG meta-graph. Subsequently, reinforcement learning is applied to fine-tune GRiD through policy gradient optimization guided directly by non-differentiable rule-quality metrics. Experiments on six benchmark datasets show that GRiD achieves competitive performance on KG completion tasks. Ablation studies confirm the efficiency and robustness of GRiD and further show that graph-like rules complement chain-like rules in KG completion. Our codes and datasets are available in https://github.com/Haoxiang-Cheng/GRiD

NED-Tree: Bridging the Semantic Gap with Nonlinear Element Decomposition Tree for LLM Nonlinear Optimization Modeling

Automating the translation of Operations Research (OR) problems from natural language to executable models is a critical challenge. While Large Language Models (LLMs) have shown promise in linear tasks, they suffer from severe performance degradation in real-world nonlinear scenarios due to semantic misalignment between mathematical formulations and solver codes, as well as unstable information extraction. In this study, we introduce NED-Tree, a systematic framework designed to bridge the semantic gap. NED-Tree employs (a) a sentence-by-sentence extraction strategy to ensure robust parameter mapping and traceability; and (b) a recursive tree-based structure that adaptively decomposes complex nonlinear terms into solver-compatible sub-elements. Additionally, we present NEXTOR, a novel benchmark specifically designed for complex nonlinear, extensive-constraint OR problems. Experiments across 10 benchmarks demonstrate that NED-Tree establishes a new state-of-the-art with 72.51% average accuracy, NED-Tree is the first framework that drives LLMs to resolve nonlinear modeling difficulties through element decomposition, achieving alignment between modeling semantics and code semantics. The NED-Tree framework and benchmark are accessible in the anonymous repository https://anonymous.4open.science/r/NORA-NEXTOR.

CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Prediction

Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in accelerating MILP solvers by predicting high-quality solutions. However, we identify that existing methods misalign with the intrinsic structure of MILP problems at two levels. At the leaning objective level, the Binary Cross-Entropy (BCE) loss treats variables independently, neglecting their relative priority and yielding plausible logits. At the model architecture level, standard GNN message passing inherently smooths the representations across variables, missing the natural competitive relationships within constraints. To address these challenges, we propose CoCo-MILP, which explicitly models inter-variable Contrast and intra-constraint Competition for advanced MILP solution prediction. At the objective level, CoCo-MILP introduces the Inter-Variable Contrastive Loss (VCL), which explicitly maximizes the embedding margin between variables assigned one versus zero. At the architectural level, we design an Intra-Constraint Competitive GNN layer that, instead of homogenizing features, learns to differentiate representations of competing variables within a constraint, capturing their exclusionary nature. Experimental results on standard benchmarks demonstrate that CoCo-MILP significantly outperforms existing learning-based approaches, reducing the solution gap by up to 68.12% compared to traditional solvers. Our code is available at https://github.com/happypu326/CoCo-MILP.

A Comprehensive Survey on Underwater Acoustic Target Positioning and Tracking: Progress, Challenges, and Perspectives

Underwater target tracking technology plays a pivotal role in marine resource exploration, environmental monitoring, and national defense security. Given that acoustic waves represent an effective medium for long-distance transmission in aquatic environments, underwater acoustic target tracking has become a prominent research area of underwater communications and networking. Existing literature reviews often offer a narrow perspective or inadequately address the paradigm shifts driven by emerging technologies like deep learning and reinforcement learning. To address these gaps, this work presents a systematic survey of this field and introduces an innovative multidimensional taxonomy framework based on target scale, sensor perception modes, and sensor collaboration patterns. Within this framework, we comprehensively survey the literature (more than 180 publications) over the period 2016-2025, spanning from the theoretical foundations to diverse algorithmic approaches in underwater acoustic target tracking. Particularly, we emphasize the transformative potential and recent advancements of machine learning techniques, including deep learning and reinforcement learning, in enhancing the performance and adaptability of underwater tracking systems. Finally, this survey concludes by identifying key challenges in the field and proposing future avenues based on emerging technologies such as federated learning, blockchain, embodied intelligence, and large models.

Transform then Explore: a Simple and Effective Technique for Exploratory Combinatorial Optimization with Reinforcement Learning

Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising direction, which treat the COPs solving as a heuristic learning problem. However, current finite-horizon-MDP based RL models have inherent limitations. They are not allowed to explore adquately for improving solutions at test time, which may be necessary given the complexity of NP-hard optimization tasks. Some recent attempts solve this issue by focusing on reward design and state feature engineering, which are tedious and ad-hoc. In this work, we instead propose a much simpler but more effective technique, named gauge transformation (GT). The technique is originated from physics, but is very effective in enabling RL agents to explore to continuously improve the solutions during test. Morever, GT is very simple, which can be implemented with less than 10 lines of Python codes, and can be applied to a vast majority of RL models. Experimentally, we show that traditional RL models with GT technique produce the state-of-the-art performances on the MaxCut problem. Furthermore, since GT is independent of any RL models, it can be seamlessly integrated into various RL frameworks, paving the way of these models for more effective explorations in the solving of general COPs.

Machine Learning for the Multi-Dimensional Bin Packing Problem: Literature Review and Empirical Evaluation

The Bin Packing Problem (BPP) is a well-established combinatorial optimization (CO) problem. Since it has many applications in our daily life, e.g. logistics and resource allocation, people are seeking efficient bin packing algorithms. On the other hand, researchers have been making constant advances in machine learning (ML), which is famous for its efficiency. In this article, we first formulate BPP, introducing its variants and practical constraints. Then, a comprehensive survey on ML for multi-dimensional BPP is provided. We further collect some public benchmarks of 3D BPP, and evaluate some online methods on the Cutting Stock Dataset. Finally, we share our perspective on challenges and future directions in BPP. To the best of our knowledge, this is the first systematic review of ML-related methods for BPP.

Finding Influencers in Complex Networks: An Effective Deep Reinforcement Learning Approach

Maximizing influences in complex networks is a practically important but computationally challenging task for social network analysis, due to its NP- hard nature. Most current approximation or heuristic methods either require tremendous human design efforts or achieve unsatisfying balances between effectiveness and efficiency. Recent machine learning attempts only focus on speed but lack performance enhancement. In this paper, different from previous attempts, we propose an effective deep reinforcement learning model that achieves superior performances over traditional best influence maximization algorithms. Specifically, we design an end-to-end learning framework that combines graph neural network as the encoder and reinforcement learning as the decoder, named DREIM. Trough extensive training on small synthetic graphs, DREIM outperforms the state-of-the-art baseline methods on very large synthetic and real-world networks on solution quality, and we also empirically show its linear scalability with regard to the network size, which demonstrates its superiority in solving this problem.

The Expressive Power of Graph Neural Networks: A Survey

Graph neural networks (GNNs) are effective machine learning models for many graph-related applications. Despite their empirical success, many research efforts focus on the theoretical limitations of GNNs, i.e., the GNNs expressive power. Early works in this domain mainly focus on studying the graph isomorphism recognition ability of GNNs, and recent works try to leverage the properties such as subgraph counting and connectivity learning to characterize the expressive power of GNNs, which are more practical and closer to real-world. However, no survey papers and open-source repositories comprehensively summarize and discuss models in this important direction. To fill the gap, we conduct a first survey for models for enhancing expressive power under different forms of definition. Concretely, the models are reviewed based on three categories, i.e., Graph feature enhancement, Graph topology enhancement, and GNNs architecture enhancement.

Inductive Meta-path Learning for Schema-complex Heterogeneous Information Networks

Heterogeneous Information Networks (HINs) are information networks with multiple types of nodes and edges. The concept of meta-path, i.e., a sequence of entity types and relation types connecting two entities, is proposed to provide the meta-level explainable semantics for various HIN tasks. Traditionally, meta-paths are primarily used for schema-simple HINs, e.g., bibliographic networks with only a few entity types, where meta-paths are often enumerated with domain knowledge. However, the adoption of meta-paths for schema-complex HINs, such as knowledge bases (KBs) with hundreds of entity and relation types, has been limited due to the computational complexity associated with meta-path enumeration. Additionally, effectively assessing meta-paths requires enumerating relevant path instances, which adds further complexity to the meta-path learning process. To address these challenges, we propose SchemaWalk, an inductive meta-path learning framework for schema-complex HINs. We represent meta-paths with schema-level representations to support the learning of the scores of meta-paths for varying relations, mitigating the need of exhaustive path instance enumeration for each relation. Further, we design a reinforcement-learning based path-finding agent, which directly navigates the network schema (i.e., schema graph) to learn policies for establishing meta-paths with high coverage and confidence for multiple relations. Extensive experiments on real data sets demonstrate the effectiveness of our proposed paradigm.