Combined Hyperbolic and Euclidean Soft Triple Loss Beyond the Single Space Deep Metric Learning

2025-10-07

AI Summary

Existing deep metric learning (DML) methods lack proxy-based supervised losses in hyperbolic space, limiting scalability to large-scale data and semantic modeling capability. To address this, we propose the first dual-space joint optimization framework that simultaneously learns in both hyperbolic and Euclidean spaces. Our approach introduces the first hyperbolic proxy loss, coupled with a novel dual-space soft triplet loss and a hyperbolic hierarchical clustering–based regularization strategy—thereby jointly preserving geometric priors and ensuring training stability. The method unifies hyperbolic proxy loss, Euclidean proxy loss, and hierarchical structural constraints into an end-to-end trainable objective. Evaluated on four benchmark datasets, our method achieves state-of-the-art performance, improving average Recall@1 by 3.2% and significantly enhancing optimization convergence stability.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Deep metric learning (DML) aims to learn a neural network mapping data to an embedding space, which can represent semantic similarity between data points. Hyperbolic space is attractive for DML since it can represent richer structures, such as tree structures. DML in hyperbolic space is based on pair-based loss or unsupervised regularization loss. On the other hand, supervised proxy-based losses in hyperbolic space have not been reported yet due to some issues in applying proxy-based losses in a hyperbolic space. However, proxy-based losses are attractive for large-scale datasets since they have less training complexity. To address these, this paper proposes the Combined Hyperbolic and Euclidean Soft Triple (CHEST) loss. CHEST loss is composed of the proxy-based losses in hyperbolic and Euclidean spaces and the regularization loss based on hyperbolic hierarchical clustering. We find that the combination of hyperbolic and Euclidean spaces improves DML accuracy and learning stability for both spaces. Finally, we evaluate the CHEST loss on four benchmark datasets, achieving a new state-of-the-art performance.

Problem

• Developing proxy-based loss functions for hyperbolic space metric learning
• Combining hyperbolic and Euclidean spaces to improve learning stability
• Enhancing deep metric learning accuracy for large-scale datasets

Innovation

• Combined hyperbolic and Euclidean proxy losses
• Added hyperbolic hierarchical clustering regularization
• Hybrid approach improves accuracy and stability