We revisit the long-standing ambiguity surrounding the complex pole structure of the $\Lambda (1405)$ resonance by reframing it as a classification problem for convolutional neural networks (CNNs). By training our models to recognize subtle geometric variations in nearly degenerate lineshapes using a targeted differential feature from empirical CLAS data, we establish a data-driven consensus on large inference samples. Our results reveal a robust preference for analytic structures containing two poles on the $[bt]$ sheet, with multi-pole $[2bt,1bb,0tb]$ structure emerging as the dominant pole topology. The inference-guided pole parameter extraction supports a two-state interpretation, characterized by a molecular state manifesting as an isolated pole in the [bt] sheet below the $\bar{K}N$ threshold and a non-molecular state appearing as a pole-shadow pair across the $[bt]$ and $[bb]$ sheets above the $\Sigma \pi$ threshold.