Most datasets in computer vision and medical imaging contain inherent symmetries—such as rotations, translations, scalings, or reparameterizations—that influence classification tasks. Traditional neural network pipelines handle these symmetries using data augmentation, which increases both computational cost and environmental impact.
This repository presents a more sustainable and principled alternative based on the geometry of principal fiber bundles. Instead of augmenting datasets, we directly mod out symmetries by constructing a section of the bundle, providing a canonical representative for each orbit under the symmetry group.
We address symmetries arising from:
- Translations
- Rotations
- Scalings
- Reparameterizations
By assigning a canonical representative to each orbit, we remove the need for augmentation and simplify the learning problem.
The method enables the use of simple metrics to measure dissimilarities between objects modulo symmetry, making training more efficient and computationally lighter.
The chosen section of the bundle can be optimized to improve class separation, providing a flexible geometric tool for symmetry-aware learning.
We introduce a 2-parameter family of canonical parameterizations of curves, containing the standard constant-speed parameterization as a special case. This family is interesting in its own right and helps illustrate the geometric principles of the method.
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Main codebase:
https://github.com/GiLonga/Geometric-Learning -
Tutorial notebook (example on a real dataset):
https://github.com/ioanaciuclea/geometric-learning-notebook
The notebook demonstrates an application of the framework to a dataset of object contours.
The dataset used in the notebook is available at the following link (hosted in another repository):
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Sweadish Leaves dataset contours
https://github.com/GiLonga/Geometric-Learning/blob/main/leaves_parameterized.mat -
Flavia_random_rotation.mat
https://github.com/ioanaciuclea/geometric-learning-notebook/blob/main/Flavia_random_rotation.mat
This repository aims to:
- Demonstrate a geometric approach to symmetry-aware learning
- Provide a sustainable alternative to data augmentation
- Offer a framework with applications in computer vision, medical imaging, and related fields
We hope this simple application illustrates the underlying geometric concepts and inspires further exploration of symmetry-informed machine learning.