mlsanityData to 7 Oct 2026

A note on the physical interpretation of neural PDE's

arXiv 2502.06739 ↗First posted 10 Feb 2025cs.LG cond-mat.dis-nn physics.comp-phcited by 7

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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.

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

Builds on

3 of 21 references.

References · 3

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 94
  3. 2024A Rapid Review of Clustering Algorithmscited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 5; 2026: 2.

7 papers.

  1. 2025The wall confronting large language modelscited by 8
  2. 2025Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantagecited by 7
  3. 2025The Effect of Label Noise on the Information Content of Neural Representationscited by 2
  4. 2025Is the end of Insight in Sight ?cited by 1
  5. 2025Randomness and signal propagation in physics-informed neural networks (PINNs): A neural PDE perspectivecited by 1
  6. 2026Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learningcited by 0
  7. 2026On the Smallness of the Large Language Models Scaling Exponentscited by 0