AAAI 2026

January 23, 2026

Singapore, Singapore

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Graph neural networks (GNNs) have shown promise on combinatorial problems such as \textsc{Max-Clique}, yet it remains unclear what algorithmic principles they actually learn. This paper introduces a concept-driven framework for evaluating and interpreting GNNs on such tasks. We begin with a principled benchmark based on synthetic graphs with known difficulty levels—easy, medium, and hard—derived from theoretical thresholds for planted cliques. Using this setup, we show that GNNs reliably learn a simple yet powerful concept: degree-based ranking. This insight motivates a new decoder, Least-Probable Removal (LPR), which significantly outperforms the common top-$k$ strategy, especially on harder and real-world instances. Our analysis pipeline connects latent representations to classical heuristics, improving both interpretability and performance. Finally, we demonstrate cross-domain generalization to sparse PCA, showing that the same GNN architecture and decoding strategy succeed in recovering sparse principal components, revealing a shared underlying principle across domains.

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AAAI 2026

+1
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