MTSSL: Meta-Thresholding Semi-Supervised Learning

2026-07-17

AI Summary

This work addresses the lack of theoretical grounding in setting the pseudo-labeling threshold τ in semi-supervised learning and questions whether an optimal fixed τ is necessary. The authors propose a unified theoretical framework that reveals how τ balances error terms in the unsupervised loss by modulating the quantities of correct and incorrect pseudo-labels. For the first time, τ is modeled as a differentiable, end-to-end trainable parameter. Building on this insight, they introduce a meta-threshold optimization method with a differentiable update strategy, overcoming the limitations of conventional fixed or heuristic thresholding schemes. Extensive experiments demonstrate that model performance remains highly consistent across a wide range of τ values, corroborating the theoretical analysis and highlighting the substantial flexibility in τ selection—offering a new paradigm for designing semi-supervised learning algorithms.

Abstract

A large body of Semi-supervised Learning~(SSL) algorithms encounter the threshold $τ$ to select pseudo-labels. The value of $τ$ across different SSL algorithms can vary depending on the learning perspective, yet they may achieve similar performance. It motivates us to establish a unified theoretical framework to explain the role of $τ$ in SSL. We statistically explained that the unsupervised loss is affected independently by correct and incorrect pseudo-labels, while $τ$ adjusts their numbers to balance the corresponding error term. This inherent trade-off indicates that SSL can reach the same loss with varying $τ$, precise optimal values of $τ$ during training may be unnecessary. With this, we treat $τ$ as an updatable parameter and optimize it via differentiation; the new policy is named \textbf{Meta-Thresholding Semi-Supervised Learning (MTSSL)}. Extensive experiments demonstrate the superior performance of MTSSL. We observe that the accuracy curves of SSL algorithms can overlap completely even when the values of $τ$ differ significantly, which supports our theoretical framework and indicates that the selection of $τ$ can be relaxed in the future design of SSL algorithms.

Problem

• Semi-supervised Learning
• pseudo-labeling
• thresholding
• meta-learning
• theoretical framework

Innovation

• Meta-Thresholding
• Semi-Supervised Learning
• Pseudo-Labeling
• Adaptive Threshold
• Differentiable Optimization