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.

我们提出了一种基于一致勒贝格测度的多标签学习器（CLML），证明了在贝叶斯风险框架下，CLML 可以实现理论上的一致性。实证证据支持了我们的理论，证明了：（1）CLML 可以始终获得最先进的结果；（2）勒贝格测度的设计是主要的性能因素，因为 CLML 优化了一个简单的前馈模型，而没有额外的标签图、扰动条件或语义嵌入；（3）结果的分析不仅可以区分 CLML 的有效性，还可以凸显代理损失函数和期望损失函数之间的不一致性。