Nonlinearity is crucial for sophisticated tasks in machine learning but is often difficult to engineer outside of electronics. By encoding the inputs in parameters of the system, linear systems can realize efficiently trainable nonlinear computations.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
References
Wetzstein, G. et al. Nature 588, 39–47 (2020).
McMahon, P. L. Nat. Rev. Phys. 5, 717–734 (2023).
Wanjura, C. C. & Marquardt, F. Nat. Phys. https://doi.org/10.1038/s41567-024-02534-9 (2024).
Eliezer, Y. et al. PNAS 120, e2305027120 (2023).
Xia, F. et al. Preprint at https://arxiv.org/abs/2307.08558 (2023).
Yildirim, M. et al. Preprint at https://arxiv.org/abs/2307.08533 (2023).
Wright, L. G. et al. Nature 601, 549–555 (2022).
Pai, S. et al. Science 380, 398–404 (2023).
Spall, J. et al. Preprint at https://arxiv.org/abs/2308.05226 (2023).
OpenAI et al. Preprint at https://arxiv.org/abs/2303.08774 (2023).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The author is listed as an inventor on several US provisional patent applications relating to optical computing (63/149,974; 63/178,318; 63/392,042).
Rights and permissions
About this article
Cite this article
McMahon, P.L. Nonlinear computation with linear systems. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02531-y
Published:
DOI: https://doi.org/10.1038/s41567-024-02531-y