# One Loss for Quantization: Deep Hashing with Discrete Wasserstein Distributional Matching

arXiv: https://arxiv.org/abs/2205.15721 · HTML: https://mlsanity.com/paper/2205.15721/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 19 of 19)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [HashNet: Deep Learning to Hash by Continuation](https://mlsanity.com/paper/1702.00758/) (2017)
- [A Survey on Learning to Hash](https://mlsanity.com/paper/1606.00185/) (2016)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Central Similarity Quantization for Efficient Image and Video Retrieval](https://mlsanity.com/paper/1908.00347/) (2019)
- [Distributional Sliced-Wasserstein and Applications to Generative Modeling](https://mlsanity.com/paper/2002.07367/) (2020)
- [One Loss for All: Deep Hashing with a Single Cosine Similarity based Learning Objective](https://mlsanity.com/paper/2109.14449/) (2021)
- [Supervised Discrete Hashing](https://mlsanity.com/paper/1503.01557/) (2015)
- [Deep Supervised Discrete Hashing](https://mlsanity.com/paper/1705.10999/) (2017)
- [DistillHash: Unsupervised Deep Hashing by Distilling Data Pairs](https://mlsanity.com/paper/1905.03465/) (2019)
- [Learning to Hash with Binary Deep Neural Network](https://mlsanity.com/paper/1607.05140/) (2016)
- [Coding for Random Projections](https://mlsanity.com/paper/1308.2218/) (2013)
- [Low-Precision Random Fourier Features for Memory-Constrained Kernel Approximation](https://mlsanity.com/paper/1811.00155/) (2018)
- [Image Generation Via Minimizing Fr'echet Distance in Discriminator Feature Space](https://mlsanity.com/paper/2003.11774/) (2020)
- [Unsupervised Triplet Hashing for Fast Image Retrieval](https://mlsanity.com/paper/1702.08798/) (2017)
- [Binary and Multi-Bit Coding for Stable Random Projections](https://mlsanity.com/paper/1503.06876/) (2015)

## Built on by (most cited first, 9 of 9)

- [Defending Backdoor Attacks on Vision Transformer via Patch Processing](https://mlsanity.com/paper/2206.12381/) (2022)
- [Semantic-Aware Adversarial Training for Reliable Deep Hashing Retrieval](https://mlsanity.com/paper/2310.14637/) (2023)
- [Influence Function Based Second-Order Channel Pruning-Evaluating True Loss Changes For Pruning Is Possible Without Retraining](https://mlsanity.com/paper/2308.06755/) (2023)
- [A Lower Bound of Hash Codes' Performance](https://mlsanity.com/paper/2210.05899/) (2022)
- [Deep Hashing via Householder Quantization](https://mlsanity.com/paper/2311.04207/) (2023)
- [CoopHash: Cooperative Learning of Multipurpose Descriptor and Contrastive Pair Generator via Variational MCMC Teaching for Supervised Image Hashing](https://mlsanity.com/paper/2210.04288/) (2022)
- [Reliable and Efficient Evaluation of Adversarial Robustness for Deep Hashing-Based Retrieval](https://mlsanity.com/paper/2303.12658/) (2023)
- [Bidirectional Knowledge Reconfiguration for Lightweight Point Cloud Analysis](https://mlsanity.com/paper/2310.05125/) (2023)
- [Cross-Domain Diffusion with Progressive Alignment for Efficient Adaptive Retrieval](https://mlsanity.com/paper/2505.13907/) (2025)

## Abstract (arXiv)

Image hashing is a principled approximate nearest neighbor approach to find similar items to a query in a large collection of images. Hashing aims to learn a binary-output function that maps an image to a binary vector. For optimal retrieval performance, producing balanced hash codes with low-quantization error to bridge the gap between the learning stage's continuous relaxation and the inference stage's discrete quantization is important. However, in the existing deep supervised hashing methods, coding balance and low-quantization error are difficult to achieve and involve several losses. We argue that this is because the existing quantization approaches in these methods are heuristically constructed and not effective to achieve these objectives. This paper considers an alternative approach to learning the quantization constraints. The task of learning balanced codes with low quantization error is re-formulated as matching the learned distribution of the continuous codes to a pre-defined discrete, uniform distribution. This is equivalent to minimizing the distance between two distributions. We then propose a computationally efficient distributional distance by leveraging the discrete property of the hash functions. This distributional distance is a valid distance and enjoys lower time and sample complexities. The proposed single-loss quantization objective can be integrated into any existing supervised hashing method to improve code balance and quantization error. Experiments confirm that the proposed approach substantially improves the performance of several representative hashing~methods.