Turing universal neural networks do not require global clocks | Nature Communications

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Turing universal neural networks do not require global clocks

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Abstract<br>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.

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Acknowledgements<br>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”.

Author information<br>Authors and Affiliations<br>Department of Computer Science, University of Massachusetts, Amherst, MA, USA<br>Hava T. Siegelmann & Chloé Becquey

Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA<br>Roy N. Siegelmann

Department of Engineering, Cambridge University, Cambridge, UK<br>Stephen Chung

AuthorsHava T. SiegelmannView author publications<br>Search author on:PubMed Google Scholar

Roy N. SiegelmannView author publications<br>Search author on:PubMed Google Scholar

Stephen ChungView author publications<br>Search author on:PubMed Google Scholar

Chloé BecqueyView author publications<br>Search author on:PubMed Google Scholar

Corresponding author<br>Correspondence to<br>Hava T. Siegelmann.

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Cite this article<br>Siegelmann, H.T., Siegelmann, R.N., Chung, S. et al. Turing universal neural networks do not require global clocks.<br>Nat Commun (2026). https://doi.org/10.1038/s41467-026-73830-6<br>Download...