Measuring Over-smoothing beyond Dirichlet energy

arXiv — cs.LGTuesday, December 9, 2025 at 5:00:00 AM
  • A new study has introduced a generalized family of node similarity measures that extend beyond Dirichlet energy, which has been a common metric for assessing over-smoothing in Graph Neural Networks (GNNs). This research highlights the limitations of Dirichlet energy in capturing higher-order feature derivatives and establishes a connection between over-smoothing decay rates and the spectral gap of the graph Laplacian.
  • The findings are significant as they provide a more comprehensive framework for understanding over-smoothing in GNNs, which is crucial for improving their performance in various applications. The empirical results indicate that attention-based GNNs are particularly affected by over-smoothing, underscoring the need for advanced metrics to evaluate their effectiveness.
  • This development reflects ongoing challenges in the field of AI, particularly in enhancing the robustness of GNNs against over-smoothing and related issues. The introduction of alternative approaches, such as Interpolated Laplacian Embeddings and new models for message passing neural networks, indicates a broader trend towards innovative solutions that address the complexities of graph-based learning and its applications in service computing and multimodal data processing.
— via World Pulse Now AI Editorial System

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