# Nonlinear Processing with Linear Optics

arXiv: https://arxiv.org/abs/2307.08533 · HTML: https://mlsanity.com/paper/2307.08533/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [fastai: A Layered API for Deep Learning](https://mlsanity.com/paper/2002.04688/) (2020)
- [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)
- [Neuromorphic Silicon Photonic Networks](https://mlsanity.com/paper/1611.02272/) (2016)
- [Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit](https://mlsanity.com/paper/2008.11659/) (2020)
- [All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces](https://mlsanity.com/paper/2108.09833/) (2021)
- [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)
- [A complete, parallel and autonomous photonic neural network in a semiconductor multimode laser](https://mlsanity.com/paper/2012.11153/) (2020)
- [Nonlinear Optical Data Transformer for Machine Learning](https://mlsanity.com/paper/2208.09398/) (2022)

## Built on by (most cited first, 20 of 20)

- [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)
- [Local Learning Rules for Out-of-Equilibrium Physical Generative Models](https://mlsanity.com/paper/2506.19136/) (2025)
- [Nonlinear Computation with Linear Optics via Source-Position Encoding](https://mlsanity.com/paper/2504.20401/) (2025)
- [Model-free Optical Processors using In Situ Reinforcement Learning with Proximal Policy Optimization](https://mlsanity.com/paper/2507.05583/) (2025)
- [Programmable k-local Ising interactions and shallow optical Kolmogorov--Arnold networks through repeated data encounters](https://mlsanity.com/paper/2508.17440/) (2025)
- [Low-rank surrogate modeling and stochastic zero-order optimization for training of neural networks with black-box layers](https://mlsanity.com/paper/2509.15113/) (2025)
- [Physical Foundation Models: Fixed hardware implementations of large-scale neural networks](https://mlsanity.com/paper/2604.27911/) (2026)
- [Metasurface-generated large and arbitrary analog convolution kernels for accelerated machine vision](https://mlsanity.com/paper/2409.18614/) (2024)
- [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)
- [Machine Intelligence on Wireless Edge Networks](https://mlsanity.com/paper/2506.12210/) (2025)
- [Universality of physical neural networks with multivariate nonlinearity](https://mlsanity.com/paper/2509.05420/) (2025)
- [Meta-training of diffractive meta-neural networks for super-resolution direction of arrival estimation](https://mlsanity.com/paper/2509.05926/) (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)
- [Pre-training Enables Extraordinary All-optical Image Denoising](https://mlsanity.com/paper/2605.07810/) (2026)
- [RAOA: Alternating-Operator Neural Computation with Programmable Radio Propagation](https://mlsanity.com/paper/2610.02683/) (2026)

## Abstract (arXiv)

Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed, the optical implementation of neural networks aims to harness the advantages of optical bandwidth and the energy efficiency of optical interconnections. In the absence of low-power optical nonlinearities, the challenge in the implementation of multilayer optical networks lies in realizing multiple optical layers without resorting to electronic components. In this study, we present a novel framework that uses multiple scattering that is capable of synthesizing programmable linear and nonlinear transformations concurrently at low optical power by leveraging the nonlinear relationship between the scattering potential, represented by data, and the scattered field. Theoretical and experimental investigations show that repeating the data by multiple scattering enables non-linear optical computing at low power continuous wave light. Moreover, we empirically found that scaling of this optical framework follows the power law as in state-of-the-art deep digital networks.