# Wave-based extreme deep learning based on non-linear time-Floquet entanglement

arXiv: https://arxiv.org/abs/2107.08564 · HTML: https://mlsanity.com/paper/2107.08564/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 100 references that are in the map.
- First posted on arXiv 19 Jul 2021.

## Builds on (most cited first, 9 of 9)

- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019)
- [Reinforcement Learning in a large scale photonic Recurrent Neural Network](https://mlsanity.com/paper/1711.05133/) (2017)
- [Theory of neuromorphic computing by waves: machine learning by rogue waves, dispersive shocks, and solitons](https://mlsanity.com/paper/1912.07044/) (2019)
- [Scalable Optical Learning Operator](https://mlsanity.com/paper/2012.12404/) (2020)
- [Random Projections through multiple optical scattering: Approximating kernels at the speed of light](https://mlsanity.com/paper/1510.06664/) (2015)
- [Scaling up Echo-State Networks with multiple light scattering](https://mlsanity.com/paper/1609.05204/) (2016)
- [A single inverse-designed photonic structure that performs parallel computing](https://mlsanity.com/paper/2009.01187/) (2020)
- [Nonreciprocal Phased-Array Antennas](https://mlsanity.com/paper/1911.02059/) (2019)

## Built on by (most cited first, 6 of 6)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Universal Approximation with XL MIMO Systems: OTA Classification via Trainable Analog Combining](https://mlsanity.com/paper/2504.12758/) (2025)
- [Model-free Optical Processors using In Situ Reinforcement Learning with Proximal Policy Optimization](https://mlsanity.com/paper/2507.05583/) (2025)
- [Over-The-Air Extreme Learning Machines with XL Reception via Nonlinear Cascaded Metasurfaces](https://mlsanity.com/paper/2601.17749/) (2026)
- [Over-The-Air Extreme Learning Machines with Nonlinear Stacked Intelligent Metasurfaces](https://mlsanity.com/paper/2608.27137/) (2026)

## Abstract (arXiv)

Wave-based analog signal processing holds the promise of extremely fast, on-the-fly, power-efficient data processing, occurring as a wave propagates through an artificially engineered medium. Yet, due to the fundamentally weak non-linearities of traditional wave materials, such analog processors have been so far largely confined to simple linear projections such as image edge detection or matrix multiplications. Complex neuromorphic computing tasks, which inherently require strong non-linearities, have so far remained out-of-reach of wave-based solutions, with a few attempts that implemented non-linearities on the digital front, or used weak and inflexible non-linear sensors, restraining the learning performance. Here, we tackle this issue by demonstrating the relevance of Time-Floquet physics to induce a strong non-linear entanglement between signal inputs at different frequencies, enabling a power-efficient and versatile wave platform for analog extreme deep learning involving a single, uniformly modulated dielectric layer and a scattering medium. We prove the efficiency of the method for extreme learning machines and reservoir computing to solve a range of challenging learning tasks, from forecasting chaotic time series to the simultaneous classification of distinct datasets. Our results open the way for wave-based machine learning with high energy efficiency, speed, and scalability.