DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing

Fuente: arXiv
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Main Authors: Li, Luxuan, Wang, Xiao, Cui, Chunfeng
Format: Preprint
Published: 2025
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author Li, Luxuan
Wang, Xiao
Cui, Chunfeng
author_facet Li, Luxuan
Wang, Xiao
Cui, Chunfeng
contents Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes. W-type regularizations, such as $||z|-1|$, have been proven effective as they encourage variables toward binary values. However, existing methods often directly optimize these regularizations without convergence guarantees. While proximal gradient methods offer a promising solution, the coupling between W-type regularizers and neural network outputs results in composite forms that generally lack closed-form proximal solutions. In this paper, we present a stochastic primal-dual hashing algorithm, referred to as DualHash, that provides rigorous complexity bounds. Using Fenchel duality, we partially transform the nonconvex W-type regularization optimization into the dual space, which results in a proximal operator that admits closed-form solutions. We derive two algorithm instances: a momentum-accelerated version with $\mathcal{O}(\varepsilon^{-4})$ complexity and an improved $\mathcal{O}(\varepsilon^{-3})$ version using variance reduction. Experiments on three image retrieval databases demonstrate the superior performance of DualHash.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18218
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing
Li, Luxuan
Wang, Xiao
Cui, Chunfeng
Optimization and Control
Computer Vision and Pattern Recognition
Deep hashing converts high-dimensional feature vectors into compact binary codes, enabling efficient large-scale retrieval. A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes. W-type regularizations, such as $||z|-1|$, have been proven effective as they encourage variables toward binary values. However, existing methods often directly optimize these regularizations without convergence guarantees. While proximal gradient methods offer a promising solution, the coupling between W-type regularizers and neural network outputs results in composite forms that generally lack closed-form proximal solutions. In this paper, we present a stochastic primal-dual hashing algorithm, referred to as DualHash, that provides rigorous complexity bounds. Using Fenchel duality, we partially transform the nonconvex W-type regularization optimization into the dual space, which results in a proximal operator that admits closed-form solutions. We derive two algorithm instances: a momentum-accelerated version with $\mathcal{O}(\varepsilon^{-4})$ complexity and an improved $\mathcal{O}(\varepsilon^{-3})$ version using variance reduction. Experiments on three image retrieval databases demonstrate the superior performance of DualHash.
title DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing
topic Optimization and Control
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2510.18218