Training Coupled Phase Oscillators as a Neuromorphic Platform using Equilibrium Propagation
Abstract: Given the rapidly growing scale and resource requirements of machine learning applications, the idea of building more efficient learning machines much closer to the laws of physics is an attractive proposition. One central question for identifying promising candidates for such neuromorphic platforms is whether not only inference but also training can exploit the physical dynamics. In this work, we show that it is possible to successfully train a system of coupled phase oscillators - one of the most widely investigated nonlinear dynamical systems with a multitude of physical implementations, comprising laser arrays, coupled mechanical limit cycles, superfluids, and exciton-polaritons. To this end, we apply the approach of equilibrium propagation, which permits to extract training gradients via a physical realization of backpropagation, based only on local interactions. The complex energy landscape of the XY/ Kuramoto model leads to multistability, and we show how to address this challenge. Our study identifies coupled phase oscillators as a new general-purpose neuromorphic platform and opens the door towards future experimental implementations.
- K. Wagner and D. Psaltis, Applied Optics 26, 5061 (1987).
- N. Pashine, Physical Review Materials 5, 065607 (2021).
- M. Stern and A. Murugan, Annual Review of Condensed Matter Physics 14, 417 (2023).
- J. Kosterlitz, Journal of Physics C: Solid State Physics 7, 1046 (1974).
- F. C. Hoppensteadt and E. M. Izhikevich, Physical Review Letters 82, 2983 (1999).
- F. C. Hoppensteadt and E. M. Izhikevich, Physical Review E 62, 4010 (2000).
- N. Stroev and N. G. Berloff, Physical Review B 104, 205435 (2021).
- G. Csaba and W. Porod, Applied physics reviews 7 (2020).
- K. Nakajima, Japanese Journal of Applied Physics 59, 060501 (2020).
- J. Spall, X. Guo, and A. I. Lvovsky, “Training neural networks with end-to-end optical backpropagation,” (2023), arXiv:2308.05226 [physics.optics] .
- C. C. Wanjura and F. Marquardt, arXiv preprint arXiv:2308.16181 (2023).
- V. Lopez-Pastor and F. Marquardt, arXiv preprint arXiv:2103.04992 (2021).
- B. Scellier and Y. Bengio, Frontiers in computational neuroscience 11, 24 (2017).
- B. Scellier, arXiv preprint arXiv:2103.09985 (2021).
- B. Scellier, M. Ernoult, J. Kendall, and S. Kumar, “Energy-based learning algorithms for analog computing: a comparative study,” (2023), arXiv:2312.15103 [cs.LG] .
- M. Stern, A. J. Liu, and V. Balasubramanian, “The physical effects of learning,” (2023), arXiv:2306.12928 [cond-mat.dis-nn] .
- B. Scellier, S. Mishra, Y. Bengio, and Y. Ollivier, “Agnostic physics-driven deep learning,” (2022), arXiv:2205.15021 [cs.LG] .
- M. Falk, A. Strupp, B. Scellier, and A. Murugan, “Contrastive learning through non-equilibrium memory,” (2023b), arXiv:2312.17723 [cond-mat.dis-nn] .
- J. Laydevant, D. Markovic, and J. Grollier, “Training an ising machine with equilibrium propagation,” (2023), arXiv:2305.18321 [cs.NE] .
- S. F. Edwards and P. W. Anderson, Journal of Physics F: Metal Physics 6, 1927 (1976).
- E. Alpaydin and C. Kaynak, “Optical Recognition of Handwritten Digits,” UCI Machine Learning Repository (1998), DOI: https://doi.org/10.24432/C50P49.
- X. Glorot and Y. Bengio, in Proceedings of the thirteenth international conference on artificial intelligence and statistics (JMLR Workshop and Conference Proceedings, 2010) pp. 249–256.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.