Multiple complementary-label learning (MCLL) is a machine learning task that involves learning a classifier from instances with multiple complementary labels (MCLs). MCLs are labels that indicate the incorrect labels of an instance. Previous methods for learning with ambiguous supervised information may not be effective because MCLs only make up a small proportion of all labels. In this paper, we propose MulCo, a simple yet effective framework that uses contrastive learning to enhance the representation capability in MCLL. Contrastive learning involves contrasting semantically similar and dissimilar pairs of instances, with the goal of benefiting from negatives whose ground-truth labels differ from those of anchors. However, it is possible for dissimilar pairs to have the same label due to the random sampling of negatives from inaccurately labeled data. To solve this problem, we design a sifted contrastive loss for MulCo to correct the sampling of same-label negative pairs. We also provide theoretical evidence for the feasibility of the sifted contrastive loss by establishing an upper bound on the ideal contrastive loss. Correspondingly, we develop two progressive solutions using the properties of complementary labels to approximate the ideal contrastive loss through weighting. Our empirical study demonstrates the effectiveness of the proposed method. The code of this paper is available at https://github.com/gaoyi439/MulCo .
Gao et al. (Mon,) studied this question.