Teaching to extract spectral densities from lattice correlators to a broad audience of learning-machines

TL;DR

This paper introduces a novel deep-learning method for extracting smeared spectral densities from Euclidean lattice correlators, emphasizing model independence and systematic uncertainty estimation, validated on mock and lattice QCD data.

Contribution

The paper presents a new supervised deep-learning approach with a model-independent training strategy and reliable systematic error estimation for spectral density extraction.

Findings

Validated on mock data and lattice QCD data.

Achieved good agreement with existing HLT method.

Provided a reliable estimate of systematic uncertainties.

Abstract

We present a new supervised deep-learning approach to the problem of the extraction of smeared spectral densities from Euclidean lattice correlators. A distinctive feature of our method is a model-independent training strategy that we implement by parametrizing the training sets over a functional space spanned by Chebyshev polynomials. The other distinctive feature is a reliable estimate of the systematic uncertainties that we achieve by introducing several ensembles of machines, the broad audience of the title. By training an ensemble of machines with the same number of neurons over training sets of fixed dimensions and complexity, we manage to provide a reliable estimate of the systematic errors by studying numerically the asymptotic limits of infinitely large networks and training sets. The method has been validated on a very large set of random mock data and also in the case of lattice QCD data. We extracted the strange-strange connected contribution to the smeared $R$-ratio from a lattice QCD correlator produced by the ETM Collaboration and compared the results of the new method with the ones previously obtained with the HLT method by finding a remarkably good agreement between the two totally unrelated approaches.