# Neural network approach to reconstructing spectral functions and complex poles of confined particles

arXiv: https://arxiv.org/abs/2203.03293 · HTML: https://mlsanity.com/paper/2203.03293/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 38 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Spectral Reconstruction with Deep Neural Networks](https://mlsanity.com/paper/1905.04305/) (2019)
- [Automatic differentiation approach for reconstructing spectral functions with neural networks](https://mlsanity.com/paper/2112.06206/) (2021)

## Built on by (most cited first, 1 of 1)

- [Neural Networks Asymptotic Behaviours for the Resolution of Inverse Problems](https://mlsanity.com/paper/2402.09338/) (2024)

## Abstract (arXiv)

Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to solve this problem and has shown promising results, either matching or improving upon the performance of other methods. We generalize this approach by not only reconstructing spectral functions, but also (possible) pairs of complex poles or an infrared (IR) cutoff. We train our network on physically motivated toy functions, examine the reconstruction accuracy and check its robustness to noise. Encouraging results are found on both toy functions and genuine lattice QCD data for the gluon propagator, suggesting that this approach may lead to significant improvements over current state-of-the-art methods.