GNN Expressivity

GNN: Graph Neural Network

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6 papers in the last four weeks, up 100% on the four weeks before. 0.1% of all new papers.

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On the Expressive Power of GNNs to Solve Linear SDPs
Apr 30, 2026Chendi Qian, Christopher MorrisSemidefinite Programming Graph Neural Networks
Faculty of Computer Science, RWTH Aachen University, Germany
On Halting vs Converging in Recurrent Graph Neural Networks
Apr 28, 2026Jeroen Bollen, Stijn VansummerenGraph Neural Networks GNN Expressivity
Hasselt University
Towards Understanding the Expressive Power of GNNs with Global Readout
Apr 23, 2026Maurice Funk, Daumantas KojelisGraph Neural Networks GNN Expressivity
Leipzig University, Germany
The Logical Expressiveness of Topological Neural Networks
Apr 21, 2026Amirreza Akbari, Amauri H. Souza, Vikas GargGraph Neural Networks GNN Expressivity
Aalto University · Federal Institute of Cear´a, 2δ AI · YaiYai Ltd
Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks
Mar 16, 2026Eran RosenbluthGraph Neural Networks GNN Expressivity
RWTH Aachen University
Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing
Nov 14, 2025Brian Godwin Lim, Galvin Brice Lim, Renzo Roel Tan +2Graph Neural Networks Graph Representation Learning
Nara Institute of Science and Technology, Kyoto University, and Ateneo de Manila University · UNI-President Information Philippines Corporation · Nara Institute of Science and Technology and Ateneo de Manila University +2

Apr 30, 2026, cs.LGJ/K move · Enter open · S save

On the Expressive Power of GNNs to Solve Linear SDPs

Chendi Qian, Christopher Morris

Faculty of Computer Science, RWTH Aachen University, Germany

Semidefinite Programming Graph Neural Networks GNN Expressivity Constrained Optimization

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Semidefinite programs (SDPs) are a powerful framework for convex optimization and for constructing strong relaxations of hard combinatorial problems. However, solving large SDPs can be computationally expensive, motivating the use of machine learning models as fast computational surrogates. Graph neural networks (GNNs) are a natural candidate in this setting due to their sparsity-awareness and ability to model variable-constraint interactions. In this work, we study what expressive power is sufficient to recover optimal SDP solutions. We first prove negative results showing that standard GNN architectures fail on recovering linear SDP solutions. We then identify a more expressive architecture that captures the key structure of SDPs and can, in particular, emulate the updates of a standard first-order solver. Empirically, on both synthetic and \textsc{SdpLib} benchmarks of various classes of SDPs, this more expressive architecture achieves consistently lower prediction error and objective gap than theoretically weaker baselines. Finally, using the learned high-quality predictions to warm-start the first-order solver yields practical speedups of up to 80%.

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Latest papers 36

On the Expressive Power of GNNs to Solve Linear SDPs

On Halting vs Converging in Recurrent Graph Neural Networks

Towards Understanding the Expressive Power of GNNs with Global Readout

The Logical Expressiveness of Topological Neural Networks

Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks

Enhancing Graph Representations with Neighborhood-Contextualized Message-Passing