This dissertation proposes Guiding Invariance with Equivariance (GIE), a self supervised framework that achieves rotation-robust representation learning by guiding invariance through group-equivariant modeling. Unlike conventional approaches that enforce invariance via data augmentation, GIE learns it by interpreting structured transformations within an exact p4-equivariant CNN backbone. A learnable orientation predictor and a guided alignment mech anism transform equivariant features into invariant embeddings, producing representations that remain discriminative under rotation. Experiments on STL-10, ImageNet-100, MTARSI, and Pascal VOC demonstrate superior ro tation robustness and generalization over prior methods. GIE establishes a unified and efficient approach to geometry-aware self-supervised learning.

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