# A Consistent Lebesgue Measure for Multi-label Learning

arXiv: https://arxiv.org/abs/2402.00324 · HTML: https://mlsanity.com/paper/2402.00324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 46 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Contrastive Audio-Visual Masked Autoencoder](https://mlsanity.com/paper/2210.07839/) (2022)
- [The Emerging Trends of Multi-Label Learning](https://mlsanity.com/paper/2011.11197/) (2020)
- [Cross-Modality Attention with Semantic Graph Embedding for Multi-Label Classification](https://mlsanity.com/paper/1912.07872/) (2019)
- [Multi-Label Classification with Label Graph Superimposing](https://mlsanity.com/paper/1911.09243/) (2019)
- [Disentangled Variational Autoencoder based Multi-Label Classification with Covariance-Aware Multivariate Probit Model](https://mlsanity.com/paper/2007.06126/) (2020)
- [Learning Deep Latent Spaces for Multi-Label Classification](https://mlsanity.com/paper/1707.00418/) (2017)
- [Deep Semantic Dictionary Learning for Multi-label Image Classification](https://mlsanity.com/paper/2012.12509/) (2020)
- [Warm Starting CMA-ES for Hyperparameter Optimization](https://mlsanity.com/paper/2012.06932/) (2020)
- [Multi-label classification: do Hamming loss and subset accuracy really conflict with each other?](https://mlsanity.com/paper/2011.07805/) (2020)
- [Graph Attention Transformer Network for Multi-Label Image Classification](https://mlsanity.com/paper/2203.04049/) (2022)
- [Learning Symbolic Model-Agnostic Loss Functions via Meta-Learning](https://mlsanity.com/paper/2209.08907/) (2022)
- [Explicit Gradient Learning](https://mlsanity.com/paper/2006.08711/) (2020)

## Abstract (arXiv)

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.