# Self-Supervised Learning by Curvature Alignment

arXiv: https://arxiv.org/abs/2511.17426 · HTML: https://mlsanity.com/paper/2511.17426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 21 Nov 2025.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Self-Supervised Learning Using Nonlinear Dependence](https://mlsanity.com/paper/2501.18875/) (2025)
- [Kernel VICReg for Self-Supervised Learning in Reproducing Kernel Hilbert Space](https://mlsanity.com/paper/2509.07289/) (2025)
- [SinSim: Sinkhorn-Regularized SimCLR](https://mlsanity.com/paper/2502.10478/) (2025)
- [Anomaly Detection and Prototype Selection Using Polyhedron Curvature](https://mlsanity.com/paper/2004.02137/) (2020)

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

- [On the Geometry of Multimodal Saturation: Riemannian VICReg](https://mlsanity.com/paper/2610.06096/) (2026)

## Abstract (arXiv)

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.