# MANGO: Learning Disentangled Image Transformation Manifolds with Grouped Operators

arXiv: https://arxiv.org/abs/2409.09542 · HTML: https://mlsanity.com/paper/2409.09542/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 14 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information](https://mlsanity.com/paper/2006.12013/) (2020)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Variational Autoencoder with Learned Latent Structure](https://mlsanity.com/paper/2006.10597/) (2020)
- [Fruit recognition from images using deep learning](https://mlsanity.com/paper/1712.00580/) (2017)
- [Representing Closed Transformation Paths in Encoded Network Latent Space](https://mlsanity.com/paper/1912.02644/) (2019)
- [Decomposed Linear Dynamical Systems (dLDS) for learning the latent components of neural dynamics](https://mlsanity.com/paper/2206.02972/) (2022)
- [Disentangling images with Lie group transformations and sparse coding](https://mlsanity.com/paper/2012.12071/) (2020)
- [Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics](https://mlsanity.com/paper/2408.16862/) (2024)
- [Manifold Contrastive Learning with Variational Lie Group Operators](https://mlsanity.com/paper/2306.13544/) (2023)
- [LINOCS: Lookahead Inference of Networked Operators for Continuous Stability](https://mlsanity.com/paper/2404.18267/) (2024)

## Abstract (arXiv)

Learning semantically meaningful image transformations (i.e. rotation, thickness, blur) directly from examples can be a challenging task. Recently, the Manifold Autoencoder (MAE) proposed using a set of Lie group operators to learn image transformations directly from examples. However, this approach has limitations, as the learned operators are not guaranteed to be disentangled and the training routine is prohibitively expensive when scaling up the model. To address these limitations, we propose MANGO (transformation Manifolds with Grouped Operators) for learning disentangled operators that describe image transformations in distinct latent subspaces. Moreover, our approach allows practitioners the ability to define which transformations they aim to model, thus improving the semantic meaning of the learned operators. Through our experiments, we demonstrate that MANGO enables composition of image transformations and introduces a one-phase training routine that leads to a 100x speedup over prior works.