# Learning Pole Structures of Hadronic States using Predictive Uncertainty Estimation

arXiv: https://arxiv.org/abs/2507.07668 · HTML: https://mlsanity.com/paper/2507.07668/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 63 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 14 of 14)

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- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [CatBoost: gradient boosting with categorical features support](https://mlsanity.com/paper/1810.11363/) (2018)
- [catch22: CAnonical Time-series CHaracteristics](https://mlsanity.com/paper/1901.10200/) (2019)
- [Uncertainty in Gradient Boosting via Ensembles](https://mlsanity.com/paper/2006.10562/) (2020)
- [Highly comparative feature-based time-series classification](https://mlsanity.com/paper/1401.3531/) (2014)
- [Classifier Chains: A Review and Perspectives](https://mlsanity.com/paper/1912.13405/) (2019)

## Abstract (arXiv)

Matching theoretical predictions to experimental data remains a central challenge in hadron spectroscopy. In particular, the identification of new hadronic states is difficult, as exotic signals near threshold can arise from a variety of physical mechanisms. A key diagnostic in this context is the pole structure of the scattering amplitude, but different configurations can produce similar signatures. The mapping between pole configurations and line shapes is especially ambiguous near the mass threshold, where analytic control is limited. In this work, we introduce an uncertainty-aware machine learning approach for classifying pole structures in S-matrix elements. Our method is based on an ensemble of classifier chains that provide both epistemic and aleatoric uncertainty estimates. We apply a rejection criterion based on predictive uncertainty, achieving a validation accuracy of nearly 95% while discarding only a small fraction of high-uncertainty predictions. Trained on synthetic data with known pole structures, the model generalizes to previously unseen experimental data, including enhancements associated with the P_cbarc(4312)^+ state observed by LHCb. In this, we infer a four-pole structure, representing the presence of a genuine compact pentaquark in the presence of a higher channel virtual state pole with non-vanishing width. While evaluated on this particular state, our framework is broadly applicable to other candidate hadronic states and offers a scalable tool for pole structure inference in scattering amplitudes.