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Efficient Graph Optimization via Distance-Aware Graph Representation Learning

Dong Liu, Yanxuan Yu

TL;DR

DRTR addresses noisy and evolving graphs by decoupling diffusion, distance recalibration, and topology reconstruction. It introduces Distance Recomputator to prune weak edges and Topology Reconstructor to add latent long-range connections, all within a heat-diffusion-inspired multi-hop aggregator. Theoretical results provide generalization, convergence, and stability guarantees, while experiments demonstrate improvements in node classification, link prediction, and molecular property prediction with modest overhead. Overall, DRTR offers a scalable, general-purpose optimization layer that enhances graph representations in challenging real-world graphs.

Abstract

We propose an efficient framework that integrates distance-aware multi-hop message passing with dynamic topology refinement. Unlike standard GNNs that rely on shallow, fixed-hop aggregation, DRTR leverages both static preprocessing and dynamic resampling to capture deeper structural dependencies. A \emph{Distance Recomputator} prunes semantically weak edges using adaptive attention, while a \emph{Topology Reconstructor} establishes latent connections among distant but relevant nodes. This joint mechanism enables more expressive and robust graph representation optimization across evolving graph structures. Extensive experiments demonstrate that DRTR outperforms baseline GNNs in both accuracy and scalability, with at most 20\% computational overhead, especially in complex and noisy graph environments.

Efficient Graph Optimization via Distance-Aware Graph Representation Learning

TL;DR

DRTR addresses noisy and evolving graphs by decoupling diffusion, distance recalibration, and topology reconstruction. It introduces Distance Recomputator to prune weak edges and Topology Reconstructor to add latent long-range connections, all within a heat-diffusion-inspired multi-hop aggregator. Theoretical results provide generalization, convergence, and stability guarantees, while experiments demonstrate improvements in node classification, link prediction, and molecular property prediction with modest overhead. Overall, DRTR offers a scalable, general-purpose optimization layer that enhances graph representations in challenging real-world graphs.

Abstract

We propose an efficient framework that integrates distance-aware multi-hop message passing with dynamic topology refinement. Unlike standard GNNs that rely on shallow, fixed-hop aggregation, DRTR leverages both static preprocessing and dynamic resampling to capture deeper structural dependencies. A \emph{Distance Recomputator} prunes semantically weak edges using adaptive attention, while a \emph{Topology Reconstructor} establishes latent connections among distant but relevant nodes. This joint mechanism enables more expressive and robust graph representation optimization across evolving graph structures. Extensive experiments demonstrate that DRTR outperforms baseline GNNs in both accuracy and scalability, with at most 20\% computational overhead, especially in complex and noisy graph environments.
Paper Structure (46 sections, 12 theorems, 65 equations, 3 figures, 5 tables, 1 algorithm)

This paper contains 46 sections, 12 theorems, 65 equations, 3 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Adaptive Structure Learning in GNNs
  4. Distance-aware Message Passing
  5. Asynchronous and Selective Aggregation
  6. Heat Diffusion in Graph Representation Learning
  7. Methodology
  8. Multi-Hop Diffusion Aggregation
  9. Distance Recomputator (DR)
  10. Topology Reconstructor (TR)
  11. DRTR Training Procedure
  12. Theoretical Analysis
  13. Preliminaries
  14. Main Theoretical Results
  15. Discussion
  16. ...and 31 more sections

Key Result

theorem 1

Let $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ be a graph with $|\mathcal{V}| = n$ nodes, and let $d_{\text{eff}}$ denote the average effective degree after DRTR's distance-based pruning. Assume the underlying ground-truth graph satisfies structural smoothness, and DRTR correctly removes $\epsilon$- where $d_{\text{eff}} = \frac{1}{n}\sum_{v \in \mathcal{V}} |\mathcal{N}_{\text{eff}}(v)|$ and $\ma

Figures (3)

  • Figure 1: Performance across datasets. (a) Accuracy heatmap showing improvements across all model-dataset combinations. (b) Average improvement by dataset. (c) Variance reduction demonstrating improved stability. (d) Best performance comparison. (e) Training time overhead showing modest computational cost.
  • Figure 2: Comprehensive performance analysis. (a) Accuracy improvement by model showing consistent gains across GCN, SGC, SSGC, and APPNP. (b) Variance reduction demonstrating improved stability. (c) Training time overhead showing modest computational cost. (d) Accuracy across datasets using GCN backbone. (e) Component contribution analysis on Cora.
  • Figure 3: Component ablation analysis. (a) Accuracy improvement by component showing individual and combined contributions. (b) Variance reduction demonstrating stability improvements. (c) Combined effect analysis showing the optimal trade-off achieved by full DRTR.

Theorems & Definitions (18)

  • theorem 1: Generalization Bound under Adaptive Neighborhood Pruning
  • proposition 1: Convergence Rate
  • proposition 2: Stability under Graph Perturbation
  • theorem 2: Complete Generalization Bound under Adaptive Neighborhood Pruning
  • proof : Complete Proof
  • lemma 1: Properties of Learning Rate Weights
  • proof : Proof of Lemma A.0
  • lemma 2: Recursion on Representation Error
  • proof : Proof of Lemma A.1
  • lemma 3: Bound on Representation Error
  • ...and 8 more