Fig. 2: Classification performance and analysis of the proposed MESEL and its four basis losses.

a AUPRC distribution of sigmoid, softmax, concurrent softmax, and local softmax. In our multi-label classification task, the performance of softmax is far inferior to that of sigmoid, and the performance of concurrent softmax gradually improves as the parameter \({\rm{\tau }}\) increases from 1 to 17. The classification performance of local softmax reaches the level of the baseline loss sigmoid in macro AUPRC. b Bland-Altman plots for sigmoid vs. local softmax, and both of them do not have an overwhelming advantage over each other in micro AUPRC across all labels, with differences even exceeding 20% in some classes. c AUPRC distribution of sigmoid (S), symbiotic sigmoid (SS), local softmax (LS), and symbiotic local softmax (SLS), and their classification performance is at an akin level with no significant statistical difference in macro AUPRC. d Two Bland-Altman plots, one for S vs. SS and the other for LS vs. SLS, and both of two plots show that the losses to be compared differ significantly in micro AUPRC across all labels. e AUPRC distribution of 254 labels from 12 “good but different” losses with yellow background, and the ensemble performance of MESEL in bold black line. f Comparison of private backbone and shared backbone schemes on AUPRC. The private backbone scheme requires 12 models to be trained, which is worse in terms of computational resources but results in better performance. The shared backbone has only one model, making it easy to train and requires less computational resources, but produces worse performance.