SimO Loss: Anchor-Free Contrastive Loss for Fine-Grained Supervised Contrastive Learning

We introduce a novel anchor-free contrastive learning (AFCL) method leveraging our proposed Similarity-Orthogonality (SimO) loss. The AFCL method, powered by SimO loss, creates a fiber bundle topological structure in the embedding space, forming class-specific, internally cohesive yet orthogonal neighborhoods. We validate the efficacy of our method on the CIFAR-10 dataset, providing visualizations that demonstrate the impact of SimO loss on the embedding space. Our results illustrate the formation of distinct, orthogonal class neighborhoods, showcasing the method's ability to create well-structured embeddings that balance class separation with intra-class variability. This work opens new avenues for understanding and leveraging the geometric properties of learned representations in various machine learning tasks. The pursuit of effective representation learning (Gidaris et al. (2018); Wu et al. (2018); Oord et al. (2019)) has been a cornerstone of modern machine learning, with contrastive methods emerging as particularly powerful tools in recent years. Despite significant advancements, the field of supervised contrastive learning (Khosla et al. (2021); Balestriero et al. (2023)) continues to grapple with fundamental challenges that impede the development of truly robust and interpretable models.