# Training neural networks with end-to-end optical backpropagation

arXiv: https://arxiv.org/abs/2308.05226 · HTML: https://mlsanity.com/paper/2308.05226/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 9 Aug 2023.

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

- [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)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit](https://mlsanity.com/paper/2008.11659/) (2020)
- [Training of photonic neural networks through in situ backpropagation](https://mlsanity.com/paper/1805.09943/) (2018)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Silicon Photonic Architecture for Training Deep Neural Networks with Direct Feedback Alignment](https://mlsanity.com/paper/2111.06862/) (2021)
- [Hybrid training of optical neural networks](https://mlsanity.com/paper/2203.11207/) (2022)

## Built on by (most cited first, 7 of 7)

- [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)
- [Asymmetrical estimator for training encapsulated deep photonic neural networks](https://mlsanity.com/paper/2405.18458/) (2024)
- [Gradients of unitary optical neural networks using parameter-shift rule](https://mlsanity.com/paper/2506.11565/) (2025)
- [Toward all-optical unsupervised Hebbian learning in deep photonic neuromorphic networks](https://mlsanity.com/paper/2601.22300/) (2026)
- [Hierarchical Zero-Order Optimization for Deep Neural Networks](https://mlsanity.com/paper/2602.10607/) (2026)
- [Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines](https://mlsanity.com/paper/2606.13454/) (2026)

## Abstract (arXiv)

Optics is an exciting route for the next generation of computing hardware for machine learning, promising several orders of magnitude enhancement in both computational speed and energy efficiency. However, to reach the full capacity of an optical neural network it is necessary that the computing not only for the inference, but also for the training be implemented optically. The primary algorithm for training a neural network is backpropagation, in which the calculation is performed in the order opposite to the information flow for inference. While straightforward in a digital computer, optical implementation of backpropagation has so far remained elusive, particularly because of the conflicting requirements for the optical element that implements the nonlinear activation function. In this work, we address this challenge for the first time with a surprisingly simple and generic scheme. Saturable absorbers are employed for the role of the activation units, and the required properties are achieved through a pump-probe process, in which the forward propagating signal acts as the pump and backward as the probe. Our approach is adaptable to various analog platforms, materials, and network structures, and it demonstrates the possibility of constructing neural networks entirely reliant on analog optical processes for both training and inference tasks.