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OTMatch: Improving Semi-Supervised Learning with Optimal Transport

Zhiquan Tan, Kaipeng Zheng, Weiran Huang

TL;DR

OTMatch tackles the overconfidence problem in pseudo-labeling for semi-supervised learning by introducing an optimal transport loss that encodes inter-class semantic relationships. By bootstrapping the transport cost from the model's learning dynamics and using a teacher–student EMA framework with dual augmentations, OTMatch aligns semantic distributions between predictions and pseudo-labels, improving robustness especially with scarce labeled data. Empirically, OTMatch delivers state-of-the-art or competitive gains on vision benchmarks (CIFAR-10/100, STL-10, ImageNet) and multilingual NLP datasets, with a low computational overhead of $O(K)$ for the OT term and effective integration with existing SSL methods. The approach advances semi-supervised learning by treating class relations as a learnable, data-driven regularizer and paves the way for broader use of OT-based semantic distribution matching in self-supervised and multi-modal settings.

Abstract

Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning image predictions with specific classes generated through self-training techniques, thereby neglecting the inherent relationships that exist within these classes. In this paper, we present a new approach called OTMatch, which leverages semantic relationships among classes by employing an optimal transport loss function to match distributions. We conduct experiments on many standard vision and language datasets. The empirical results show improvements in our method above baseline, this demonstrates the effectiveness and superiority of our approach in harnessing semantic relationships to enhance learning performance in a semi-supervised setting.

OTMatch: Improving Semi-Supervised Learning with Optimal Transport

TL;DR

OTMatch tackles the overconfidence problem in pseudo-labeling for semi-supervised learning by introducing an optimal transport loss that encodes inter-class semantic relationships. By bootstrapping the transport cost from the model's learning dynamics and using a teacher–student EMA framework with dual augmentations, OTMatch aligns semantic distributions between predictions and pseudo-labels, improving robustness especially with scarce labeled data. Empirically, OTMatch delivers state-of-the-art or competitive gains on vision benchmarks (CIFAR-10/100, STL-10, ImageNet) and multilingual NLP datasets, with a low computational overhead of for the OT term and effective integration with existing SSL methods. The approach advances semi-supervised learning by treating class relations as a learnable, data-driven regularizer and paves the way for broader use of OT-based semantic distribution matching in self-supervised and multi-modal settings.

Abstract

Semi-supervised learning has made remarkable strides by effectively utilizing a limited amount of labeled data while capitalizing on the abundant information present in unlabeled data. However, current algorithms often prioritize aligning image predictions with specific classes generated through self-training techniques, thereby neglecting the inherent relationships that exist within these classes. In this paper, we present a new approach called OTMatch, which leverages semantic relationships among classes by employing an optimal transport loss function to match distributions. We conduct experiments on many standard vision and language datasets. The empirical results show improvements in our method above baseline, this demonstrates the effectiveness and superiority of our approach in harnessing semantic relationships to enhance learning performance in a semi-supervised setting.
Paper Structure (23 sections, 2 theorems, 27 equations, 2 figures, 6 tables, 1 algorithm)

This paper contains 23 sections, 2 theorems, 27 equations, 2 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary
  4. Problem setting and notations
  5. Optimal transport
  6. Understanding FreeMatch via Optimal Transport
  7. OTMatch: Improving Semi-Supervised Learning with Optimal Transport
  8. Experiments
  9. Setup
  10. Results
  11. Performance improvements.
  12. Analysis
  13. Conclusion
  14. More on proofs
  15. Proof of lemma \ref{['mean lemma']}
  16. ...and 8 more sections

Key Result

Lemma 4.2

$\frac{\sum^{m}_{i=1} s_i}{m}$ is the unique solution of the optimization problem: where the underlying cost is the square of $l^2$ distance.

Figures (2)

  • Figure 1: To obtain a pseudo-label, a model is fed with a weakly augmented image. Then, the model predicts the probability of a strongly augmented version of the same image. The loss includes cross-entropy and optimal transport loss, which considers the probability and pseudo-label. The cost used in optimal transport is adjusted based on the model's classification head weight.
  • Figure 2: Hierarchical clustering results of the learned cost matrix on CIFAR-10.

Theorems & Definitions (5)

  • Definition 4.1
  • Lemma 4.2
  • Lemma 5.1
  • proof
  • proof