# Robust Canonicalization through Bootstrapped Data Re-Alignment

arXiv: https://arxiv.org/abs/2510.08178 · HTML: https://mlsanity.com/paper/2510.08178/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [A Kernel Theory of Modern Data Augmentation](https://mlsanity.com/paper/1803.06084/) (2018)
- [The Effects of Regularization and Data Augmentation are Class Dependent](https://mlsanity.com/paper/2204.03632/) (2022)
- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [Inverse Compositional Spatial Transformer Networks](https://mlsanity.com/paper/1612.03897/) (2016)
- [A Canonicalization Perspective on Invariant and Equivariant Learning](https://mlsanity.com/paper/2405.18378/) (2024)
- [In What Ways Are Deep Neural Networks Invariant and How Should We Measure This?](https://mlsanity.com/paper/2210.03773/) (2022)
- [Tilt your Head: Activating the Hidden Spatial-Invariance of Classifiers](https://mlsanity.com/paper/2405.03730/) (2024)
- [Improved Canonicalization for Model Agnostic Equivariance](https://mlsanity.com/paper/2405.14089/) (2024)
- [Deep Learning Pipeline for Automated Visual Moth Monitoring: Insect Localization and Species Classification](https://mlsanity.com/paper/2307.15427/) (2023)
- [Learning Continuous Rotation Canonicalization with Radial Beam Sampling](https://mlsanity.com/paper/2206.10690/) (2022)
- [Rotation-Scale Equivariant Steerable Filters](https://mlsanity.com/paper/2304.04600/) (2023)
- [Geometrically Constrained and Token-Based Probabilistic Spatial Transformers](https://mlsanity.com/paper/2509.11218/) (2025)

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

- [Zero-Shot Test-Time Canonicalization using Out-of-Distribution Scoring](https://mlsanity.com/paper/2606.24178/) (2026)

## Abstract (arXiv)

Fine-grained visual classification (FGVC) tasks, such as insect and bird identification, demand sensitivity to subtle visual cues while remaining robust to spatial transformations. A key challenge is handling geometric biases and noise, such as different orientations and scales of objects. Existing remedies rely on heavy data augmentation, which demands powerful models, or on equivariant architectures, which constrain expressivity and add cost. Canonicalization offers an alternative by shielding such biases from the downstream model. In practice, such functions are often obtained using canonicalization priors, which assume aligned training data. Unfortunately, real-world datasets never fulfill this assumption, causing the obtained canonicalizer to be brittle. We propose a bootstrapping algorithm that iteratively re-aligns training samples by progressively reducing variance and recovering the alignment assumption. We establish convergence guarantees under mild conditions for arbitrary compact groups, and show on four FGVC benchmarks that our method consistently outperforms equivariant, and canonicalization baselines while performing on par with augmentation.