# Curvature Enhanced Data Augmentation for Regression

arXiv: https://arxiv.org/abs/2506.06853 · HTML: https://mlsanity.com/paper/2506.06853/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 85 references that are in the map.
- First posted on arXiv 7 Jun 2025.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation](https://mlsanity.com/paper/1609.08144/) (2016)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition](https://mlsanity.com/paper/1904.08779/) (2019)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Show and Tell: A Neural Image Caption Generator](https://mlsanity.com/paper/1411.4555/) (2014)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [A Survey of Data Augmentation Approaches for NLP](https://mlsanity.com/paper/2105.03075/) (2021)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Development](https://mlsanity.com/paper/2102.09548/) (2021)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Learning Multi-Domain Convolutional Neural Networks for Visual Tracking](https://mlsanity.com/paper/1510.07945/) (2015)
- [Contextual Augmentation: Data Augmentation by Words with Paradigmatic Relations](https://mlsanity.com/paper/1805.06201/) (2018)
- [DeepDTA: Deep Drug-Target Binding Affinity Prediction](https://mlsanity.com/paper/1801.10193/) (2018)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [MixUp as Locally Linear Out-Of-Manifold Regularization](https://mlsanity.com/paper/1809.02499/) (2018)

## Built on by (most cited first, 1 of 1)

- [When the Specification Emerges: Benchmarking Faithfulness Loss in Long-Horizon Coding Agents](https://mlsanity.com/paper/2603.17104/) (2026)

## Abstract (arXiv)

Deep learning models with a large number of parameters, often referred to as over-parameterized models, have achieved exceptional performance across various tasks. Despite concerns about overfitting, these models frequently generalize well to unseen data, thanks to effective regularization techniques, with data augmentation being among the most widely used. While data augmentation has shown great success in classification tasks using label-preserving transformations, its application in regression problems has received less attention. Recently, a novel manifold learning approach for generating synthetic data was proposed, utilizing a first-order approximation of the data manifold. Building on this foundation, we present a theoretical framework and practical tools for approximating and sampling general data manifolds. Furthermore, we introduce the Curvature-Enhanced Manifold Sampling (CEMS) method for regression tasks. CEMS leverages a second-order representation of the data manifold to enable efficient sampling and reconstruction of new data points. Extensive evaluations across multiple datasets and comparisons with state-of-the-art methods demonstrate that CEMS delivers superior performance in both in-distribution and out-of-distribution scenarios, while introducing only minimal computational overhead. Code is available at https://github.com/azencot-group/CEMS.