Understanding Hyperbolic Metric Learning through Hard Negative Sampling

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).

published in Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. 2024

References in corpus (9)

• A Survey on Multi-view Learning
• Learning Representations by Maximizing Mutual Information Across Views
• Demystifying Contrastive Self-Supervised Learning: Invariances, Augmentations and Dataset Biases
• Training Vision Transformers for Image Retrieval
• MixCo: Mix-up Contrastive Learning for Visual Representation
• Rethinking the compositionality of point clouds through regularization in the hyperbolic space
• Self-supervised Pre-training with Hard Examples Improves Visual Representations
• Enhancing Hyperbolic Graph Embeddings via Contrastive Learning
• Hyperbolic Contrastive Learning