Poincaré Ideal Prototypes Deep Learning Network for Image Classification

Among various computer vision tasks, such as image classification, few-shot learning, and image retrieval, processing typically occurs in Euclidean and hyperspherical spaces. In prototype-based image classification, category prototypes are typically determined as the average output vectors of their corresponding training samples. This paper introduces the Poincaré Ideal Prototype Deep Learning Network, which aims to place category prototypes uniformly at the boundary of Poincaré without requiring labeled information. Category prototypes are predicted by calculating distances between samples and prototypes. Prototypes are positioned at the boundary of Poincaré, and categories are determined based on distances between samples and prototypes. Because the distance from any point inside Poincaré to its boundary is infinite, the Busemann function is employed to measure this distance. To prevent samples from approaching too close to the boundary during training, a Busemann loss function with a penalty term is introduced. The penalty strengths are adjusted according to the dimensions of the output space. We conclude that output spaces with larger dimensions should incur smaller penalties, whereas those with smaller dimensions require stronger penalties to achieve optimal classification performance. Through extensive experiments with varying settings, we validate the reasonableness of our selected penalty strength. This provides a reference for selecting the appropriate penalty strength for different output spaces in future work.