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arXiv · 2610.10520

Distilling Graph Geometry: Knowledge Gap from GNNs to MLPs

Zhewei Chen·Hao Zhu·Jiaojiao Jiang·Ahad N. Zehmakan
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Abstract

GNN-to-MLP distillation aims to retain the predictive accuracy of a message-passing teacher while deploying a graph-free MLP at inference. Existing methods mainly transfer node-wise predictions or use confidence-based reweighting, but they do not specify where the student should preserve the teacher's graph-induced geometry. We show that this omission leads to two spectral failure modes in the student's representation space. On sparse graphs, the student suffers from spectral underfit, missing high-energy teacher directions concentrated near boundary regions. On dense graphs, it suffers from spectral overfit, retaining spurious directions that the teacher has collapsed through aggregation. Motivated by an energy-weighted teacher-student alignment objective, we propose Graph Geometry-aware MLP (G^2MLP), a training-time distillation framework guided by Ollivier-Ricci curvature. Curvature identifies where the two spectral errors concentrate and is used to allocate supervision between prediction-level and representation-level alignment. The deployed model remains a standard MLP and requires no graph access at inference. Across node-classification benchmarks, G^2MLP consistently improves over graph-free distillation baselines, reduces the teacher-student rank gap in both regimes, and transfers without architectural changes to Graph Transformer teachers and link prediction.

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Zhewei Chen, Hao Zhu, Jiaojiao Jiang, Ahad N. Zehmakan. 2026-10-07. Distilling Graph Geometry: Knowledge Gap from GNNs to MLPs. https://arxiv.org/abs/2610.10520

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