Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Better Not to Propagate: Understanding Edge Uncertainty and Over-smoothing in Signed Graph Neural Networks

Yoonhyuk Choi, Jiho Choi, Taewook Ko, Chong-Kwon Kim

TL;DR

This work proposes a novel method for estimating homophily and edge error ratio, integrated with dynamic selection between blocked and signed propagation during training, and demonstrates that blocking MP can be more effective than signed propagation under high edge error ratios.

Abstract

Traditional Graph Neural Networks (GNNs) rely on network homophily, which can lead to performance degradation due to over-smoothing in many real-world heterophily scenarios. Recent studies analyze the smoothing effect (separability) after message-passing (MP), depending on the expectation of node features. Regarding separability gain, they provided theoretical backgrounds on over-smoothing caused by various propagation schemes, including positive, signed, and blocked MPs. More recently, by extending these theorems, some works have suggested improvements in signed propagation under multiple classes. However, prior works assume that the error ratio of all propagation schemes is fixed, failing to investigate this phenomenon correctly. To solve this problem, we propose a novel method for estimating homophily and edge error ratio, integrated with dynamic selection between blocked and signed propagation during training. Our theoretical analysis, supported by extensive experiments, demonstrates that blocking MP can be more effective than signed propagation under high edge error ratios, improving the performance in both homophilic and heterophilic graphs.

Better Not to Propagate: Understanding Edge Uncertainty and Over-smoothing in Signed Graph Neural Networks

TL;DR

This work proposes a novel method for estimating homophily and edge error ratio, integrated with dynamic selection between blocked and signed propagation during training, and demonstrates that blocking MP can be more effective than signed propagation under high edge error ratios.

Abstract

Traditional Graph Neural Networks (GNNs) rely on network homophily, which can lead to performance degradation due to over-smoothing in many real-world heterophily scenarios. Recent studies analyze the smoothing effect (separability) after message-passing (MP), depending on the expectation of node features. Regarding separability gain, they provided theoretical backgrounds on over-smoothing caused by various propagation schemes, including positive, signed, and blocked MPs. More recently, by extending these theorems, some works have suggested improvements in signed propagation under multiple classes. However, prior works assume that the error ratio of all propagation schemes is fixed, failing to investigate this phenomenon correctly. To solve this problem, we propose a novel method for estimating homophily and edge error ratio, integrated with dynamic selection between blocked and signed propagation during training. Our theoretical analysis, supported by extensive experiments, demonstrates that blocking MP can be more effective than signed propagation under high edge error ratios, improving the performance in both homophilic and heterophilic graphs.
Paper Structure (23 sections, 13 theorems, 37 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 23 sections, 13 theorems, 37 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Motivation
  4. Local Smoothing on Message-Passing Schemes
  5. Necessity of Blocked MP
  6. Methodology
  7. (E-Step) Parameter Estimation
  8. (M-Step) Optimization with Calibration
  9. Theoretical Justification
  10. Experiments
  11. Performance Analysis (Q1)
  12. Analysis on Discrimination Power (Q2)
  13. Importance of Proper MP Schemes (Q3)
  14. Analysis on Large Graphs (Q4)
  15. Related Work
  16. ...and 8 more sections

Key Result

Lemma 3

Given $y_i=0$, let us assume ego $k$$\sim$$(\mu,\pi/2,0)$ and aggregated neighbors $k'$$\sim$$(\mu,\pi/2,\theta')$. By replacing the $\mathds{E}_p(h^{(1)}_i|y_i,d_i)$ as $\mathds{E}_p(\cdot)$, the expectation after plane MP is as follows: The $k'$ always satisfies $||k'|| \leq ||\mu||$ regardless of the normalized degree and homophily ratio since $1-b_i \leq 1$.

Figures (4)

  • Figure 1: Empirical analysis on (a) homophily and (b) edge error estimation. More details can be found in Appendix D
  • Figure 2: (Q2) We take three signed GNNs (GPRGNN, FAGCN, and GGCN) and measure the inter-class distances to show that our method improves the discrimination power
  • Figure 3: (Q3) Performance gain concerning signed/blocked propagation using FAGCN$^*$ model
  • Figure 4: Homophily and edge accuracy (1-error) estimation under i.i.d. graphs

Theorems & Definitions (17)

  • Definition 1: Message-Passing Schemes
  • Definition 2: CSBM under binary class scenario
  • Lemma 3: Multi-class CSBM, Plane MP
  • Lemma 4: Multi-class CSBM, Signed MP
  • Lemma 5: Multi-class CSBM, Blocked MP
  • Corollary 6: Plane vs Other MPs
  • Corollary 7: Signed vs Blocked MP
  • Corollary 8: Numerical example on edge error ratio
  • Theorem 9: Uncertainty
  • Theorem 10: Homophily estimation
  • ...and 7 more