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

• URL: http://arxiv.org/abs/2510.18218v1
• Date: Tue, 21 Oct 2025 01:52:46 GMT
• Title: DualHash: A Stochastic Primal-Dual Algorithm with Theoretical Guarantee for Deep Hashing
• Authors: Luxuan Li, Xiao Wang, Chunfeng Cui,
• Abstract summary: A fundamental challenge in deep hashing stems from the discrete nature of quantization in generating the codes.<n>We present a primal-composite hashing algorithm, referred as DualHash, that provides rigorous bounds.<n>Three image retrieval databases demonstrate the superior performance of DualHash.
• Score: 6.024178662558234
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Blockwise Stochastic Variance-Reduced Methods with Parallel Speedup for Multi-Block Bilevel Optimization [43.74656748515853]
  Non-stationary multi-block bilevel optimization problems involve $mgg 1$ lower level problems and have important applications in machine learning. We aim to achieve three properties for our algorithm: a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling $I$ samples for each sampled block per-iteration; and (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator.
  arXiv  Detail & Related papers  (2023-05-30T04:10:11Z)
• A One-Sample Decentralized Proximal Algorithm for Non-Convex Stochastic Composite Optimization [10.762749887051546]
  We propose two-time scale algorithms: ProxDAS-A and Proxcal$DASA-GT. Unlike prior work, our algorithms achieve comparable complexity without requiring large batch sizes, more complex per-it operations, or stronger assumptions.
  arXiv  Detail & Related papers  (2023-02-20T05:16:18Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Asymmetric Scalable Cross-modal Hashing [51.309905690367835]
  Cross-modal hashing is a successful method to solve large-scale multimedia retrieval issue. We propose a novel Asymmetric Scalable Cross-Modal Hashing (ASCMH) to address these issues. Our ASCMH outperforms the state-of-the-art cross-modal hashing methods in terms of accuracy and efficiency.
  arXiv  Detail & Related papers  (2022-07-26T04:38:47Z)
• CIMON: Towards High-quality Hash Codes [63.37321228830102]
  We propose a new method named textbfComprehensive stextbfImilarity textbfMining and ctextbfOnsistency leartextbfNing (CIMON) First, we use global refinement and similarity statistical distribution to obtain reliable and smooth guidance. Second, both semantic and contrastive consistency learning are introduced to derive both disturb-invariant and discriminative hash codes.
  arXiv  Detail & Related papers  (2020-10-15T14:47:14Z)
• Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learning [145.54544979467872]
  We propose two single-timescale single-loop algorithms that require only one data point each step. Our results are expressed in a form of simultaneous primal and dual side convergence.
  arXiv  Detail & Related papers  (2020-08-23T20:36:49Z)
• Generative Semantic Hashing Enhanced via Boltzmann Machines [61.688380278649056]
  Existing generative-hashing methods mostly assume a factorized form for the posterior distribution. We propose to employ the distribution of Boltzmann machine as the retrievalal posterior. We show that by effectively modeling correlations among different bits within a hash code, our model can achieve significant performance gains.
  arXiv  Detail & Related papers  (2020-06-16T01:23:39Z)
• Procrustean Orthogonal Sparse Hashing [3.302605292858623]
  We show that insect olfaction is structurally and functionally analogous to sparse hashing. We present a novel method, Procrustean Orthogonal Sparse Hashing (POSH), that unifies these findings. We propose two new methods, Binary OSL and SphericalHash, to address these deficiencies.
  arXiv  Detail & Related papers  (2020-06-08T18:09:33Z)
• Pairwise Supervised Hashing with Bernoulli Variational Auto-Encoder and Self-Control Gradient Estimator [62.26981903551382]
  Variational auto-encoders (VAEs) with binary latent variables provide state-of-the-art performance in terms of precision for document retrieval. We propose a pairwise loss function with discrete latent VAE to reward within-class similarity and between-class dissimilarity for supervised hashing. This new semantic hashing framework achieves superior performance compared to the state-of-the-arts.
  arXiv  Detail & Related papers  (2020-05-21T06:11:33Z)
• Sparse Hashing for Scalable Approximate Model Counting: Theory and Practice [36.8421113576893]
  Given a CNF formula F on n variables, the problem of model counting or #SAT is to compute the number of satisfying assignments of F. Recent years have witnessed a surge of effort towards developing efficient algorithmic techniques.
  arXiv  Detail & Related papers  (2020-04-30T11:17:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.