# Blind Recovery of Latent Domains via Unsupervised Symmetry Discovery

arXiv: https://arxiv.org/abs/2606.17782 · HTML: https://mlsanity.com/paper/2606.17782/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Meta-Learning Symmetries by Reparameterization](https://mlsanity.com/paper/2007.02933/) (2020)
- [A Survey on Graph Structure Learning: Progress and Opportunities](https://mlsanity.com/paper/2103.03036/) (2021)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Stochastic Pooling for Regularization of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1301.3557/) (2013)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Generative Adversarial Symmetry Discovery](https://mlsanity.com/paper/2302.00236/) (2023)
- [Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Space](https://mlsanity.com/paper/2310.02970/) (2023)
- [LieGG: Studying Learned Lie Group Generators](https://mlsanity.com/paper/2210.04345/) (2022)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Noether Networks: Meta-Learning Useful Conserved Quantities](https://mlsanity.com/paper/2112.03321/) (2021)
- [Neural Estimation of Statistical Divergences](https://mlsanity.com/paper/2110.03652/) (2021)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [A Differential Entropy Estimator for Training Neural Networks](https://mlsanity.com/paper/2202.06618/) (2022)
- [Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks](https://mlsanity.com/paper/2307.11013/) (2023)
- [Unsupervised Learning of Equivariant Structure from Sequences](https://mlsanity.com/paper/2210.05972/) (2022)
- [Symmetry Discovery Beyond Affine Transformations](https://mlsanity.com/paper/2406.03619/) (2024)
- [Neural Fourier Transform: A General Approach to Equivariant Representation Learning](https://mlsanity.com/paper/2305.18484/) (2023)
- [Neural Isometries: Taming Transformations for Equivariant ML](https://mlsanity.com/paper/2405.19296/) (2024)
- [AtlasD: Automatic Local Symmetry Discovery](https://mlsanity.com/paper/2504.10777/) (2025)
- [SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservation](https://mlsanity.com/paper/2410.05232/) (2024)

## Abstract (arXiv)

Primary motivation in blind inverse problems is to recover signals of interest from corrupted observations without knowing the obfuscating mechanism. Blind deconvolution is a prominent approach when the corruption is convolutional, but it is not applicable when general linear transformations obfuscate the domain structure. In this work, we propose an unsupervised framework for recovering latent domains and signals by discovering symmetries of the data distribution. Our framework models observations as linear measurements of signals sampled from a latent random field, and optimizes a shallow group-convolutional network by imposing stationarity and locality regularization at the model output. The model learns a latent symmetry action and an appropriate filter, thereby mapping unstructured observations to a symmetry-based representation that reveals latent signals. Experiments on stochastic processes, Ising models, shuffled and bit-scrambled images, and neural recordings show that the method recovers latent domains and signals from unstructured observations, suggesting symmetry discovery as a new direction for unsupervised structure learning and blind inverse problems.