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Methods/Laplacian PE

Laplacian PE

Laplacian Positional Encodings

GraphsIntroduced 2000296 papers
Source Paper

Description

Laplacian eigenvectors represent a natural generalization of the Transformer positional encodings (PE) for graphs as the eigenvectors of a discrete line (NLP graph) are the cosine and sinusoidal functions. They help encode distance-aware information (i.e., nearby nodes have similar positional features and farther nodes have dissimilar positional features).

Hence, Laplacian Positional Encoding (PE) is a general method to encode node positions in a graph. For each node, its Laplacian PE is the k smallest non-trivial eigenvectors.

Papers Using This Method

HGFormer: A Hierarchical Graph Transformer Framework for Two-Stage Colonel Blotto Games via Reinforcement Learning2025-06-10H$^2$GFM: Towards unifying Homogeneity and Heterogeneity on Text-Attributed Graphs2025-06-10Quantum Graph Transformer for NLP Sentiment Classification2025-06-09OpenGT: A Comprehensive Benchmark For Graph Transformers2025-06-05Learning Pyramid-structured Long-range Dependencies for 3D Human Pose Estimation2025-06-03Relational Graph Transformer2025-05-16All You Need Is Synthetic Task Augmentation2025-05-15Structural-Temporal Coupling Anomaly Detection with Dynamic Graph Transformer2025-05-13SAR-GTR: Attributed Scattering Information Guided SAR Graph Transformer Recognition Algorithm2025-05-13Fused3S: Fast Sparse Attention on Tensor Cores2025-05-12Mitigating Degree Bias in Graph Representation Learning with Learnable Structural Augmentation and Structural Self-Attention2025-04-21HAECcity: Open-Vocabulary Scene Understanding of City-Scale Point Clouds with Superpoint Graph Clustering2025-04-18GT-SVQ: A Linear-Time Graph Transformer for Node Classification Using Spiking Vector Quantization2025-04-16Towards A Universal Graph Structural Encoder2025-04-15Ensemble-Enhanced Graph Autoencoder with GAT and Transformer-Based Encoders for Robust Fault Diagnosis2025-04-13NetTAG: A Multimodal RTL-and-Layout-Aligned Netlist Foundation Model via Text-Attributed Graph2025-04-12Leveraging Auto-Distillation and Generative Self-Supervised Learning in Residual Graph Transformers for Enhanced Recommender Systems2025-04-08Graphs are everywhere -- Psst! In Music Recommendation too2025-04-03Graph Transformer-Based Flood Susceptibility Mapping: Application to the French Riviera and Railway Infrastructure Under Climate Change2025-03-31TacticExpert: Spatial-Temporal Graph Language Model for Basketball Tactics2025-03-13