Symmetry

Research

23 pages, 1299 KB

Open AccessArticle

Target-Guided Asymmetric Path Modeling in Equipment Maintenance Knowledge Graphs

by Meng Chen and Yuming Bo

Symmetry 2026, 18(3), 439; https://doi.org/10.3390/sym18030439 - 3 Mar 2026

Viewed by 561

Knowledge graph completion via link prediction is critical for intelligent equipment maintenance systems to support accurate fault diagnosis and maintenance decision making. However, existing approaches struggle to simultaneously capture local structural dependencies and perform effective multi-hop reasoning due to limited receptive fields or [...] Read more.

Knowledge graph completion via link prediction is critical for intelligent equipment maintenance systems to support accurate fault diagnosis and maintenance decision making. However, existing approaches struggle to simultaneously capture local structural dependencies and perform effective multi-hop reasoning due to limited receptive fields or inefficient path exploration mechanisms. Traditional path-based methods implicitly assume path symmetry, treating all reasoning chains equally without considering their task-specific relevance. To address this issue, we propose a Graph Attention Network (GAT)-guided semantic path reasoning framework that breaks this symmetry through attention-driven asymmetric weighting, integrating local structural encoding with global multi-hop inference. The key innovation lies in a target-guided biased path sampling strategy, which transforms GAT attention weights into probabilistic transition biases, enabling adaptive exploration of high-quality semantic paths relevant to specific prediction targets. GATs learn importance-aware local representations, which guide biased random walks to efficiently sample task-relevant reasoning paths. The sampled paths are encoded and aggregated to form global semantic context representations, which are then fused with local embeddings through a gating mechanism for final link prediction. Experimental evaluations on FB15k-237, WN18RR, and a real-world equipment maintenance knowledge graph demonstrate that the proposed method consistently outperforms state-of-the-art baselines, achieving an MRR of 0.614 on the maintenance dataset and 0.485 on WN18RR. Further analysis shows that the learned path attention weights provide interpretable asymmetric reasoning evidence, enhancing transparency for safety-critical maintenance applications. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

25 pages, 2963 KB

Open AccessArticle

LawLLM-DS: A Two-Stage LoRA Framework for Multi-Label Legal Judgment Prediction with Structured Label Dependencies

by Pengcheng Zhao, Chengcheng Han and Kun Han

Symmetry 2026, 18(1), 150; https://doi.org/10.3390/sym18010150 - 13 Jan 2026

Viewed by 701

Abstract

Legal judgment prediction (LJP) increasingly relies on large language models whose full fine-tuning is memory-intensive and susceptible to catastrophic forgetting. We present LawLLM-DS, a two-stage Low-Rank Adaptation (LoRA) framework that first performs legal knowledge pre-tuning with an aggressive learning rate and subsequently refines [...] Read more.

Legal judgment prediction (LJP) increasingly relies on large language models whose full fine-tuning is memory-intensive and susceptible to catastrophic forgetting. We present LawLLM-DS, a two-stage Low-Rank Adaptation (LoRA) framework that first performs legal knowledge pre-tuning with an aggressive learning rate and subsequently refines judgment relations with conservative updates, using dedicated LoRA adapters, 4-bit quantization, and targeted modification of seven Transformer projection matrices to keep only 0.21% of parameters trainable. From a structural perspective, the twenty annotated legal elements form a symmetric label co-occurrence graph that exhibits both cluster-level regularities and asymmetric sparsity patterns, and LawLLM-DS implicitly captures these graph-informed dependencies while remaining compatible with downstream GNN-based representations. Experiments on 5096 manually annotated divorce cases show that LawLLM-DS lifts macro F1 to 0.8893 and achieves an accuracy of 0.8786, outperforming single-stage LoRA and BERT baselines under the same data regime. Ablation studies further verify the contributions of stage-wise learning rates, adapter placement, and low-rank settings. These findings demonstrate that curriculum-style, parameter-efficient adaptation provides a practical path toward lightweight yet structure-aware LJP systems for judicial decision support. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

23 pages, 6381 KB

Open AccessArticle

Temporal Convolutional and LSTM Networks for Complex Mechanical Drilling Speed Prediction

by Yang Huang, Wu Yang, Junrui Hu and Yihang Zhao

Symmetry 2025, 17(11), 1962; https://doi.org/10.3390/sym17111962 - 14 Nov 2025

Viewed by 749

Abstract

Accurate prediction of drilling speed is essential in mechanical drilling operations, as it improves operational efficiency, enhances safety, and reduces overall costs. Traditional prediction methods, however, are often constrained by delayed responsiveness, limited exploitation of real-time parameters, and inadequate capability to model complex [...] Read more.

Accurate prediction of drilling speed is essential in mechanical drilling operations, as it improves operational efficiency, enhances safety, and reduces overall costs. Traditional prediction methods, however, are often constrained by delayed responsiveness, limited exploitation of real-time parameters, and inadequate capability to model complex temporal dependencies, ultimately resulting in suboptimal performance. To overcome these limitations, this study introduces a novel model termed CTLSF (CNN-TCN-LSTM with Self-Attention), which integrates multiple neural network architectures within a symmetry-aware framework. The model achieves architectural symmetry through the coordinated interplay of spatial and temporal learning modules, each contributing complementary strengths to the prediction task. Specifically, Convolutional Neural Networks (CNNs) extract localized spatial features from sequential drilling data, while Temporal Convolutional Networks (TCNs) capture long-range temporal dependencies through dilated convolutions and residual connections. In parallel, Long Short-Term Memory (LSTM) networks model unidirectional temporal dynamics, and a self-attention mechanism adaptively highlights salient temporal patterns. Furthermore, a sliding window strategy is employed to enable real-time prediction on streaming data. Comprehensive experiments conducted on the Volve oilfield dataset demonstrate that the proposed CTLSF model substantially outperforms conventional data-driven approaches, achieving a low Mean Absolute Error (MAE) of 0.8439, a Mean Absolute Percentage Error (MAPE) of 2.19%, and a high coefficient of determination (R²) of 0.9831. These results highlight the effectiveness, robustness, and symmetry-aware design of the CTLSF model in predicting mechanical drilling speed under complex real-world conditions. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

18 pages, 1350 KB

Open AccessArticle

S-ResGCN-I: A Symmetry-Enhanced Residual Graph Convolutional Network for MRI-Based Brain Tumor Classification

by Qiujing Gan, Yingzhou Bi, Jiangtao Huang, Leigang Huo, Shanrui Liu and Kairui Xiong

Symmetry 2025, 17(11), 1946; https://doi.org/10.3390/sym17111946 - 13 Nov 2025

Cited by 1 | Viewed by 680

Abstract

Early and accurate detection of brain tumors is critical for MRI-based diagnosis. Conventional convolutional neural networks often struggle to capture fine-grained details, small or boundary-ambiguous lesions, and hemispheric symmetry patterns. To address these limitations, we propose S-ResGCN, a symmetry-aware framework integrating hierarchical feature [...] Read more.

Early and accurate detection of brain tumors is critical for MRI-based diagnosis. Conventional convolutional neural networks often struggle to capture fine-grained details, small or boundary-ambiguous lesions, and hemispheric symmetry patterns. To address these limitations, we propose S-ResGCN, a symmetry-aware framework integrating hierarchical feature extraction, attention mechanisms, and graph-based classification. S-ResGCN employs a ResNet50 backbone to extract multi-level features, with Convolutional Block Attention Modules applied to intermediate and deep layers to enhance key information and discriminative features. Furthermore, we introduce a novel self-paired regularization to enforce feature consistency between original and horizontally flipped images, improving sensitivity to bilateral symmetric structures. Extracted features are converted into nodes and modeled as a small graph, and a graph convolutional network captures inter-node relationships to generate symmetry-aware predictions. Evaluation on three publicly available brain tumor MRI datasets demonstrates that S-ResGCN achieves average accuracies of 99.83%, 99.37% and 99.26% ± 0.16, with consistently high precision, recall, and F1-scores. These results indicate that S-ResGCN effectively captures fine-grained and symmetric tumor characteristics often overlooked by conventional models, providing a robust and efficient tool for automated, graph convolutional network. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

26 pages, 3998 KB

Open AccessArticle

Graph-Symmetry Cognitive Learning for Multi-Scale Cloud Imaging: An Uncertainty-Quantified Geometric Paradigm via Hierarchical Graph Networks

by Qing Xu, Zichen Zhang, Guanfang Wang and Yunjie Chen

Symmetry 2025, 17(9), 1477; https://doi.org/10.3390/sym17091477 - 7 Sep 2025

Cited by 1 | Viewed by 911

Abstract

Cloud imagery analysis from terrestrial observation points represents a fundamental capability within contemporary atmospheric monitoring infrastructure, serving essential functions in meteorological prediction, climatic surveillance, and hazard alert systems. However, traditional ground-based cloud image segmentation methods have fundamental limitations, particularly their inability to effectively [...] Read more.

Cloud imagery analysis from terrestrial observation points represents a fundamental capability within contemporary atmospheric monitoring infrastructure, serving essential functions in meteorological prediction, climatic surveillance, and hazard alert systems. However, traditional ground-based cloud image segmentation methods have fundamental limitations, particularly their inability to effectively model the graph structure and symmetry in cloud data. To address this, we propose G-CLIP, a ground-based cloud image segmentation method based on graph symmetry. G-CLIP synergistically integrates four innovative modules. First, the Prototype-Driven Asymmetric Attention (PDAA) module is designed to reduce complexity and enhance feature learning by leveraging permutation invariance and graph symmetry principles. Second, the Symmetry-Adaptive Graph Convolution Layer (SAGCL) is constructed, modeling pixels as graph nodes, using cosine similarity to build a sparse discriminative structure, and ensuring stability through symmetry and degree normalization. Third, the Multi-Scale Directional Edge Optimizer (MSDER) is developed to explicitly model complex symmetric relationships in cloud features from a graph theory perspective. Finally, the Uncertainty-Driven Loss Optimizer (UDLO) is proposed to dynamically adjust weights to address foreground–background imbalance and provide uncertainty quantification. Extensive experiments on four benchmark datasets demonstrate that our method achieves state-of-the-art performance across all evaluation metrics. Our work provides a novel theoretical framework and practical solution for applying graph neural networks (GNNs) to meteorology, particularly by integrating graph properties with uncertainty and leveraging symmetries from graph theory for complex spatial modeling. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

45 pages, 3249 KB

Open AccessArticle

Dynamic State Equations and Distributed Blockchain Control: A Differential Game Model for Optimal Emission Trajectories in Shipping Networks

by Zhongmiao Sun, Yike Xi, Baoli Shi and Jinrong Liu

Symmetry 2025, 17(6), 817; https://doi.org/10.3390/sym17060817 - 23 May 2025

Cited by 2 | Viewed by 1488

Abstract

The shipping industry, a cornerstone of global trade, faces emissions reduction challenges amid tightening environmental policies. Blockchain technology, leveraging distributed symmetric architectures, enhances supply chain transparency by reducing information asymmetry, yet its dynamic interplay with emissions strategies remains underexplored. This study employs symmetry-driven [...] Read more.

The shipping industry, a cornerstone of global trade, faces emissions reduction challenges amid tightening environmental policies. Blockchain technology, leveraging distributed symmetric architectures, enhances supply chain transparency by reducing information asymmetry, yet its dynamic interplay with emissions strategies remains underexplored. This study employs symmetry-driven differential game theory to model four blockchain scenarios in port-shipping networks: no blockchain (N), port-led (PB), shipping company-led (CB), and a joint platform (FB). By solving Hamilton–Jacobi–Bellman equations, we derive optimal emissions reduction efforts, green investments, and blockchain strategies under symmetric and asymmetric decision-making frameworks. Results show blockchain adoption improves emissions reduction and service quality under cost thresholds, with port-led systems maximizing low-cost profits and shipping firms gaining asymmetrically in high-freight contexts. Joint platforms achieve symmetry in profit distribution through fee-trust synergy, enabling win–win outcomes. Integrating graph-theoretic principles, we have designed dynamic state equations for emissions and service levels, segmenting shippers by low-carbon preferences. This work bridges dynamic emissions strategies with blockchain’s network symmetry, fostering economic–environmental synergies to advance sustainable maritime supply chains. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

24 pages, 2062 KB

Open AccessEditor’s ChoiceArticle

Hybrid Optimization of Phase Masks: Integrating Non-Iterative Methods with Simulated Annealing and Validation via Tomographic Measurements

by Zhiwen Li, Chao Sun, Haihua Wang and Rui-Feng Wang

Symmetry 2025, 17(4), 530; https://doi.org/10.3390/sym17040530 - 31 Mar 2025

Cited by 11 | Viewed by 2549

Abstract

The development of holography has facilitated significant advancements across a wide range of disciplines. A phase-only spatial light modulator (SLM) plays a crucial role in realizing digital holography, typically requiring a phase mask as its input. Non-iterative (NI) algorithms are widely used for [...] Read more.

The development of holography has facilitated significant advancements across a wide range of disciplines. A phase-only spatial light modulator (SLM) plays a crucial role in realizing digital holography, typically requiring a phase mask as its input. Non-iterative (NI) algorithms are widely used for phase mask generation, yet they often fall short in delivering precise solutions and lack adaptability in complex scenarios. In contrast, the Simulated Annealing (SA) algorithm provides a global optimization approach capable of addressing these limitations. This study investigates the integration of NI algorithms with the SA algorithm to enhance the optimization of phase mask generation in digital holography. Furthermore, we examine how adjusting annealing parameters, especially the cooling strategy, can significantly improve system optimization performance and symmetry. Notably, we observe a considerable improvement in the efficiency of the SA algorithm when non-iterative methods are employed to generate the initial phase mask. Our method achieves a perfect representation of the symmetry in desired light fields. The efficacy of the optimized phase masks is evaluated through optical tomographic measurements using two-dimensional mutually unbiased bases (MUBs), with the resulting average similarity reaching 0.99. These findings validate the effectiveness of our methodin optimizing phase mask generation and underscore its potential for high-precision optical mode recognition and analysis. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

20 pages, 2943 KB

Open AccessArticle

The Heterogeneous Network Community Detection Model Based on Self-Attention

by Gaofeng Zhou and Rui-Feng Wang

Symmetry 2025, 17(3), 432; https://doi.org/10.3390/sym17030432 - 13 Mar 2025

Cited by 20 | Viewed by 2906

Abstract

With the advancement of representation learning, graph representation learning has gained significant attention in the field of community detection for heterogeneous networks. A prominent approach in this domain involves the use of meta-paths to capture higher-order relationships between nodes, particularly when bidirectional or [...] Read more.

With the advancement of representation learning, graph representation learning has gained significant attention in the field of community detection for heterogeneous networks. A prominent approach in this domain involves the use of meta-paths to capture higher-order relationships between nodes, particularly when bidirectional or reciprocal relationships exist. However, defining effective meta-paths often requires substantial domain expertise. Moreover, these methods typically depend on additional clustering algorithms, which can limit their practical applicability. To address these challenges, context paths have been introduced as an alternative to meta-paths. When combined with a self-attention mechanism, models can dynamically assess the relative importance of different context paths. By leveraging the inherent symmetry within context paths, models enhance their ability to capture balanced relationships between nodes, thereby improving their representation of complex interactions. Building on this idea, we propose BP-GCN, a self-attention-based model for heterogeneous community detection. BP-GCN autonomously identifies node relationships within symmetric context paths, significantly improving community detection accuracy. Furthermore, the model integrates the Bernoulli–Poisson framework to establish an end-to-end detection system that eliminates the need for auxiliary clustering algorithms. Extensive experiments on multiple real-world datasets demonstrate that BP-GCN consistently outperforms existing benchmark methods. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

25 pages, 2726 KB

Open AccessArticle

HybridGNN: A Self-Supervised Graph Neural Network for Efficient Maximum Matching in Bipartite Graphs

by Chun-Hui Pan, Yi Qu, Yao Yao and Mu-Jiang-Shan Wang

Symmetry 2024, 16(12), 1631; https://doi.org/10.3390/sym16121631 - 9 Dec 2024

Cited by 21 | Viewed by 4708

Abstract

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of [...] Read more.

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel Graph Neural Network model designed to efficiently address complex matching problems at scale. HybridGNN leverages a combination of Graph Attention Networks (GATv2), Graph SAGE (SAGEConv), and Graph Isomorphism Networks (GIN) layers to enhance computational efficiency and model performance. Through extensive ablation experiments, we identify that while the SAGEConv layer demonstrates suboptimal performance in terms of accuracy and F₁-score, configurations incorporating GATv2 and GIN layers show significant improvements. Specifically, in six-layer GNN architectures, the combinations of GATv2 and GIN layers with ratios of 4:2 and 5:1 yield superior accuracy and F₁-score. Therefore, we name these GNN configurations HybridGNN₁ and HybridGNN₂. Additionally, techniques such as mixed precision training, gradient accumulation, and Jumping Knowledge networks are integrated to further optimize performance. Evaluations on an email communication dataset reveal that HybridGNNs outperform traditional algorithms such as the Hopcroft–Karp algorithm, the Hungarian algorithm, and the Blossom/Edmonds’ algorithm, particularly for large and complex graphs. These findings highlight HybridGNN’s robust capability to solve maximum matching problems in bipartite graphs, making it a powerful tool for analyzing large-scale and intricate graph data. Furthermore, our study aligns with the goals of the Symmetry and Asymmetry Study in Graph Theory special issue by exploring the role of symmetry in bipartite graph structures. By leveraging GNNs, we address the challenges related to symmetry and asymmetry in graph properties, thereby improving the reliability and fault tolerance of complex networks. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry Study in Graph Theory)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry and Asymmetry Study in Graph Theory

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI