PD-Loss: Proxy-Decidability for Efficient Metric Learning

2025-08-23

AI Summary

Existing deep metric learning methods face a fundamental trade-off: pairwise losses rely on complex sample mining and suffer from slow convergence; proxy-based losses improve efficiency but neglect global distribution structure; while the D-Loss—grounded in the statistical decidability index (d′)—enhances inter-class separability, it demands large batch sizes and incurs high computational overhead. To address these limitations, we propose PD-Loss, the first method that unifies learnable proxy mechanisms with statistical decidability theory within a proxy-based framework, directly optimizing d′ to model the global separability between positive and negative class distributions in an end-to-end manner. PD-Loss significantly reduces batch-size dependency and accelerates training, while achieving state-of-the-art performance on fine-grained classification and face verification benchmarks. It thus strikes an optimal balance among scalability, discriminative power, and computational efficiency.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Deep Metric Learning (DML) aims to learn embedding functions that map semantically similar inputs to proximate points in a metric space while separating dissimilar ones. Existing methods, such as pairwise losses, are hindered by complex sampling requirements and slow convergence. In contrast, proxy-based losses, despite their improved scalability, often fail to optimize global distribution properties. The Decidability-based Loss (D-Loss) addresses this by targeting the decidability index (d') to enhance distribution separability, but its reliance on large mini-batches imposes significant computational constraints. We introduce Proxy-Decidability Loss (PD-Loss), a novel objective that integrates learnable proxies with the statistical framework of d' to optimize embedding spaces efficiently. By estimating genuine and impostor distributions through proxies, PD-Loss combines the computational efficiency of proxy-based methods with the principled separability of D-Loss, offering a scalable approach to distribution-aware DML. Experiments across various tasks, including fine-grained classification and face verification, demonstrate that PD-Loss achieves performance comparable to that of state-of-the-art methods while introducing a new perspective on embedding optimization, with potential for broader applications.

Problem

• Addresses inefficient convergence in deep metric learning
• Overcomes proxy-based losses' global distribution optimization failure
• Reduces computational constraints of decidability-based loss methods

Innovation

• Integrates learnable proxies with statistical decidability index
• Estimates genuine and impostor distributions through proxy representations
• Combines computational efficiency with principled distribution separability