# Rediscovery of Numerical L"uscher's Formula from the Neural Network

arXiv: https://arxiv.org/abs/2210.02184 · HTML: https://mlsanity.com/paper/2210.02184/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 43 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 5 of 5)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [Machine learning spectral functions in lattice QCD](https://mlsanity.com/paper/2110.13521/) (2021)

## Abstract (arXiv)

We present that by predicting the spectrum in discrete space from the phase shift in continuous space, the neural network can remarkably reproduce the numerical L"uscher's formula to a high precision. The model-independent property of the L"uscher's formula is naturally realized by the generalizability of the neural network. This exhibits the great potential of the neural network to extract model-independent relation between model-dependent quantities, and this data-driven approach could greatly facilitate the discovery of the physical principles underneath the intricate data.