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InfoMatch: Entropy Neural Estimation for Semi-Supervised Image Classification

Qi Han, Zhibo Tian, Chengwei Xia, Kun Zhan

TL;DR

This work addresses semi-supervised image classification under limited labels by introducing InfoMatch, an entropy-based framework that jointly optimizes the posterior-entropy upper bound via softmax likelihood and the data-entropy lower bound via mutual information between augmented views. By employing two-view augmentation, pseudo supervision, and CutMix, InfoMatch integrates a dual-entropy perspective with strong regularization to exploit unlabeled data more effectively. The approach delivers consistent improvements across standard SSL benchmarks, notably achieving substantial gains when labels are scarce and outperforming several fully supervised baselines in some settings. This dual-entropy formulation provides a principled, information-theoretic path to better utilize unlabeled data for robust image classification.

Abstract

Semi-supervised image classification, leveraging pseudo supervision and consistency regularization, has demonstrated remarkable success. However, the ongoing challenge lies in fully exploiting the potential of unlabeled data. To address this, we employ information entropy neural estimation to utilize the potential of unlabeled samples. Inspired by contrastive learning, the entropy is estimated by maximizing a lower bound on mutual information across different augmented views. Moreover, we theoretically analyze that the information entropy of the posterior of an image classifier is approximated by maximizing the likelihood function of the softmax predictions. Guided by these insights, we optimize our model from both perspectives to ensure that the predicted probability distribution closely aligns with the ground-truth distribution. Given the theoretical connection to information entropy, we name our method InfoMatch. Through extensive experiments, we show its superior performance. The source code is available at https://github.com/kunzhan/InfoMatch.

InfoMatch: Entropy Neural Estimation for Semi-Supervised Image Classification

TL;DR

This work addresses semi-supervised image classification under limited labels by introducing InfoMatch, an entropy-based framework that jointly optimizes the posterior-entropy upper bound via softmax likelihood and the data-entropy lower bound via mutual information between augmented views. By employing two-view augmentation, pseudo supervision, and CutMix, InfoMatch integrates a dual-entropy perspective with strong regularization to exploit unlabeled data more effectively. The approach delivers consistent improvements across standard SSL benchmarks, notably achieving substantial gains when labels are scarce and outperforming several fully supervised baselines in some settings. This dual-entropy formulation provides a principled, information-theoretic path to better utilize unlabeled data for robust image classification.

Abstract

Semi-supervised image classification, leveraging pseudo supervision and consistency regularization, has demonstrated remarkable success. However, the ongoing challenge lies in fully exploiting the potential of unlabeled data. To address this, we employ information entropy neural estimation to utilize the potential of unlabeled samples. Inspired by contrastive learning, the entropy is estimated by maximizing a lower bound on mutual information across different augmented views. Moreover, we theoretically analyze that the information entropy of the posterior of an image classifier is approximated by maximizing the likelihood function of the softmax predictions. Guided by these insights, we optimize our model from both perspectives to ensure that the predicted probability distribution closely aligns with the ground-truth distribution. Given the theoretical connection to information entropy, we name our method InfoMatch. Through extensive experiments, we show its superior performance. The source code is available at https://github.com/kunzhan/InfoMatch.
Paper Structure (16 sections, 3 theorems, 16 equations, 2 figures, 3 tables, 1 algorithm)

This paper contains 16 sections, 3 theorems, 16 equations, 2 figures, 3 tables, 1 algorithm.

Key Result

Theorem 1

For an i.i.d. finite dataset $({\mathcal{X}},{\mathcal{C}})$, the approximation ${\rm H}({\mathcal{C}}|{\mathcal{X}})\simeq-\ln p({\mathcal{C}}|{\mathcal{X}})$ holds .

Figures (2)

  • Figure 1: Ablation studies on the Cifar-10 dataset with 40 labels.
  • Figure 2: Compare InfoMatch with FixMatch, FlexMatch, and FreeMatch on the CIFAR-10 dataset with 40 labeled data in terms of Top-1 accuracy and utilization of unlabeled data. (a) Top-1 accuracy, and (b) Utilization of unlabeled data.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Lemma 1
  • Lemma 2