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DuoGNN: Topology-aware Graph Neural Network with Homophily and Heterophily Interaction-Decoupling

K. Mancini, I. Rekik

TL;DR

A scalable and generalizable architecture which leverages topology to decouple homophilic and heterophilic edges and capture both short-range and long-range interactions, and a dual homophilic and heterophilic aggregation pipeline which prevents over-smoothing and over-squashing during the message passing.

Abstract

Graph Neural Networks (GNNs) have proven effective in various medical imaging applications, such as automated disease diagnosis. However, due to the local neighborhood aggregation paradigm in message passing which characterizes these models, they inherently suffer from two fundamental limitations: first, indistinguishable node embeddings due to heterophilic node aggregation (known as over-smoothing), and second, impaired message passing due to aggregation through graph bottlenecks (known as over-squashing). These challenges hinder the model expressiveness and prevent us from using deeper models to capture long-range node dependencies within the graph. Popular solutions in the literature are either too expensive to process large graphs due to high time complexity or do not generalize across all graph topologies. To address these limitations, we propose DuoGNN, a scalable and generalizable architecture which leverages topology to decouple homophilic and heterophilic edges and capture both short-range and long-range interactions. Our three core contributions introduce (i) a topological edge-filtering algorithm which extracts homophilic interactions and enables the model to generalize well for any graph topology, (ii) a heterophilic graph condensation technique which extracts heterophilic interactions and ensures scalability, and (iii) a dual homophilic and heterophilic aggregation pipeline which prevents over-smoothing and over-squashing during the message passing. We benchmark our model on medical and non-medical node classification datasets and compare it with its variants, showing consistent improvements across all tasks. Our DuoGNN code is available at https://github.com/basiralab/DuoGNN.

DuoGNN: Topology-aware Graph Neural Network with Homophily and Heterophily Interaction-Decoupling

TL;DR

A scalable and generalizable architecture which leverages topology to decouple homophilic and heterophilic edges and capture both short-range and long-range interactions, and a dual homophilic and heterophilic aggregation pipeline which prevents over-smoothing and over-squashing during the message passing.

Abstract

Graph Neural Networks (GNNs) have proven effective in various medical imaging applications, such as automated disease diagnosis. However, due to the local neighborhood aggregation paradigm in message passing which characterizes these models, they inherently suffer from two fundamental limitations: first, indistinguishable node embeddings due to heterophilic node aggregation (known as over-smoothing), and second, impaired message passing due to aggregation through graph bottlenecks (known as over-squashing). These challenges hinder the model expressiveness and prevent us from using deeper models to capture long-range node dependencies within the graph. Popular solutions in the literature are either too expensive to process large graphs due to high time complexity or do not generalize across all graph topologies. To address these limitations, we propose DuoGNN, a scalable and generalizable architecture which leverages topology to decouple homophilic and heterophilic edges and capture both short-range and long-range interactions. Our three core contributions introduce (i) a topological edge-filtering algorithm which extracts homophilic interactions and enables the model to generalize well for any graph topology, (ii) a heterophilic graph condensation technique which extracts heterophilic interactions and ensures scalability, and (iii) a dual homophilic and heterophilic aggregation pipeline which prevents over-smoothing and over-squashing during the message passing. We benchmark our model on medical and non-medical node classification datasets and compare it with its variants, showing consistent improvements across all tasks. Our DuoGNN code is available at https://github.com/basiralab/DuoGNN.
Paper Structure (6 sections, 3 equations, 6 figures, 3 tables)

This paper contains 6 sections, 3 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Methodology: DuoGNN
  4. Results and Discussion
  5. Conclusion
  6. Supplementary material

Figures (6)

  • Figure 1: Bottleneck in a graph. The nodes are samples from OrganSMNIST of two distinct classes and the edges connect similar nodes. The edge color indicates the variation of the receptor field, which increases as nodes get closer to the bottleneck.
  • Figure 2: DuoGNN's three-stage architecture pipeline
  • Figure 3: The DuoGNN pipeline graph flow includes: (a) An interaction-decoupling stage responsible for extracting the homophilic and heterophilic edges from the input graph. Nodes are colored based on their class, blue-shaded edges indicate the value of the topological measure, and red edges are used to show the LRI preservation throughout the process. (b) A parallel transformation stage that independently processes the two output graphs from the previous stage. Node colors represent node representations. (c) A prediction stage that concatenates the results from the previous stage.
  • Figure 4: Homophily ratio distribution shift during the interaction-decoupling stage (Cora Dataset)
  • Figure 5: Homophily ratio distribution shift during the interaction-decoupling stage (Organ-S Dataset)
  • ...and 1 more figures

Theorems & Definitions (3)

  • definition thmcounterdefinition: Over-smoothing
  • definition thmcounterdefinition: Over-squashing
  • definition thmcounterdefinition: Homophily