T-REGS: Minimum Spanning Tree Regularization for Self-Supervised Learning
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915779490873344 |
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| author | Mordacq, Julie Loiseaux, David Kalogeiton, Vicky Oudot, Steve |
| author_facet | Mordacq, Julie Loiseaux, David Kalogeiton, Vicky Oudot, Steve |
| contents | Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds. Several experiments on synthetic data and on classical SSL benchmarks validate the effectiveness of our approach at enhancing representation quality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | T-REGS: Minimum Spanning Tree Regularization for Self-Supervised Learning Mordacq, Julie Loiseaux, David Kalogeiton, Vicky Oudot, Steve Machine Learning Computational Geometry Computer Vision and Pattern Recognition Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds. Several experiments on synthetic data and on classical SSL benchmarks validate the effectiveness of our approach at enhancing representation quality. |
| title | T-REGS: Minimum Spanning Tree Regularization for Self-Supervised Learning |
| topic | Machine Learning Computational Geometry Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2510.23484 |