# Symmetry-Based Representations for Artificial and Biological General Intelligence

arXiv: https://arxiv.org/abs/2203.09250 · HTML: https://mlsanity.com/paper/2203.09250/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 81 of its 192 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 30 of 81)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Rotation Equivariant CNNs for Digital Pathology](https://mlsanity.com/paper/1806.03962/) (2018)
- [Reinforcement Learning with Unsupervised Auxiliary Tasks](https://mlsanity.com/paper/1611.05397/) (2016)
- [Quantifying Generalization in Reinforcement Learning](https://mlsanity.com/paper/1812.02341/) (2018)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)

## Built on by (most cited first, 26 of 26)

- [From Bricks to Bridges: Product of Invariances to Enhance Latent Space Communication](https://mlsanity.com/paper/2310.01211/) (2023)
- [Bispectral Neural Networks](https://mlsanity.com/paper/2209.03416/) (2022)
- [Equivariant Representation Learning via Class-Pose Decomposition](https://mlsanity.com/paper/2207.03116/) (2022)
- [Unsupervised Learning of Equivariant Structure from Sequences](https://mlsanity.com/paper/2210.05972/) (2022)
- [Morphological Symmetries in Robotics](https://mlsanity.com/paper/2402.15552/) (2024)
- [Morphologically Symmetric Reinforcement Learning for Ambidextrous Bimanual Manipulation](https://mlsanity.com/paper/2505.05287/) (2025)
- [Symmetry and Complexity in Object-Centric Deep Active Inference Models](https://mlsanity.com/paper/2304.14493/) (2023)
- [Topological Obstructions and How to Avoid Them](https://mlsanity.com/paper/2312.07529/) (2023)
- [α-TCVAE: On the relationship between Disentanglement and Diversity](https://mlsanity.com/paper/2411.00588/) (2024)
- [Thousand-Brains Systems: Sensorimotor Intelligence for Rapid, Robust Learning and Inference](https://mlsanity.com/paper/2507.04494/) (2025)
- [A Causal Ordering Prior for Unsupervised Representation Learning](https://mlsanity.com/paper/2307.05704/) (2023)
- [Dynamics Harmonic Analysis of Robotic Systems: Application in Data-Driven Koopman Modelling](https://mlsanity.com/paper/2312.07457/) (2023)
- [Infinite dSprites for Disentangled Continual Learning: Separating Memory Edits from Generalization](https://mlsanity.com/paper/2312.16731/) (2023)
- [Algebras of actions in an agent's representations of the world](https://mlsanity.com/paper/2310.01536/) (2023)
- [Representation Learning in a Decomposed Encoder Design for Bio-inspired Hebbian Learning](https://mlsanity.com/paper/2401.08603/) (2023)
- [The Role of Fibration Symmetries in Geometric Deep Learning](https://mlsanity.com/paper/2408.15894/) (2024)
- [The Thousand Brains Theory 2.0: An Extension for the Long-Range Connections of the Neocortical Heterarchy](https://mlsanity.com/paper/2507.05888/) (2025)
- [Spatio-temporally separable non-linear latent factor learning: an application to somatomotor cortex fMRI data](https://mlsanity.com/paper/2205.13640/) (2022)
- [SymmetryLens: Unsupervised Symmetry Learning via Locality and Density Preservation](https://mlsanity.com/paper/2410.05232/) (2024)
- [Symmetry Defense Against CNN Adversarial Perturbation Attacks](https://mlsanity.com/paper/2210.04087/) (2022)
- [Equivariant Representation Learning in the Presence of Stabilizers](https://mlsanity.com/paper/2301.05231/) (2023)
- [Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEs](https://mlsanity.com/paper/2502.03740/) (2025)
- [The Space Between: On Folding, Symmetries and Sampling](https://mlsanity.com/paper/2503.08502/) (2025)
- [Developmental Symmetry-Loss: A Free-Energy Perspective on Brain-Inspired Invariance Learning](https://mlsanity.com/paper/2512.10984/) (2025)
- [Morphologically Equivariant Flow Matching for Bimanual Mobile Manipulation](https://mlsanity.com/paper/2605.12228/) (2026)
- [Twincher: Bijective Representation Learning for Robust Inversion of Continuous Systems](https://mlsanity.com/paper/2605.13470/) (2026)

## Abstract (arXiv)

Biological intelligence is remarkable in its ability to produce complex behaviour in many diverse situations through data efficient, generalisable and transferable skill acquisition. It is believed that learning "good" sensory representations is important for enabling this, however there is little agreement as to what a good representation should look like. In this review article we are going to argue that symmetry transformations are a fundamental principle that can guide our search for what makes a good representation. The idea that there exist transformations (symmetries) that affect some aspects of the system but not others, and their relationship to conserved quantities has become central in modern physics, resulting in a more unified theoretical framework and even ability to predict the existence of new particles. Recently, symmetries have started to gain prominence in machine learning too, resulting in more data efficient and generalisable algorithms that can mimic some of the complex behaviours produced by biological intelligence. Finally, first demonstrations of the importance of symmetry transformations for representation learning in the brain are starting to arise in neuroscience. Taken together, the overwhelming positive effect that symmetries bring to these disciplines suggest that they may be an important general framework that determines the structure of the universe, constrains the nature of natural tasks and consequently shapes both biological and artificial intelligence.