Hyperbolic Prototypical Entailment Cones for Image Classification

Non-Euclidean geometries have garnered significant research interest, particularly in their application to Deep Learning. Utilizing specific manifolds as embedding spaces has been shown to enhance neural network representational capabilities by aligning these spaces with the data's latent structure. In this paper, we focus on hyperbolic manifolds and introduce a novel framework, Hyperbolic Prototypical Entailment Cones (HPEC). The core innovation of HPEC lies in utilizing angular relationships, rather than traditional distance metrics, to more effectively capture the similarity between data representations and their corresponding prototypes. This is achieved by leveraging hyperbolic entailment cones, a mathematical construct particularly suited for embedding hierarchical structures in the Poincare' Ball, along with a novel Backclip mechanism. Our experimental results demonstrate that this approach significantly enhances performance in high-dimensional embedding spaces. To substantiate these findings, we evaluate HPEC on four diverse datasets across various embedding dimensions, consistently surpassing state-of-the-art methods in Prototype Learning.