CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with
  Noisy Labels
Wanxing Chang Ye Shi Jingya Wang
Learning with noisy labels (LNL) poses a significant challenge in training a
well-generalized model while avoiding overfitting to corrupted labels. Recent
advances have achieved impressive performance by identifying clean labels and
correcting corrupted labels for training. However, the current approaches rely
heavily on the model's predictions and evaluate each sample independently
without considering either the global and local structure of the sample
distribution. These limitations typically result in a suboptimal solution for
the identification and correction processes, which eventually leads to models
overfitting to incorrect labels. In this paper, we propose a novel optimal
transport (OT) formulation, called Curriculum and Structure-aware Optimal
Transport (CSOT). CSOT concurrently considers the inter- and intra-distribution
structure of the samples to construct a robust denoising and relabeling
allocator. During the training process, the allocator incrementally assigns
reliable labels to a fraction of the samples with the highest confidence. These
labels have both global discriminability and local coherence. Notably, CSOT is
a new OT formulation with a nonconvex objective function and curriculum
constraints, so it is not directly compatible with classical OT solvers. Here,
we develop a lightspeed computational method that involves a scaling iteration
within a generalized conditional gradient framework to solve CSOT efficiently.
Extensive experiments demonstrate the superiority of our method over the
current state-of-the-arts in LNL. Code is available at
https://github.com/changwxx/CSOT-for-LNL.