# A note on the physical interpretation of neural PDE's

arXiv: https://arxiv.org/abs/2502.06739 · HTML: https://mlsanity.com/paper/2502.06739/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 3 of 3)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't](https://mlsanity.com/paper/2009.10713/) (2020)
- [A Rapid Review of Clustering Algorithms](https://mlsanity.com/paper/2401.07389/) (2024)

## Built on by (most cited first, 7 of 7)

- [The wall confronting large language models](https://mlsanity.com/paper/2507.19703/) (2025)
- [Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage](https://mlsanity.com/paper/2507.19861/) (2025)
- [The Effect of Label Noise on the Information Content of Neural Representations](https://mlsanity.com/paper/2510.06401/) (2025)
- [Is the end of Insight in Sight ?](https://mlsanity.com/paper/2505.04627/) (2025)
- [Randomness and signal propagation in physics-informed neural networks (PINNs): A neural PDE perspective](https://mlsanity.com/paper/2509.18131/) (2025)
- [Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning](https://mlsanity.com/paper/2601.00473/) (2026)
- [On the Smallness of the Large Language Models Scaling Exponents](https://mlsanity.com/paper/2606.24504/) (2026)

## Abstract (arXiv)

We highlight a formal and substantial analogy between Machine Learning (ML) algorithms and discrete dynamical systems (DDS) in relaxation form. The analogy offers a transparent interpretation of the weights in terms of physical information-propagation processes and identifies the model function of the forward ML step with the local attractor of the corresponding discrete dynamics. Besides improving the explainability of current ML applications, this analogy may also facilitate the development of a new class ML algorithms with a reduced number of weights.