# Oracle-Preserving Latent Flows

arXiv: https://arxiv.org/abs/2302.00806 · HTML: https://mlsanity.com/paper/2302.00806/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 30 of 34)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Discovering physical concepts with neural networks](https://mlsanity.com/paper/1807.10300/) (2018)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [The Lie Derivative for Measuring Learned Equivariance](https://mlsanity.com/paper/2210.02984/) (2022)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Detecting Symmetries with Neural Networks](https://mlsanity.com/paper/2003.13679/) (2020)
- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [LieGG: Studying Learned Lie Group Generators](https://mlsanity.com/paper/2210.04345/) (2022)
- [Symmetry Group Equivariant Architectures for Physics](https://mlsanity.com/paper/2203.06153/) (2022)
- [Permutationless Many-Jet Event Reconstruction with Symmetry Preserving Attention Networks](https://mlsanity.com/paper/2010.09206/) (2020)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [SPANet: Generalized Permutationless Set Assignment for Particle Physics using Symmetry Preserving Attention](https://mlsanity.com/paper/2106.03898/) (2021)
- [Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression](https://mlsanity.com/paper/2112.11600/) (2021)
- [Simplifying Polylogarithms with Machine Learning](https://mlsanity.com/paper/2206.04115/) (2022)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Machine Learning Lie Structures & Applications to Physics](https://mlsanity.com/paper/2011.00871/) (2020)
- [Symmetry meets AI](https://mlsanity.com/paper/2103.06115/) (2021)
- [SYMBA: Symbolic Computation of Squared Amplitudes in High Energy Physics with Machine Learning](https://mlsanity.com/paper/2206.08901/) (2022)
- [Toward an AI Physicist for Unsupervised Learning](https://mlsanity.com/paper/1810.10525/) (2018)

## Built on by (most cited first, 5 of 5)

- [Discovering Sparse Representations of Lie Groups with Machine Learning](https://mlsanity.com/paper/2302.05383/) (2023)
- [Accelerated Discovery of Machine-Learned Symmetries: Deriving the Exceptional Lie Groups G2, F4 and E6](https://mlsanity.com/paper/2307.04891/) (2023)
- [Identifying the Group-Theoretic Structure of Machine-Learned Symmetries](https://mlsanity.com/paper/2309.07860/) (2023)
- [A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks](https://mlsanity.com/paper/2311.18672/) (2023)
- [Lie-Equivariant Quantum Graph Neural Networks](https://mlsanity.com/paper/2411.15315/) (2024)

## Abstract (arXiv)

We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset.