# Nonlinear Computation with Linear Optics via Source-Position Encoding

arXiv: https://arxiv.org/abs/2504.20401 · HTML: https://mlsanity.com/paper/2504.20401/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [In-Datacenter Performance Analysis of a Tensor Processing Unit](https://mlsanity.com/paper/1704.04760/) (2017)
- [Data Movement Is All You Need: A Case Study on Optimizing Transformers](https://mlsanity.com/paper/2007.00072/) (2020)
- [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)
- [Nonlinear Processing with Linear Optics](https://mlsanity.com/paper/2307.08533/) (2023)
- [Nonlinear optical encoding enabled by recurrent linear scattering](https://mlsanity.com/paper/2307.08558/) (2023)

## Built on by (most cited first, 2 of 2)

- [Local Learning Rules for Out-of-Equilibrium Physical Generative Models](https://mlsanity.com/paper/2506.19136/) (2025)
- [Unifying Physical Backpropagation](https://mlsanity.com/paper/2608.11585/) (2026)

## Abstract (arXiv)

Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement for realizing neural networks -- is a conspicuous missing link. In this work we introduce a novel method to achieve nonlinear computation in fully linear media. Our method can operate at low power and requires only the ability to drive the optical system at a data-dependent spatial position. Leveraging this positional encoding, we formulate a fully automated, topology-optimization-based hardware design framework for extremely specialized optical neural networks, drawing on modern advancements in optimization and machine learning. We evaluate our optical designs on machine learning classification tasks: demonstrating significant improvements over linear methods, and competitive performance when compared to standard artificial neural networks.