# RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization

arXiv: https://arxiv.org/abs/2505.13289 · HTML: https://mlsanity.com/paper/2505.13289/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 74 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 54)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [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)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Self-supervised Equivariant Attention Mechanism for Weakly Supervised Semantic Segmentation](https://mlsanity.com/paper/2004.04581/) (2020)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [Benchmarking Robustness of 3D Point Cloud Recognition Against Common Corruptions](https://mlsanity.com/paper/2201.12296/) (2022)
- [Meta-Learning Symmetries by Reparameterization](https://mlsanity.com/paper/2007.02933/) (2020)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold](https://mlsanity.com/paper/2106.05965/) (2021)
- [Attentive Group Equivariant Convolutional Networks](https://mlsanity.com/paper/2002.03830/) (2020)
- [Group Equivariant Stand-Alone Self-Attention For Vision](https://mlsanity.com/paper/2010.00977/) (2020)
- [Deforming Autoencoders: Unsupervised Disentangling of Shape and Appearance](https://mlsanity.com/paper/1806.06503/) (2018)
- [Learning Invariances in Neural Networks](https://mlsanity.com/paper/2010.11882/) (2020)

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

- [Neural Field Tokenizations with Hierarchy and Spatial Locality Priors](https://mlsanity.com/paper/2606.08204/) (2026)

## Abstract (arXiv)

Real world data often exhibits unknown, instance-specific symmetries that rarely exactly match a transformation group G fixed a priori. Class-pose decompositions aim to create disentangled representations by factoring inputs into invariant features and a pose g∈ G defined relative to a training-dependent, arbitrary canonical representation. We introduce RECON, a class-pose agnostic canonical orientation normalization that corrects arbitrary canonicals via a simple right translation, yielding natural, data-aligned canonicalizations. This enables (i) unsupervised discovery of instance-specific pose distributions, (ii) detection of out-of-distribution poses and (iii) a plug-and-play test-time canonicalization layer. This layer can be attached on top of any pre-trained model to infuse group invariance, improving its performance without retraining. We validate on images and molecular ensembles, demonstrating accurate symmetry discovery, and matching or outperforming other canonicalizations in downstream classification.