The Boolean Power of ReLU
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Computer Science > Machine Learning
Title:The Boolean Power of ReLU
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.
| Comments: | 10 pages, 2 figures, comes with AI declaration |
| Subjects: | Machine Learning (cs.LG); Logic in Computer Science (cs.LO) |
| Cite as: | arXiv:2608.12617 [cs.LG] |
| (or arXiv:2608.12617v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.12617
arXiv-issued DOI via DataCite (pending registration)
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