# Arbitrary control over multimode wave propagation for machine learning

arXiv: https://arxiv.org/abs/2402.17750 · HTML: https://mlsanity.com/paper/2402.17750/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 51 references that are in the map.
- First posted on arXiv 27 Feb 2024.

## Builds on (most cited first, 12 of 12)

- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [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)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019)
- [The physics of optical computing](https://mlsanity.com/paper/2308.00088/) (2023)
- [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)
- [Optical Transformers](https://mlsanity.com/paper/2302.10360/) (2023)
- [Silicon photonic-electronic neural network for fibre nonlinearity compensation](https://mlsanity.com/paper/2110.12833/) (2021)
- [M3ICRO: Machine Learning-Enabled Compact Photonic Tensor Core based on PRogrammable Multi-Operand Multimode Interference](https://mlsanity.com/paper/2305.19505/) (2023)

## Built on by (most cited first, 9 of 9)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Photonics-Enhanced Graph Convolutional Networks](https://mlsanity.com/paper/2512.15549/) (2025)
- [Quantum-secure multiparty deep learning](https://mlsanity.com/paper/2408.05629/) (2024)
- [Physical Foundation Models: Fixed hardware implementations of large-scale neural networks](https://mlsanity.com/paper/2604.27911/) (2026)
- [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)
- [Analog Physical Systems Can Exhibit Double Descent](https://mlsanity.com/paper/2511.17825/) (2025)
- [Laser interferometry as a robust neuromorphic platform for machine learning](https://mlsanity.com/paper/2601.18047/) (2026)
- [Fully Analog Resonant Recurrent Neural Network via Metacircuit](https://mlsanity.com/paper/2604.17277/) (2026)

## Abstract (arXiv)

Controlled multimode wave propagation can enable more space-efficient photonic processors than architectures based on discrete components connected by single-mode waveguides. Instead of defining discrete elements, one can sculpt the continuous substrate of a photonic processor to perform computations through multimode interference in two dimensions. Here we designed and demonstrated a device with a refractive index that can be rapidly reprogrammed across space, allowing arbitrary control of wave propagation. The device, a two-dimensional programmable waveguide, uses parallel electro-optic modulation of the refractive index of a slab waveguide with about 104 programmable spatial degrees of freedom. We implemented neural network inference on benchmark tasks with up to 49-dimensional vectors in a single pass, without digital pre-processing or post-processing. Theoretical and numerical analyses further indicated that two-dimensional programmable waveguides may offer not only a constant-factor reduction in device area but also a scaling benefit, with the area required growing as N1.5 rather than N2.