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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2511.17426 |
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| _version_ | 1866917496613765120 |
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| author | Ghojogh, Benyamin Sepanj, M. Hadi Fieguth, Paul |
| author_facet | Ghojogh, Benyamin Sepanj, M. Hadi Fieguth, Paul |
| contents | Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. While such objectives shape first- and second-order statistics of the representation, they largely ignore the local geometry of the underlying data manifold. In this paper, we introduce CurvSSL, a curvature-regularized self-supervised learning framework, and its RKHS extension, kernel CurvSSL. Our approach retains a standard two-view encoder-projector architecture with a Barlow Twins-style redundancy-reduction loss on projected features, but augments it with a curvature-based regularizer. Each embedding is treated as a vertex whose $k$ nearest neighbors define a discrete curvature score via cosine interactions on the unit hypersphere; in the kernel variant, curvature is computed from a normalized local Gram matrix in an RKHS. These scores are aligned and decorrelated across augmentations by a Barlow-style loss on a curvature-derived matrix, encouraging both view invariance and consistency of local manifold bending. Experiments on MNIST and CIFAR-10 datasets with a ResNet-18 backbone show that curvature-regularized SSL yields competitive or improved linear evaluation performance compared to Barlow Twins and VICReg. Our results indicate that explicitly shaping local geometry is a simple and effective complement to purely statistical SSL regularizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-Supervised Learning by Curvature Alignment Ghojogh, Benyamin Sepanj, M. Hadi Fieguth, Paul Machine Learning Computer Vision and Pattern Recognition Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. While such objectives shape first- and second-order statistics of the representation, they largely ignore the local geometry of the underlying data manifold. In this paper, we introduce CurvSSL, a curvature-regularized self-supervised learning framework, and its RKHS extension, kernel CurvSSL. Our approach retains a standard two-view encoder-projector architecture with a Barlow Twins-style redundancy-reduction loss on projected features, but augments it with a curvature-based regularizer. Each embedding is treated as a vertex whose $k$ nearest neighbors define a discrete curvature score via cosine interactions on the unit hypersphere; in the kernel variant, curvature is computed from a normalized local Gram matrix in an RKHS. These scores are aligned and decorrelated across augmentations by a Barlow-style loss on a curvature-derived matrix, encouraging both view invariance and consistency of local manifold bending. Experiments on MNIST and CIFAR-10 datasets with a ResNet-18 backbone show that curvature-regularized SSL yields competitive or improved linear evaluation performance compared to Barlow Twins and VICReg. Our results indicate that explicitly shaping local geometry is a simple and effective complement to purely statistical SSL regularizers. |
| title | Self-Supervised Learning by Curvature Alignment |
| topic | Machine Learning Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2511.17426 |