# Nonlinear optical encoding enabled by recurrent linear scattering

arXiv: https://arxiv.org/abs/2307.08558 · HTML: https://mlsanity.com/paper/2307.08558/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 64 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 19 of 19)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020)
- [Neuromorphic Silicon Photonic Networks](https://mlsanity.com/paper/1611.02272/) (2016)
- [Training of photonic neural networks through in situ backpropagation](https://mlsanity.com/paper/1805.09943/) (2018)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Image sensing with multilayer, nonlinear optical neural networks](https://mlsanity.com/paper/2207.14293/) (2022)
- [Reprogrammable Electro-Optic Nonlinear Activation Functions for Optical Neural Networks](https://mlsanity.com/paper/1903.04579/) (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)
- [Adversarial Robustness by Design through Analog Computing and Synthetic Gradients](https://mlsanity.com/paper/2101.02115/) (2021)
- [A complete, parallel and autonomous photonic neural network in a semiconductor multimode laser](https://mlsanity.com/paper/2012.11153/) (2020)
- [Photonic Differential Privacy with Direct Feedback Alignment](https://mlsanity.com/paper/2106.03645/) (2021)
- [LightOn Optical Processing Unit: Scaling-up AI and HPC with a Non von Neumann co-processor](https://mlsanity.com/paper/2107.11814/) (2021)
- [Facial Keypoints Detection](https://mlsanity.com/paper/1710.05279/) (2017)
- [Physics-inspired Neuroacoustic Computing Based on Tunable Nonlinear Multiple-scattering](https://mlsanity.com/paper/2304.08380/) (2023)
- [Privacy-Enhancing Optical Embeddings for Lensless Classification](https://mlsanity.com/paper/2211.12864/) (2022)

## Built on by (most cited first, 15 of 15)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity](https://mlsanity.com/paper/2406.06482/) (2024)
- [Optical Generative Models](https://mlsanity.com/paper/2410.17970/) (2024)
- [A universal approximation theorem for nonlinear resistive networks](https://mlsanity.com/paper/2312.15063/) (2023)
- [Transferable polychromatic optical encoder for neural networks](https://mlsanity.com/paper/2411.02697/) (2024)
- [Nonlinear Computation with Linear Optics via Source-Position Encoding](https://mlsanity.com/paper/2504.20401/) (2025)
- [Physical Foundation Models: Fixed hardware implementations of large-scale neural networks](https://mlsanity.com/paper/2604.27911/) (2026)
- [Exploring Structural Nonlinearity in Binary Polariton-Based Neuromorphic Architectures](https://mlsanity.com/paper/2411.06124/) (2024)
- [Programmable metasurfaces for future photonic artificial intelligence](https://mlsanity.com/paper/2505.11659/) (2025)
- [Universality of physical neural networks with multivariate nonlinearity](https://mlsanity.com/paper/2509.05420/) (2025)
- [Spatially Parallel All-optical Neural Networks](https://mlsanity.com/paper/2509.23611/) (2025)
- [Laser interferometry as a robust neuromorphic platform for machine learning](https://mlsanity.com/paper/2601.18047/) (2026)
- [ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity](https://mlsanity.com/paper/2602.23616/) (2026)
- [Physical policy gradient theorem for in situ stochastic-adjoint training](https://mlsanity.com/paper/2609.05808/) (2026)
- [RAOA: Alternating-Operator Neural Computation with Programmable Radio Propagation](https://mlsanity.com/paper/2610.02683/) (2026)

## Abstract (arXiv)

Optical information processing and computing can potentially offer enhanced performance, scalability and energy efficiency. However, achieving nonlinearity-a critical component of computation-remains challenging in the optical domain. Here we introduce a design that leverages a multiple-scattering cavity to passively induce optical nonlinear random mapping with a continuous-wave laser at a low power. Each scattering event effectively mixes information from different areas of a spatial light modulator, resulting in a highly nonlinear mapping between the input data and output pattern. We demonstrate that our design retains vital information even when the readout dimensionality is reduced, thereby enabling optical data compression. This capability allows our optical platforms to offer efficient optical information processing solutions across applications. We demonstrate our design's efficacy across tasks, including classification, image reconstruction, keypoint detection and object detection, all of which are achieved through optical data compression combined with a digital decoder. In particular, high performance at extreme compression ratios is observed in real-time pedestrian detection. Our findings open pathways for novel algorithms and unconventional architectural designs for optical computing.