Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generalization of Graph Neural Networks is Robust to Model Mismatch

Zhiyang Wang, Juan Cervino, Alejandro Ribeiro

TL;DR

This analysis reveals the robustness of the GNN generalization in the presence of such model mismatch, and indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold.

Abstract

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data are independent and identically distributed (i.i.d). This imposes limitations on the cases where a model mismatch exists when generating testing data. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models, explicitly focusing on scenarios where there is a mismatch between manifold models generating training and testing data. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch. This indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold. We attribute this mismatch to both node feature perturbations and edge perturbations within the generated graph. Our findings indicate that the generalization gap decreases as the number of nodes grows in the training graph while increasing with larger manifold dimension as well as larger mismatch. Importantly, we observe a trade-off between the generalization of GNNs and the capability to discriminate high-frequency components when facing a model mismatch. The most important practical consequence of this analysis is to shed light on the filter design of generalizable GNNs robust to model mismatch. We verify our theoretical findings with experiments on multiple real-world datasets.

Generalization of Graph Neural Networks is Robust to Model Mismatch

TL;DR

This analysis reveals the robustness of the GNN generalization in the presence of such model mismatch, and indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold.

Abstract

Graph neural networks (GNNs) have demonstrated their effectiveness in various tasks supported by their generalization capabilities. However, the current analysis of GNN generalization relies on the assumption that training and testing data are independent and identically distributed (i.i.d). This imposes limitations on the cases where a model mismatch exists when generating testing data. In this paper, we examine GNNs that operate on geometric graphs generated from manifold models, explicitly focusing on scenarios where there is a mismatch between manifold models generating training and testing data. Our analysis reveals the robustness of the GNN generalization in the presence of such model mismatch. This indicates that GNNs trained on graphs generated from a manifold can still generalize well to unseen nodes and graphs generated from a mismatched manifold. We attribute this mismatch to both node feature perturbations and edge perturbations within the generated graph. Our findings indicate that the generalization gap decreases as the number of nodes grows in the training graph while increasing with larger manifold dimension as well as larger mismatch. Importantly, we observe a trade-off between the generalization of GNNs and the capability to discriminate high-frequency components when facing a model mismatch. The most important practical consequence of this analysis is to shed light on the filter design of generalizable GNNs robust to model mismatch. We verify our theoretical findings with experiments on multiple real-world datasets.
Paper Structure (29 sections, 49 equations, 6 figures)

This paper contains 29 sections, 49 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. In-Distribution Generalization of GNNs
  4. Out-of-Distribution Generalization of GNNs
  5. GNNs and Manifold Neural Networks
  6. Neural Networks on Manifolds
  7. Geometric Graph Neural Networks
  8. Generalization of GNNs to model mismatch
  9. Manifold Model Mismatch
  10. Generalization of GNNs on node-level
  11. Remark 1
  12. Remark 2
  13. Extension to Graph Classification
  14. Experiments
  15. Node classification with Arxiv Dataset
  16. ...and 14 more sections

Figures (6)

  • Figure 1: Example of model mismatch. (a) The original manifold with a generated graph based on sampled points ($P1,\cdots, P6$). (b) The mismatched manifold with the sampled points also shifted, resulting in a perturbed graph. (c) The manifold mismatch can be seen as the perturbation of manifold function values, which leads to perturbed node features on the generated graph.
  • Figure 2: Generalization gap as a function of the percentage of perturbed feature values in node feature perturbation.
  • Figure 3: Generalization gap as a function of the percentage of perturbed edges values in node removal perturbation.
  • Figure 4: Generalization gap for edge and node perturbation for the Arxiv dataset for a $3$ layered, $256$ feature GNN.
  • Figure 5: Generalization gap as a function of number of nodes in the Point Cloud Classification.
  • ...and 1 more figures

Theorems & Definitions (3)

  • proof
  • proof
  • proof