Turing universal neural networks do not require global clocks
Published: 05 June 2026
DOI: https://doi.org/10.1038/s41467-026-73830-6
Received: 14 August 2023 | Accepted: 21 May 2026
Abstract
Recurrent neural networks were proven to be Turing universal in the 1990s, motivating computational complexity studies of spiking networks, neural Turing machines with differentiable activations, and transformers. At the time, neural networks were exploratory and small, whereas today large-scale deployment makes energy efficiency critical. We thus extend the development of computational foundations of neural networks to asynchronous networks. Asynchrony is modeled by updating a single randomly selected neuron per step, eliminating global updates and reducing energy use. While asynchrony introduces variability in update sequences and thus has often been considered impractical for computing, we introduce design constraints which lead to Turing universal asynchronous architectures. We prove universality both for asynchronous fixed architectures with varying-precision neurons and for variable architectures with fixed-precision neurons. These results advance the theoretical understanding of asynchronous networks, suggesting that they preserve full computational power, remain amenable for efficient training, and may achieve substantial reductions in energy use.
Subjects
- Computational science
- Computer science
Authors and Affiliations
- Hava T. Siegelmann — Department of Computer Science, University of Massachusetts, Amherst, MA, USA
- Roy N. Siegelmann — Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
- Stephen Chung — Department of Engineering, Cambridge University, Cambridge, UK
- Chloé Becquey — Department of Computer Science, University of Massachusetts, Amherst, MA, USA
Corresponding author: Hava T. Siegelmann
Acknowledgements
We thank Eric Goldstein for providing editing and language clarification. H.S. discloses support for the research of this work from the National Science Foundation under Award No. 2231463 (“EAGER: Neural Networks that Temporally Change (NOTCH)”) and from the Air Force Office of Scientific Research through Acceptance Letter 24IOE006 for the project “Cooperative Multi-Agent Lifelong Learners for Scalable AI”.
Ethics declarations
The authors declare no competing interests.
License
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Citation
Siegelmann, H.T., Siegelmann, R.N., Chung, S. et al. Turing universal neural networks do not require global clocks. Nat Commun (2026). https://doi.org/10.1038/s41467-026-73830-6