# X-model: Improving Data Efficiency in Deep Learning with A Minimax Model

arXiv: https://arxiv.org/abs/2110.04572 · HTML: https://mlsanity.com/paper/2110.04572/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 9 Oct 2021.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [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)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [Regularization With Stochastic Transformations and Perturbations for Deep Semi-Supervised Learning](https://mlsanity.com/paper/1606.04586/) (2016)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [Data Distillation: Towards Omni-Supervised Learning](https://mlsanity.com/paper/1712.04440/) (2017)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [Distributional Smoothing with Virtual Adversarial Training](https://mlsanity.com/paper/1507.00677/) (2015)
- [Self-Tuning for Data-Efficient Deep Learning](https://mlsanity.com/paper/2102.12903/) (2021)

## Abstract (arXiv)

To mitigate the burden of data labeling, we aim at improving data efficiency for both classification and regression setups in deep learning. However, the current focus is on classification problems while rare attention has been paid to deep regression, which usually requires more human effort to labeling. Further, due to the intrinsic difference between categorical and continuous label space, the common intuitions for classification, e.g., cluster assumptions or pseudo labeling strategies, cannot be naturally adapted into deep regression. To this end, we first delved into the existing data-efficient methods in deep learning and found that they either encourage invariance to data stochasticity (e.g., consistency regularization under different augmentations) or model stochasticity (e.g., difference penalty for predictions of models with different dropout). To take the power of both worlds, we propose a novel X-model by simultaneously encouraging the invariance to {data stochasticity} and {model stochasticity}. Further, the X-model plays a minimax game between the feature extractor and task-specific heads to further enhance the invariance to model stochasticity. Extensive experiments verify the superiority of the X-model among various tasks, from a single-value prediction task of age estimation to a dense-value prediction task of keypoint localization, a 2D synthetic, and a 3D realistic dataset, as well as a multi-category object recognition task.