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CTQW-GNN Overcomes GNN Over-smoothing and Heterophily Issues

Yuliang Zhan, Zefeng Gao, Jian Li, Yang Liu, Hao sun· August 24, 2026 View original

Key takeaways

  • CTQW-GNN addresses GNN over-smoothing and poor performance on heterophilic graphs.
  • Its design uses Continuous-Time Quantum Walks to preserve feature norms and prevent signal damping.
  • The model combines three aggregation modules for robust performance across diverse graph types.
  • CTQW-GNN offers a theoretically justified approach to overcome fundamental GNN limitations.

Who benefits

Social MediaPharmaceuticalsCybersecurityE-commerceMaterials Science

Summary

CTQW-GNN is a novel Graph Neural Network based on Continuous-Time Quantum Walks that addresses common GNN weaknesses like over-smoothing and poor performance on heterophilic graphs. Its unitary propagator preserves feature norms and prevents exponential decay of Dirichlet energy, combining three aggregation modules for robust performance across diverse graph types.

Graph Neural Networks (GNNs) are powerful tools for graph-structured data, but they commonly suffer from two critical limitations: the "low-pass filter" effect, which causes poor performance on graphs where connected nodes have dissimilar features (heterophily), and "over-smoothing," where node features converge to constant values as layers are stacked, reducing model expressiveness. Existing solutions often tackle these issues separately or rely on empirical fixes that can compromise model capabilities. This paper introduces CTQW-GNN, a new GNN architecture grounded in Continuous-Time Quantum Walks (CTQW), offering a theoretically justified solution to both problems. The design leverages the unitary nature of the CTQW propagator, which ensures that no frequency components are damped, thereby counteracting the low-pass bias and preserving mid- and high-frequency signals crucial for heterophilic graphs. Additionally, this unitarity maintains feature norms and prevents the exponential decay of Dirichlet energy, effectively mitigating over-smoothing without sacrificing expressiveness. CTQW-GNN integrates three complementary aggregation modules: a CTQW-based aggregation for unitary evolution, a CTQW-Attention Aggregation for multi-hop neighbor access, and a standard low-pass GAT branch to ensure strong performance on homophilic graphs.

Why it matters

For professionals working with complex graph data in areas like social networks, drug discovery, or recommendation systems, CTQW-GNN offers a more robust and theoretically sound approach to overcome fundamental GNN limitations, leading to more accurate and expressive models.

How to implement this in your domain

  1. 1Evaluate existing GNN models for over-smoothing and performance on heterophilic graph datasets.
  2. 2Explore implementing CTQW-GNN for graph-structured data analysis, especially in domains with diverse node relationships.
  3. 3Leverage the CTQW-based aggregation to preserve high-frequency signals in heterophilic graphs.
  4. 4Utilize the CTQW-Attention Aggregation for improved multi-hop neighbor information access.
  5. 5Integrate CTQW-GNN into applications requiring robust graph representation learning, such as fraud detection or molecular modeling.

Original post by Yuliang Zhan, Zefeng Gao, Jian Li, Yang Liu, Hao sun

"arXiv:2608.20738v1 Announce Type: new Abstract: Graph Neural Networks (GNNs) are widely used on graph-structured data, but most suffer from two key weaknesses. First, message passing behaves as a low-pass filter under the homophily assumption, leading to poor performance on heter…"

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Originally posted by Yuliang Zhan, Zefeng Gao, Jian Li, Yang Liu, Hao sun on X · view source

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