# A Mathematics Framework of Artificial Shifted Population Risk and Its Further Understanding Related to Consistency Regularization

arXiv: https://arxiv.org/abs/2502.10723 · HTML: https://mlsanity.com/paper/2502.10723/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Fast AutoAugment](https://mlsanity.com/paper/1905.00397/) (2019)
- [Towards the Generalization of Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2111.00743/) (2021)
- [DADA: Differentiable Automatic Data Augmentation](https://mlsanity.com/paper/2003.03780/) (2020)
- [Data Augmentation Revisited: Rethinking the Distribution Gap between Clean and Augmented Data](https://mlsanity.com/paper/1909.09148/) (2019)
- [Toward Learning Robust and Invariant Representations with Alignment Regularization and Data Augmentation](https://mlsanity.com/paper/2206.01909/) (2022)

## Abstract (arXiv)

Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency regularization term, there is a lack of research on the relationship between them. To address this gap, this paper introduces a more comprehensive mathematical framework for data augmentation. Through this framework, we establish that the expected risk of the shifted population is the sum of the original population risk and a gap term, which can be interpreted as a consistency regularization term. The paper also provides a theoretical understanding of this gap, highlighting its negative effects on the early stages of training. We also propose a method to mitigate these effects. To validate our approach, we conducted experiments using same data augmentation techniques and computing resources under several scenarios, including standard training, out-of-distribution, and imbalanced classification. The results demonstrate that our methods surpass compared methods under all scenarios in terms of generalization ability and convergence stability. We provide our code implementation at the following link: https://github.com/ydlsfhll/ASPR.