# Training of photonic neural networks through in situ backpropagation

arXiv: https://arxiv.org/abs/1805.09943 · HTML: https://mlsanity.com/paper/1805.09943/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2018.

## Built on by (most cited first, 30 of 45)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Self-learning Machines based on Hamiltonian Echo Backpropagation](https://mlsanity.com/paper/2103.04992/) (2021)
- [L2ight: Enabling On-Chip Learning for Optical Neural Networks via Efficient in-situ Subspace Optimization](https://mlsanity.com/paper/2110.14807/) (2021)
- [Silicon Photonic Architecture for Training Deep Neural Networks with Direct Feedback Alignment](https://mlsanity.com/paper/2111.06862/) (2021)
- [Nonlinear optical encoding enabled by recurrent linear scattering](https://mlsanity.com/paper/2307.08558/) (2023)
- [A compact butterfly-style silicon photonic-electronic neural chip for hardware-efficient deep learning](https://mlsanity.com/paper/2111.06705/) (2021)
- [Dual adaptive training of photonic neural networks](https://mlsanity.com/paper/2212.06141/) (2022)
- [Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity](https://mlsanity.com/paper/2406.06482/) (2024)
- [Training neural networks with end-to-end optical backpropagation](https://mlsanity.com/paper/2308.05226/) (2023)
- [Photonic Differential Privacy with Direct Feedback Alignment](https://mlsanity.com/paper/2106.03645/) (2021)
- [Training all-mechanical neural networks for task learning through in situ backpropagation](https://mlsanity.com/paper/2404.15471/) (2024)
- [BPLight-CNN: A Photonics-based Backpropagation Accelerator for Deep Learning](https://mlsanity.com/paper/2102.10140/) (2021)
- [Integrated multi-operand optical neurons for scalable and hardware-efficient deep learning](https://mlsanity.com/paper/2305.19592/) (2023)
- [Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training](https://mlsanity.com/paper/2401.00413/) (2023)
- [FatNet: High Resolution Kernels for Classification Using Fully Convolutional Optical Neural Networks](https://mlsanity.com/paper/2210.16914/) (2022)
- [Digital Modeling on Large Kernel Metamaterial Neural Network](https://mlsanity.com/paper/2307.11862/) (2023)
- [Asymmetrical estimator for training encapsulated deep photonic neural networks](https://mlsanity.com/paper/2405.18458/) (2024)
- [Mirage: An RNS-Based Photonic Accelerator for DNN Training](https://mlsanity.com/paper/2311.17323/) (2023)
- [ExtremeMETA: High-speed Lightweight Image Segmentation Model by Remodeling Multi-channel Metamaterial Imagers](https://mlsanity.com/paper/2405.17568/) (2024)
- [Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.12384/) (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)
- [Integration of Programmable Diffraction with Digital Neural Networks](https://mlsanity.com/paper/2406.10688/) (2024)
- [Circuit realization and hardware linearization of monotone operator equilibrium networks](https://mlsanity.com/paper/2509.13793/) (2025)
- [Backpropagation-Free Trunk Training via the Split Forward Gradients](https://mlsanity.com/paper/2607.16612/) (2026)
- [Physical Deep Learning with Biologically Plausible Training Method](https://mlsanity.com/paper/2204.13991/) (2022)
- [Adversarial attacks on an optical neural network](https://mlsanity.com/paper/2205.01226/) (2022)

## Abstract (arXiv)

Recently, integrated optics has gained interest as a hardware platform for implementing machine learning algorithms. Of particular interest are artificial neural networks, since matrix-vector multi- plications, which are used heavily in artificial neural networks, can be done efficiently in photonic circuits. The training of an artificial neural network is a crucial step in its application. However, currently on the integrated photonics platform there is no efficient protocol for the training of these networks. In this work, we introduce a method that enables highly efficient, in situ training of a photonic neural network. We use adjoint variable methods to derive the photonic analogue of the backpropagation algorithm, which is the standard method for computing gradients of conventional neural networks. We further show how these gradients may be obtained exactly by performing intensity measurements within the device. As an application, we demonstrate the training of a numerically simulated photonic artificial neural network. Beyond the training of photonic machine learning implementations, our method may also be of broad interest to experimental sensitivity analysis of photonic systems and the optimization of reconfigurable optics platforms.