Understanding Hyperbolic Metric Learning through Hard Negative Sampling

TL;DR

This paper explores the benefits of hyperbolic metric learning in computer vision, analyzing its theoretical foundations, comparing it with Euclidean space, and highlighting its connection to hard negative sampling for improved image embeddings.

Contribution

It provides a comprehensive benchmark of hyperbolic versus Euclidean spaces in vision transformers and offers a theoretical explanation for performance gains.

Findings

Hyperbolic space improves metric learning performance.

Hyperbolic metric learning is closely related to hard negative sampling.

Hybrid Euclidean-hyperbolic loss enhances vision transformer results.

Abstract

In recent years, there has been a growing trend of incorporating hyperbolic geometry methods into computer vision. While these methods have achieved state-of-the-art performance on various metric learning tasks using hyperbolic distance measurements, the underlying theoretical analysis supporting this superior performance remains under-exploited. In this study, we investigate the effects of integrating hyperbolic space into metric learning, particularly when training with contrastive loss. We identify a need for a comprehensive comparison between Euclidean and hyperbolic spaces regarding the temperature effect in the contrastive loss within the existing literature. To address this gap, we conduct an extensive investigation to benchmark the results of Vision Transformers (ViTs) using a hybrid objective function that combines loss from Euclidean and hyperbolic spaces. Additionally, we provide a theoretical analysis of the observed performance improvement. We also reveal that hyperbolic metric learning is highly related to hard negative sampling, providing insights for future work. This work will provide valuable data points and experience in understanding hyperbolic image embeddings. To shed more light on problem-solving and encourage further investigation into our approach, our code is available online (https://github.com/YunYunY/HypMix).