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

### Submission summary

 As Contributors: Thibault Lechien Preprint link: scipost_202203_00028v1 Code repository: https://github.com/thibaultLe/SpectralANN Data repository: https://github.com/thibaultLe/SpectralANN Date submitted: 2022-03-21 10:59 Submitted by: Lechien, Thibault Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Phenomenology Approach: Computational

### Abstract

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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_202203_00028v1 on 21 March 2022

## Reports on this Submission

### Strengths

1 - Well written
2 - Reproducibility
3 - Useful extension of NN based approaches to the problem of spectral reconstruction

### Weaknesses

1 - Interpretation whether cc poles exist in a propagator
2 - Explanation of chosen parameter ranges
3 - Using the fourth constraint

### Report

The paper is very well written and easily understandable. Particularly, it excels at begin reproducible with easily readable and runnable code.

My major criticism concerns the parameter ranges chosen in (8)-(10), which seem to be rather small. This goes hand in hand with the conclusion that the NN is capable to decide whether cc poles are present in a correlator. The case of no cc poles is only considered as an edge case in the training data. Additionally, the number of cc pole pairs is fixed to three.
For me, it seems inconclusive if the NN can really differentiate the two cases with the current training data.
Another point concerns the fourth constraint (14). For the spectral function of the gluon this constraint has significant predictive power (negative IR) in the absence of cc poles. Unfortunately, after its introduction, the constraint is not referenced again.

From the plots, it seems like $\sigma=0$ is always favored in the reconstruction, but most likely this is not the case in the training data, maybe the authors would be kind enough to comment on this.

### Requested changes

I would suggest adding comments regarding the following two points to the paper:
- Connection between the chosen parameter ranges and if it's sufficient to decide whether cc poles are present
- Discuss the implications and conformity of the fourth constraint with the gluon reconstruction

• validity: good
• significance: good
• originality: good
• clarity: top
• formatting: excellent
• grammar: excellent