# Learning by non-interfering feedback chemical signaling in physical networks

arXiv: https://arxiv.org/abs/2203.12098 · HTML: https://mlsanity.com/paper/2203.12098/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 61 references that are in the map.
- First posted on arXiv 22 Mar 2022.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Training End-to-End Analog Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2006.01981/) (2020)
- [Artificial neural networks for neuroscientists: A primer](https://mlsanity.com/paper/2006.01001/) (2020)
- [A deep learning theory for neural networks grounded in physics](https://mlsanity.com/paper/2103.09985/) (2021)
- [A Biologically Plausible Learning Rule for Deep Learning in the Brain](https://mlsanity.com/paper/1811.01768/) (2018)

## Built on by (most cited first, 11 of 11)

- [Energy-based learning algorithms for analog computing: a comparative study](https://mlsanity.com/paper/2312.15103/) (2023)
- [Agnostic Physics-Driven Deep Learning](https://mlsanity.com/paper/2205.15021/) (2022)
- [Frequency propagation: Multi-mechanism learning in nonlinear physical networks](https://mlsanity.com/paper/2208.08862/) (2022)
- [Training all-mechanical neural networks for task learning through in situ backpropagation](https://mlsanity.com/paper/2404.15471/) (2024)
- [Noise-based Local Learning using Stochastic Magnetic Tunnel Junctions](https://mlsanity.com/paper/2412.12783/) (2024)
- [Harnessing intuitive local evolution rules for physical learning](https://mlsanity.com/paper/2507.19561/) (2025)
- [Emergent learning in physical systems as feedback-based aging in a glassy landscape](https://mlsanity.com/paper/2309.04382/) (2023)
- [Laser interferometry as a robust neuromorphic platform for machine learning](https://mlsanity.com/paper/2601.18047/) (2026)
- [Perturbative Contrastive Physical Learning](https://mlsanity.com/paper/2606.09756/) (2026)
- [Reciprocity Separates Gradient Flow from Rotation in Conservative Physical Learning](https://mlsanity.com/paper/2608.30778/) (2026)
- [An all-transistor physical-learning transformer can be trained to perform in-context learning](https://mlsanity.com/paper/2610.12571/) (2026)

## Abstract (arXiv)

Both non-neural and neural biological systems can learn. So rather than focusing on purely brain-like learning, efforts are underway to study learning in physical systems. Such efforts include equilibrium propagation (EP) and coupled learning (CL), which require storage of two different states-the free state and the perturbed state-during the learning process to retain information about gradients. Inspired by slime mold, we propose a new learning algorithm rooted in chemical signaling that does not require storage of two different states. Rather, the output error information is encoded in a chemical signal that diffuses into the network in a similar way as the activation/feedforward signal. The steady state feedback chemical concentration, along with the activation signal, stores the required gradient information locally. We apply our algorithm using a physical, linear flow network and test it using the Iris data set with 93% accuracy. We also prove that our algorithm performs gradient descent. Finally, in addition to comparing our algorithm directly with EP and CL, we address the biological plausibility of the algorithm.