Barlag, T., Holzapfel, V., Strieker, L. et al. (2 more authors) (2024) Graph neural networks and arithmetic circuits. In: Advances in Neural Information Processing Systems (NeurIPS 2024). 38th Annual Conference on Neural Information Processing Systems (NeurIPS 2024), 10-15 Dec 2024, Vancouver, Canada. NeurIPS
Abstract
We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the expressivity of GNNs using diverse activation functions and arithmetic circuits over real numbers. In our results the activation function of the network becomes a gate type in the circuit. Our result holds for families of constant depth circuits and networks, both uniformly and non-uniformly, for all common activation functions.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2024 The Authors. For reuse permissions, please contact the Author(s). |
Keywords: | Machine Learning; Graph Neural Networks; Arithmetic Circuits; Computational Complexity |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Funding Information: | Funder Grant number DEUTSCHE FORSCHUNGSGEMEINSCHAFT 432788559 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 22 Nov 2024 13:05 |
Last Modified: | 07 Feb 2025 12:20 |
Published Version: | https://papers.nips.cc/paper_files/paper/2024/hash... |
Status: | Published |
Publisher: | NeurIPS |
Refereed: | Yes |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:219966 |