# Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation

arXiv: https://arxiv.org/abs/1510.02795 · HTML: https://mlsanity.com/paper/1510.02795/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2015.

## Built on by (most cited first, 24 of 24)

- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [Grounding inductive biases in natural images:invariance stems from variations in data](https://mlsanity.com/paper/2106.05121/) (2021)
- [CADDA: Class-wise Automatic Differentiable Data Augmentation for EEG Signals](https://mlsanity.com/paper/2106.13695/) (2021)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Understanding the Detrimental Class-level Effects of Data Augmentation](https://mlsanity.com/paper/2401.01764/) (2023)
- [Relative stability toward diffeomorphisms indicates performance in deep nets](https://mlsanity.com/paper/2105.02468/) (2021)
- [In What Ways Are Deep Neural Networks Invariant and How Should We Measure This?](https://mlsanity.com/paper/2210.03773/) (2022)
- [Sill-Net: Feature Augmentation with Separated Illumination Representation](https://mlsanity.com/paper/2102.03539/) (2021)
- [Trainable Highly-expressive Activation Functions](https://mlsanity.com/paper/2407.07564/) (2024)
- [Whole Brain Segmentation with Full Volume Neural Network](https://mlsanity.com/paper/2110.15601/) (2021)
- [Learning Identity-Preserving Transformations on Data Manifolds](https://mlsanity.com/paper/2106.12096/) (2021)
- [MGAug: Multimodal Geometric Augmentation in Latent Spaces of Image Deformations](https://mlsanity.com/paper/2312.13440/) (2023)
- [Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averaging](https://mlsanity.com/paper/2502.06591/) (2025)
- [Learning Internal Representations of 3D Transformations from 2D Projected Inputs](https://mlsanity.com/paper/2303.17776/) (2023)
- [Slice Imputation: Intermediate Slice Interpolation for Anisotropic 3D Medical Image Segmentation](https://mlsanity.com/paper/2203.10773/) (2022)
- [CLR-GAM: Contrastive Point Cloud Learning with Guided Augmentation and Feature Mapping](https://mlsanity.com/paper/2302.14306/) (2023)
- [Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbits](https://mlsanity.com/paper/2305.19889/) (2023)
- [AutoML Systems For Medical Imaging](https://mlsanity.com/paper/2306.04750/) (2023)
- [Spot the Difference: Detection of Topological Changes via Geometric Alignment](https://mlsanity.com/paper/2106.08233/) (2021)
- [What augmentations are sensitive to hyper-parameters and why?](https://mlsanity.com/paper/2111.03861/) (2021)
- [Learning Transferable Object-Centric Diffeomorphic Transformations for Data Augmentation in Medical Image Segmentation](https://mlsanity.com/paper/2307.13645/) (2023)
- [Class-specific Data Augmentation for Plant Stress Classification](https://mlsanity.com/paper/2406.13081/) (2024)
- [Diffeomorphism-Equivariant Neural Networks](https://mlsanity.com/paper/2602.06695/) (2026)
- [Covariance Shrinkage via Stochastic Interpolation](https://mlsanity.com/paper/2606.07382/) (2026)

## Abstract (arXiv)

Data augmentation is a key element in training high-dimensional models. In this approach, one synthesizes new observations by applying pre-specified transformations to the original training data; e.g.~new images are formed by rotating old ones. Current augmentation schemes, however, rely on manual specification of the applied transformations, making data augmentation an implicit form of feature engineering. With an eye towards true end-to-end learning, we suggest learning the applied transformations on a per-class basis. Particularly, we align image pairs within each class under the assumption that the spatial transformation between images belongs to a large class of diffeomorphisms. We then learn a class-specific probabilistic generative models of the transformations in a Riemannian submanifold of the Lie group of diffeomorphisms. We demonstrate significant performance improvements in training deep neural nets over manually-specified augmentation schemes. Our code and augmented datasets are available online.