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Enhancing GNNs with Architecture-Agnostic Graph Transformations: A Systematic Analysis

Zhifei Li, Gerrit Großmann, Verena Wolf

TL;DR

The findings reveal that certain transformations, particularly those augmenting node features with centrality measures, consistently improve expressivity, however, these gains come with trade-offs, as methods like graph encoding, while enhancing expressivity, introduce numerical inaccuracies widely-used python packages.

Abstract

In recent years, a wide variety of graph neural network (GNN) architectures have emerged, each with its own strengths, weaknesses, and complexities. Various techniques, including rewiring, lifting, and node annotation with centrality values, have been employed as pre-processing steps to enhance GNN performance. However, there are no universally accepted best practices, and the impact of architecture and pre-processing on performance often remains opaque. This study systematically explores the impact of various graph transformations as pre-processing steps on the performance of common GNN architectures across standard datasets. The models are evaluated based on their ability to distinguish non-isomorphic graphs, referred to as expressivity. Our findings reveal that certain transformations, particularly those augmenting node features with centrality measures, consistently improve expressivity. However, these gains come with trade-offs, as methods like graph encoding, while enhancing expressivity, introduce numerical inaccuracies widely-used python packages. Additionally, we observe that these pre-processing techniques are limited when addressing complex tasks involving 3-WL and 4-WL indistinguishable graphs.

Enhancing GNNs with Architecture-Agnostic Graph Transformations: A Systematic Analysis

TL;DR

The findings reveal that certain transformations, particularly those augmenting node features with centrality measures, consistently improve expressivity, however, these gains come with trade-offs, as methods like graph encoding, while enhancing expressivity, introduce numerical inaccuracies widely-used python packages.

Abstract

In recent years, a wide variety of graph neural network (GNN) architectures have emerged, each with its own strengths, weaknesses, and complexities. Various techniques, including rewiring, lifting, and node annotation with centrality values, have been employed as pre-processing steps to enhance GNN performance. However, there are no universally accepted best practices, and the impact of architecture and pre-processing on performance often remains opaque. This study systematically explores the impact of various graph transformations as pre-processing steps on the performance of common GNN architectures across standard datasets. The models are evaluated based on their ability to distinguish non-isomorphic graphs, referred to as expressivity. Our findings reveal that certain transformations, particularly those augmenting node features with centrality measures, consistently improve expressivity. However, these gains come with trade-offs, as methods like graph encoding, while enhancing expressivity, introduce numerical inaccuracies widely-used python packages. Additionally, we observe that these pre-processing techniques are limited when addressing complex tasks involving 3-WL and 4-WL indistinguishable graphs.

Paper Structure

This paper contains 36 sections, 1 theorem, 6 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Graph Isomorphism
  4. Graph Neural Networks
  5. Message Passing Neural Networks (MPNNs)
  6. Input and Computational Graph
  7. Graph Transformation Function
  8. Separation Ability
  9. Weisfeiler-Leman (WL) Test
  10. Methodology
  11. Datasets
  12. EXP Dataset
  13. BREC Dataset
  14. Task and Dataset Augmentation
  15. Graph Transformations
  16. ...and 21 more sections

Key Result

Lemma 1

Let $G_1$ and $G_2$ be any two non-isomorphic graphs. If a graph neural network $\mathcal{A} : G \to \mathbb{R}^d$ maps $G_1$ and $G_2$ to different embeddings, the Weisfeiler-Lehman graph isomorphism test also decides $G_1$ and $G_2$ are not isomorphic.

Figures (3)

  • Figure 1: Transformation Example. For Virtual Node method, red indicates an added virtual node. For Extra Node method, orange indicates an added extra node, and green represents the original node.
  • Figure 2: Two simple graphs that cannot be distinguished by the 1-WL test.
  • Figure 3: Dataset samples

Theorems & Definitions (1)

  • Lemma 1