Diffeomorphism-Equivariant Neural Networks
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911427925639168 |
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| author | Oettinger, Josephine Elisabeth Shumaylov, Zakhar Bostelmann, Johannes Lellmann, Jan Schönlieb, Carola-Bibiane |
| author_facet | Oettinger, Josephine Elisabeth Shumaylov, Zakhar Bostelmann, Johannes Lellmann, Jan Schönlieb, Carola-Bibiane |
| contents | Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and averaging-based methods, focus on compact, finite, or low-dimensional groups with linear actions, this work explores how equivariance can be extended to infinite-dimensional groups. We propose a strategy designed to induce diffeomorphism equivariance in pre-trained neural networks via energy-based canonicalisation. Formulating equivariance as an optimisation problem allows us to access the rich toolbox of already established differentiable image registration methods. Empirical results on segmentation and classification tasks confirm that our approach achieves approximate equivariance and generalises to unseen transformations without relying on extensive data augmentation or retraining. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06695 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diffeomorphism-Equivariant Neural Networks Oettinger, Josephine Elisabeth Shumaylov, Zakhar Bostelmann, Johannes Lellmann, Jan Schönlieb, Carola-Bibiane Machine Learning Computer Vision and Pattern Recognition Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While most existing approaches, such as group convolutions and averaging-based methods, focus on compact, finite, or low-dimensional groups with linear actions, this work explores how equivariance can be extended to infinite-dimensional groups. We propose a strategy designed to induce diffeomorphism equivariance in pre-trained neural networks via energy-based canonicalisation. Formulating equivariance as an optimisation problem allows us to access the rich toolbox of already established differentiable image registration methods. Empirical results on segmentation and classification tasks confirm that our approach achieves approximate equivariance and generalises to unseen transformations without relying on extensive data augmentation or retraining. |
| title | Diffeomorphism-Equivariant Neural Networks |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2602.06695 |