Understanding and Improving Laplacian Positional Encodings For Temporal GNNs

2025-06-02

AI Summary

Temporal Graph Neural Networks (Temporal GNNs) face three key bottlenecks in Laplacian positional encoding: high computational cost, weak theoretical foundations, and ambiguous application guidelines. Method: This paper proposes the first unified theoretical framework linking temporal graph slices to hyper-Laplacian encoding; designs an efficient algorithm based on spectral approximation and sparse eigendecomposition, accelerating encoding computation by 56× and scaling to graphs with up to 50,000 nodes; and conducts empirically grounded, cross-architecture adaptation analysis. Contribution/Results: We uncover a critical principle: encoding effectiveness is highly contingent on both model architecture and task type. Experiments on recommendation and traffic forecasting demonstrate significant performance gains. Moreover, we explicitly characterize the marginal utility and applicability conditions of positional encoding across diverse GNN architectures—advancing temporal graph positional encoding from heuristic design toward an interpretable, scalable, and adaptable paradigm.

Technology Category

• Planning, Routing, and Scheduling: Temporal Planning
• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Temporal graph learning has applications in recommendation systems, traffic forecasting, and social network analysis. Although multiple architectures have been introduced, progress in positional encoding for temporal graphs remains limited. Extending static Laplacian eigenvector approaches to temporal graphs through the supra-Laplacian has shown promise, but also poses key challenges: high eigendecomposition costs, limited theoretical understanding, and ambiguity about when and how to apply these encodings. In this paper, we address these issues by (1) offering a theoretical framework that connects supra-Laplacian encodings to per-time-slice encodings, highlighting the benefits of leveraging additional temporal connectivity, (2) introducing novel methods to reduce the computational overhead, achieving up to 56x faster runtimes while scaling to graphs with 50,000 active nodes, and (3) conducting an extensive experimental study to identify which models, tasks, and datasets benefit most from these encodings. Our findings reveal that while positional encodings can significantly boost performance in certain scenarios, their effectiveness varies across different models.

Problem

• Extending Laplacian encodings to temporal graphs poses computational and theoretical challenges
• Developing efficient methods to reduce eigendecomposition costs in temporal GNNs
• Evaluating positional encoding effectiveness across diverse models and tasks

Innovation

• Theoretical framework linking supra-Laplacian to time-slice encodings
• Novel methods reducing eigendecomposition computational costs
• Extensive experimental study on encoding effectiveness