# Forward-Forward Training of an Optical Neural Network

arXiv: https://arxiv.org/abs/2305.19170 · HTML: https://mlsanity.com/paper/2305.19170/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 10 of 10)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [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)
- [Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit](https://mlsanity.com/paper/2008.11659/) (2020)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Reprogrammable Electro-Optic Nonlinear Activation Functions for Optical Neural Networks](https://mlsanity.com/paper/1903.04579/) (2019)
- [Scalable Optical Learning Operator](https://mlsanity.com/paper/2012.12404/) (2020)
- [Nonlinear Optical Data Transformer for Machine Learning](https://mlsanity.com/paper/2208.09398/) (2022)

## Built on by (most cited first, 19 of 19)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Self-Contrastive Forward-Forward Algorithm](https://mlsanity.com/paper/2409.11593/) (2024)
- [Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignment](https://mlsanity.com/paper/2312.09257/) (2023)
- [Training Convolutional Neural Networks with the Forward-Forward algorithm](https://mlsanity.com/paper/2312.14924/) (2023)
- [A Review of Neuroscience-Inspired Machine Learning](https://mlsanity.com/paper/2403.18929/) (2024)
- [Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training](https://mlsanity.com/paper/2401.00413/) (2023)
- [Towards training digitally-tied analog blocks via hybrid gradient computation](https://mlsanity.com/paper/2409.03306/) (2024)
- [Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.12384/) (2025)
- [Forward Learning of Graph Neural Networks](https://mlsanity.com/paper/2403.11004/) (2024)
- [On the Improvement of Generalization and Stability of Forward-Only Learning via Neural Polarization](https://mlsanity.com/paper/2408.09210/) (2024)
- [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)
- [Training deep physical neural networks with local physical information bottleneck](https://mlsanity.com/paper/2602.09569/) (2026)
- [Physical Foundation Models: Fixed hardware implementations of large-scale neural networks](https://mlsanity.com/paper/2604.27911/) (2026)
- [Thermal Crosstalk Modelling and Compensation Methods for Programmable Photonic Integrated Circuits](https://mlsanity.com/paper/2404.10589/) (2024)
- [Training Large-Scale Optical Neural Networks with Two-Pass Forward Propagation](https://mlsanity.com/paper/2408.08337/) (2024)
- [Training Hybrid Neural Networks with Multimode Optical Nonlinearities Using Digital Twins](https://mlsanity.com/paper/2501.07991/) (2025)
- [Programmable metasurfaces for future photonic artificial intelligence](https://mlsanity.com/paper/2505.11659/) (2025)
- [Laser interferometry as a robust neuromorphic platform for machine learning](https://mlsanity.com/paper/2601.18047/) (2026)
- [Synthetic Benchmarks Overstate Forward-Forward Scaling: Real-Data Limits of Layer-Local Training](https://mlsanity.com/paper/2606.06539/) (2026)

## Abstract (arXiv)

Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as silicon photonics and spatial light modulators, offer promising avenues for achieving this goal. However, training multiple trainable layers in tandem with these physical systems poses challenges, as they are difficult to fully characterize and describe with differentiable functions, hindering the use of error backpropagation algorithm. The recently introduced Forward-Forward Algorithm (FFA) eliminates the need for perfect characterization of the learning system and shows promise for efficient training with large numbers of programmable parameters. The FFA does not require backpropagating an error signal to update the weights, rather the weights are updated by only sending information in one direction. The local loss function for each set of trainable weights enables low-power analog hardware implementations without resorting to metaheuristic algorithms or reinforcement learning. In this paper, we present an experiment utilizing multimode nonlinear wave propagation in an optical fiber demonstrating the feasibility of the FFA approach using an optical system. The results show that incorporating optical transforms in multilayer NN architectures trained with the FFA, can lead to performance improvements, even with a relatively small number of trainable weights. The proposed method offers a new path to the challenge of training optical NNs and provides insights into leveraging physical transformations for enhancing NN performance.