# EnergyMatch: Energy-based Pseudo-Labeling for Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2206.06359 · HTML: https://mlsanity.com/paper/2206.06359/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 13 Jun 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2101.06329/) (2021)
- [Label Propagation for Deep Semi-supervised Learning](https://mlsanity.com/paper/1904.04717/) (2019)
- [CReST: A Class-Rebalancing Self-Training Framework for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2102.09559/) (2021)
- [Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2007.08844/) (2020)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [ABC: Auxiliary Balanced Classifier for Class-imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2110.10368/) (2021)

## Abstract (arXiv)

Recent state-of-the-art methods in semi-supervised learning (SSL) combine consistency regularization with confidence-based pseudo-labeling. To obtain high-quality pseudo-labels, a high confidence threshold is typically adopted. However, it has been shown that softmax-based confidence scores in deep networks can be arbitrarily high for samples far from the training data, and thus, the pseudo-labels for even high-confidence unlabeled samples may still be unreliable. In this work, we present a new perspective of pseudo-labeling: instead of relying on model confidence, we instead measure whether an unlabeled sample is likely to be "in-distribution"; i.e., close to the current training data. To classify whether an unlabeled sample is "in-distribution" or "out-of-distribution", we adopt the energy score from out-of-distribution detection literature. As training progresses and more unlabeled samples become in-distribution and contribute to training, the combined labeled and pseudo-labeled data can better approximate the true distribution to improve the model. Experiments demonstrate that our energy-based pseudo-labeling method, albeit conceptually simple, significantly outperforms confidence-based methods on imbalanced SSL benchmarks, and achieves competitive performance on class-balanced data. For example, it produces a 4-6% absolute accuracy improvement on CIFAR10-LT when the imbalance ratio is higher than 50. When combined with state-of-the-art long-tailed SSL methods, further improvements are attained.