# Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons

arXiv: https://arxiv.org/abs/1912.07044 · HTML: https://mlsanity.com/paper/1912.07044/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2019.

## Built on by (most cited first, 19 of 19)

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- [Gaussian boson sampling and multi-particle event optimization by machine learning in the quantum phase space](https://mlsanity.com/paper/2102.12142/) (2021)
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- [Variational quantum algorithm for Gaussian discrete solitons and their boson sampling](https://mlsanity.com/paper/2110.12379/) (2021)
- [Programmable metasurfaces for future photonic artificial intelligence](https://mlsanity.com/paper/2505.11659/) (2025)

## Abstract (arXiv)

We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an encoding input layer, a wave layer, and a decoding readout, behaves as a conventional neural network in approximating mathematical functions, real-world datasets, and universal Boolean gates. The rank of the transmission matrix has a fundamental role in assessing the learning abilities of the wave. For a given set of training points, a threshold nonlinearity for universal interpolation exists. When considering the nonlinear Schroedinger equation, the use of highly nonlinear regimes implies that solitons, rogue, and shock waves do have a leading role in training and computing. Our results may enable the realization of novel machine learning devices by using diverse physical systems, as nonlinear optics, hydrodynamics, polaritonics, and Bose-Einstein condensates. The application of these concepts to photonics opens the way to a large class of accelerators and new computational paradigms. In complex wave systems, as multimodal fibers, integrated optical circuits, random, topological devices, and metasurfaces, nonlinear waves can be employed to perform computation and solve complex combinatorial optimization.