# Neural CRNs: A Natural Implementation of Learning in Chemical Reaction Networks

arXiv: https://arxiv.org/abs/2409.00034 · HTML: https://mlsanity.com/paper/2409.00034/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 156 references that are in the map.
- First posted on arXiv 18 Aug 2024.

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

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [A Comparative Study of Reservoir Computing for Temporal Signal Processing](https://mlsanity.com/paper/1401.2224/) (2014)
- [On reaction network implementations of neural networks](https://mlsanity.com/paper/2010.13290/) (2020)
- [Programming and Training Rate-Independent Chemical Reaction Networks](https://mlsanity.com/paper/2109.11422/) (2021)
- [Autonomous Learning of Generative Models with Chemical Reaction Network Ensembles](https://mlsanity.com/paper/2311.00975/) (2023)
- [Learning Two-input Linear and Nonlinear Analog Functions with a Simple Chemical System](https://mlsanity.com/paper/1404.0427/) (2014)
- [From Electric Circuits to Chemical Networks](https://mlsanity.com/paper/1812.03308/) (2018)

## Abstract (arXiv)

Molecular circuits capable of autonomous learning could unlock novel applications in fields such as bioengineering and synthetic biology. To this end, existing chemical implementations of neural computing have mainly relied on emulating discrete-layered neural architectures using steady-state computations of mass action kinetics. In contrast, we propose an alternative dynamical systems-based approach in which neural computations are modeled as the time evolution of molecular concentrations. The analog nature of our framework naturally aligns with chemical kinetics-based computation, leading to more compact circuits. We present the advantages of our framework through three key demonstrations. First, we assemble an end-to-end supervised learning pipeline using only two sequential phases, the minimum required number for supervised learning. Then, we show (through appropriate simplifications) that both linear and nonlinear modeling circuits can be implemented solely using unimolecular and bimolecular reactions, avoiding the complexities of higher-order chemistries. Finally, we demonstrate that first-order gradient approximations can be natively incorporated into the framework, enabling nonlinear models to scale linearly rather than combinatorially with input dimensionality. All the circuit constructions are validated through training and inference simulations across various regression and classification tasks. Our work presents a viable pathway toward embedding learning behaviors in synthetic biochemical systems.