  Multi-label loss functions are usually non-differentiable, requiring
surrogate loss functions for gradient-based optimisation. The consistency of
surrogate loss functions is not proven and is exacerbated by the conflicting
nature of multi-label loss functions. To directly learn from multiple related,
yet potentially conflicting multi-label loss functions, we propose a Consistent
Lebesgue Measure-based Multi-label Learner (CLML) and prove that CLML can
achieve theoretical consistency under a Bayes risk framework. Empirical
evidence supports our theory by demonstrating that: (1) CLML can consistently
achieve state-of-the-art results; (2) the primary performance factor is the
Lebesgue measure design, as CLML optimises a simpler feedforward model without
additional label graph, perturbation-based conditioning, or semantic
embeddings; and (3) an analysis of the results not only distinguishes CLML's
effectiveness but also highlights inconsistencies between the surrogate and the
desired loss functions.
