# Tangent-Normal Adversarial Regularization for Semi-supervised Learning

arXiv: https://arxiv.org/abs/1808.06088 · HTML: https://mlsanity.com/paper/1808.06088/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2018.

## Built on by (most cited first, 10 of 10)

- [Unbiased Teacher for Semi-Supervised Object Detection](https://mlsanity.com/paper/2102.09480/) (2021)
- [Robust Semi-Supervised Learning in Open Environments](https://mlsanity.com/paper/2412.18256/) (2024)
- [Learning to Predict Gradients for Semi-Supervised Continual Learning](https://mlsanity.com/paper/2201.09196/) (2022)
- [Semi-Supervised Learning with Pseudo-Negative Labels for Image Classification](https://mlsanity.com/paper/2301.03976/) (2023)
- [When does the student surpass the teacher? Federated Semi-supervised Learning with Teacher-Student EMA](https://mlsanity.com/paper/2301.10114/) (2023)
- [Learning Privacy-Preserving Student Networks via Discriminative-Generative Distillation](https://mlsanity.com/paper/2409.02404/) (2024)
- [Robust Deep Semi-Supervised Learning: A Brief Introduction](https://mlsanity.com/paper/2202.05975/) (2022)
- [Deep Invertible Approximation of Topologically Rich Maps between Manifolds](https://mlsanity.com/paper/2210.00577/) (2022)
- [Training Image Derivatives: Increased Accuracy and Universal Robustness](https://mlsanity.com/paper/2310.14045/) (2023)
- [One-bit Supervision for Image Classification: Problem, Solution, and Beyond](https://mlsanity.com/paper/2311.15225/) (2023)

## Abstract (arXiv)

Compared with standard supervised learning, the key difficulty in semi-supervised learning is how to make full use of the unlabeled data. A recently proposed method, virtual adversarial training (VAT), smartly performs adversarial training without label information to impose a local smoothness on the classifier, which is especially beneficial to semi-supervised learning. In this work, we propose tangent-normal adversarial regularization (TNAR) as an extension of VAT by taking the data manifold into consideration. The proposed TNAR is composed by two complementary parts, the tangent adversarial regularization (TAR) and the normal adversarial regularization (NAR). In TAR, VAT is applied along the tangent space of the data manifold, aiming to enforce local invariance of the classifier on the manifold, while in NAR, VAT is performed on the normal space orthogonal to the tangent space, intending to impose robustness on the classifier against the noise causing the observed data deviating from the underlying data manifold. Demonstrated by experiments on both artificial and practical datasets, our proposed TAR and NAR complement with each other, and jointly outperforms other state-of-the-art methods for semi-supervised learning.