# Artificial Intelligence and Symmetries: Learning, Encoding, and Discovering Structure in Physical Data

arXiv: https://arxiv.org/abs/2602.02351 · HTML: https://mlsanity.com/paper/2602.02351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 2 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Better Latent Spaces for Better Autoencoders](https://mlsanity.com/paper/2104.08291/) (2021)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Symmetry meets AI](https://mlsanity.com/paper/2103.06115/) (2021)
- [Exploring how a Generative AI interprets music](https://mlsanity.com/paper/2308.00015/) (2023)

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

- [Latent Spectroscopy: Posterior Collapse as a Feature](https://mlsanity.com/paper/2605.22691/) (2026)

## Abstract (arXiv)

Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a remarkable ability to extract low-dimensional structure from high-dimensional data through representation learning. This review examines the interplay between these two perspectives, focusing on the extent to which symmetry-induced constraints can be identified, encoded, or diagnosed using machine learning techniques. Rather than emphasizing architectures that enforce known symmetries by construction, we concentrate on data-driven approaches and latent representation learning, with particular attention to variational autoencoders. We discuss how symmetries and conservation laws reduce the intrinsic dimensionality of physical datasets, and how this reduction may manifest itself through self-organization of latent spaces in generative models trained to balance reconstruction and compression. We review recent results, including case studies from simple geometric systems and particle physics processes, and analyze the theoretical and practical limitations of inferring symmetry structure without explicit inductive bias.