Equivariance-Guided Rotation-Invariant Self-Supervised Learning with p4-Equivariant CNNs

Self-supervised learning (SSL) in computer vision has advanced through joint-embedding methods that learn representations invariant to semantic transformations between image pairs. However, although geometric transformations such as rotation are semantically invariant, learning rotation-invariant representations remains challenging due to the inherently rotation-equivariant nature of object images. Previous methods attempted to improve rotation robustness via equivariant learning, yet a clear performance gap persists between non-rotated and rotated samples. To address these limitations, we propose GIE (Guiding Invariance with Equivariance), a framework that forms rotation-invariant representations guided by the rotation-equivariant structure of images. GIE employs group-equivariant convolutional networks to produce strictly rotation-equivariant feature maps. An equivariance-guided orientation-alignment step then transforms equivariant features into invariant embeddings while preserving discriminative information. This eliminates the need for repeated inferences required in canonicalization, enabling computationally efficient and scalable training within standard SSL frameworks. Experimental results show that across multiple SSL frameworks—including SimCLR, SimSiam, and MoCo v2—GIE significantly improves robustness on rotated data. Notably, it yields up to a 7% gain over the base p4-equivariant CNN and up to a 24% gain over standard ResNet backbones. These results demonstrate the effectiveness of GIE in learning robust, rotation-invariant representations.