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arXiv · 2507.13703

Binarizing Physics-Inspired GNNs for Combinatorial Optimization

Martin Krutský·Gustav Šír·Vyacheslav Kungurtsev·Georgios Korpas
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Abstract

Physics-inspired graph neural networks (PI-GNNs) have been utilized as an efficient unsupervised framework for relaxing combinatorial optimization problems encoded through a specific graph structure and loss, reflecting dependencies between the problem's variables. While the framework has yielded promising results in various combinatorial problems, we show that the performance of PI-GNNs systematically plummets with an increasing density of the combinatorial problem graphs. Our analysis reveals an interesting phase transition in the PI-GNNs' training dynamics, associated with degenerate solutions for the denser problems, highlighting a discrepancy between the relaxed, real-valued model outputs and the binary-valued problem solutions. To address the discrepancy, we propose principled alternatives to the naive strategy used in PI-GNNs by building on insights from fuzzy logic and binarized neural networks. Our experiments demonstrate that the portfolio of proposed methods significantly improves the performance of PI-GNNs in increasingly dense settings.

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Martin Krutský, Gustav Šír, Vyacheslav Kungurtsev, Georgios Korpas. 2025-08-01. Binarizing Physics-Inspired GNNs for Combinatorial Optimization. https://doi.org/10.3233/faia251038

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