# Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networks

arXiv: https://arxiv.org/abs/2502.19053 · HTML: https://mlsanity.com/paper/2502.19053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [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)
- [Brain-inspired computing: We need a master plan](https://mlsanity.com/paper/2104.14517/) (2021)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective](https://mlsanity.com/paper/1908.10920/) (2019)
- [Photonic Delay Systems as Machine Learning Implementations](https://mlsanity.com/paper/1501.02592/) (2015)
- [Physical deep learning based on optimal control of dynamical systems](https://mlsanity.com/paper/2012.08761/) (2020)

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

- [Self-Organising Digital Circuits](https://mlsanity.com/paper/2608.02606/) (2026)
- [Extraction of linearized models from pre-trained networks via knowledge distillation](https://mlsanity.com/paper/2604.06732/) (2026)

## Abstract (arXiv)

The rapidly increasing computational demands for artificial intelligence (AI) have spurred the exploration of computing principles beyond conventional digital computers. Physical neural networks (PNNs) offer efficient neuromorphic information processing by harnessing the innate computational power of physical processes; however, training their weight parameters is computationally expensive. We propose a training approach for substantially reducing this training cost. Our training approach merges an optimal control method for continuous-time dynamical systems with a biologically plausible training method--direct feedback alignment. In addition to the reduction of training time, this approach achieves robust processing even under measurement errors and noise without requiring detailed system information. The effectiveness was numerically and experimentally verified in an optoelectronic delay system. Our approach significantly extends the range of physical systems practically usable as PNNs.