The Boolean Power of ReLU
Pablo Barceló, Floris Geerts, Matthias Lanzinger, Klara Pakhomenko, Jan Van den Bussche
Abstract
We prove that, on finite simple undirected graphs equipped with a single Boolean node feature, the Boolean queries expressible in Σ-MPLang, for any collection Σ 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.
Create a lesson
Related papers
How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents
Zixi Chen, Akshay Vegesna, Samip Dahal et al.
Evidence-Grounded Agentic Formulation Development in an Autonomous Laboratory
Michael M. Craig, Riley J. Hickman, Yingshan Ma et al.
Probabilistic Linear Explanations
Frederic Koriche, Jean-Marie Lagniez, Chi Tran
Double descent is the principle of least action
Congzhou M Sha
RLLBC-Lib: An Educational Code Library for Reinforcement Learning and Learning-Based Control
Bernd Frauenknecht, Emma Cramer, Artur Eisele et al.
Higher-order pruning of experts in mixture-of-experts language models
Alex M. Tseng, Prannay Kaul, Luca Zancato et al.