Graph Neural Networks

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Graph Neural Networks

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Graph Representations

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Graph Representation Learning

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Heterogeneous Graph Transformers

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Graph Foundation Model

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Maximum Independent Set

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Text-Attributed Graph

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Message Passing Neural Networks

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Subgraphs

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Gnn-Based Detectors

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Graph Theory

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Exponential Random Graph Models

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Bilevel Graph Structure Learning, Revisited: Inner-Channel Origins of the Reported Gain
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May 8, 2026 · cs.LGJ/K move · Enter open · S save

Bilevel Graph Structure Learning, Revisited: Inner-Channel Origins of the Reported Gain

Minkyoung Kim, Beakcheol Jang

Graduate School of Information, Yonsei University

Bilevel graph structure learning is widely understood to improve graph neural networks by jointly optimizing model parameters and a learned graph structure, with the resulting performance gain attributed to the rewired adjacency. We find that this attribution may be overstated: training-dynamics effects in the inner loop, rather than the rewiring itself, capture a substantial share of the gain. To establish this, we introduce frozen-

φ

, a control that freezes the graph while retaining the inner-loop training schedule. This decomposes the bilevel gain into an inner channel of

T

-step training dynamics with implicit gradient regularization and a graph channel of the graph rewiring itself. On spatio-temporal flow forecasting the inner channel matches or exceeds the full bilevel pipeline, accounting for 78-101% of the gain; on node classification it accounts for 37-44% under a Bernoulli edge-level parameterization. We also verify that classical spectral diagnostics can dissociate from task gain. We propose frozen-

φ

as a standardized diagnostic for bilevel graph structure learning, with graph distillation as a method-agnostic complement. A three-precondition framework further predicts the sign of the bilevel gain on all six benchmarks.

Graph Representation Learning Bilevel Optimization

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