Identifying the nature of near-threshold enhancements is hindered by the limited resolution of experimental data leading to multiple conflicting interpretations. A prominent example of ambiguous line shape is the set of pentaquark signals observed by LHCb in 2019. Some of these signals can be interpreted as hadronic molecule, compact state, virtual state, or due to a kinematical triangle mechanism. In this work, we leverage the model-selection capability of deep neural networks to analyze and identify the nature of the $P_{c\bar{c}}(4457)^+$. We trained a set of deep neural networks using line shapes with enhancements produced by triangle singularities and those produced by nearby poles. The training dataset for the triangle enhancements are generated by using a set of hadrons satisfying the required mass condition. The training line shapes for the pole-based classifications are generated using uniformized independent $S$-matrix poles configured to appear close to the relevant threshold. We found that, despite the presence of experimental uncertainties, the triangle mechanism is ruled out by the experimental data. The results also suggest that the data favor the pole-shadow pair interpretation for the $P_{c\bar{c}}(4457)^+$, which corresponds to a characteristic pole structure involving a resonance in a two-channel scattering system. Our result is consistent with the initial analysis done by LHCb favoring the Breit-Wigner fit over the triangle singularity. The present analysis offers an alternative approach to studying line shapes, supplementing the standard fitting methods.