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arXiv · 2608.12617

The Boolean Power of ReLU

Pablo Barceló·Floris Geerts·Matthias Lanzinger·Klara Pakhomenko·Jan Van den Bussche
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Abstract

We prove that, on finite simple undirected graphs equipped with a single Boolean node feature, the Boolean queries expressible in $\Sigma$-MPLang, for any collection $\Sigma$ of eventually constant activation functions and with arbitrary real coefficients, form a strict subclass of the Boolean queries expressible in ReLU-MPLang. We thereby settle a recently posed open problem: whether ReLU-MPLang is more powerful than trReLU-MPLang when it comes to Boolean queries. In particular, this implies that ReLU-GNNs are strictly more expressive than {TrReLU,id}-GNNs with respect to Boolean queries on Boolean-featured graphs.

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Pablo Barceló, Floris Geerts, Matthias Lanzinger, Klara Pakhomenko, Jan Van den Bussche. 2026-08-12. The Boolean Power of ReLU. https://arxiv.org/abs/2608.12617

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