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On the Utilization of Unique Node Identifiers in Graph Neural Networks

Maya Bechler-Speicher, Moshe Eliasof, Carola-Bibiane Schönlieb, Ran Gilad-Bachrach, Amir Globerson

TL;DR

This work argues that despite the advantages of UIDs, one of their disadvantages is that they lose the desirable property of permutation-equivariance, and proposes a method to regularize UID models towards permutation equivariance, via a contrastive loss.

Abstract

Graph Neural Networks have inherent representational limitations due to their message-passing structure. Recent work has suggested that these limitations can be overcome by using unique node identifiers (UIDs). Here we argue that despite the advantages of UIDs, one of their disadvantages is that they lose the desirable property of permutation-equivariance. We thus propose to focus on UID models that are permutation-equivariant, and present theoretical arguments for their advantages. Motivated by this, we propose a method to regularize UID models towards permutation equivariance, via a contrastive loss. We empirically demonstrate that our approach improves generalization and extrapolation abilities while providing faster training convergence. On the recent BREC expressiveness benchmark, our proposed method achieves state-of-the-art performance compared to other random-based approaches.

On the Utilization of Unique Node Identifiers in Graph Neural Networks

TL;DR

This work argues that despite the advantages of UIDs, one of their disadvantages is that they lose the desirable property of permutation-equivariance, and proposes a method to regularize UID models towards permutation equivariance, via a contrastive loss.

Abstract

Graph Neural Networks have inherent representational limitations due to their message-passing structure. Recent work has suggested that these limitations can be overcome by using unique node identifiers (UIDs). Here we argue that despite the advantages of UIDs, one of their disadvantages is that they lose the desirable property of permutation-equivariance. We thus propose to focus on UID models that are permutation-equivariant, and present theoretical arguments for their advantages. Motivated by this, we propose a method to regularize UID models towards permutation equivariance, via a contrastive loss. We empirically demonstrate that our approach improves generalization and extrapolation abilities while providing faster training convergence. On the recent BREC expressiveness benchmark, our proposed method achieves state-of-the-art performance compared to other random-based approaches.

Paper Structure

This paper contains 39 sections, 5 theorems, 6 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Unique Identifiers and Expressiveness in GNNs
  4. Learning Invariances in Neural Networks
  5. Theoretical Analysis
  6. Preliminaries
  7. Learning Invariance to UIDs
  8. Task Loss ($\mathcal{L}_{\text{task}}$).
  9. Experimental Evaluation
  10. Baselines
  11. Experimental Settings
  12. Improving Generalization and Extrapolation
  13. Dataset
  14. Setup
  15. Results
  16. ...and 24 more sections

Key Result

Theorem 3.2

A function $f$ can be UIDs-invariant with respect to a set of graphs $S$ and non-UIDs-invariant with respect to another set of graphs $S'$.

Figures (2)

  • Figure 1: The UID invariance ratio curves obtained with SIRI compared to RNI, with respect to the train set (a) and test set (b).
  • Figure 2: The learning curves of RNI SIRI on the EXP and CEXP daatasets. While both methods reach almost perfect accuracy, our SIRI offers faster convergence.

Theorems & Definitions (7)

  • Definition 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Theorem 3.4
  • Theorem 3.5
  • Theorem 6.1: informal
  • Conjecture 6.2: informal