# Deep Hashing via Householder Quantization

arXiv: https://arxiv.org/abs/2311.04207 · HTML: https://mlsanity.com/paper/2311.04207/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 7 Nov 2023.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Proxy Anchor Loss for Deep Metric Learning](https://mlsanity.com/paper/2003.13911/) (2020)
- [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)
- [Efficient Riemannian Optimization on the Stiefel Manifold via the Cayley Transform](https://mlsanity.com/paper/2002.01113/) (2020)
- [Trivializations for Gradient-Based Optimization on Manifolds](https://mlsanity.com/paper/1909.09501/) (2019)
- [Central Similarity Quantization for Efficient Image and Video Retrieval](https://mlsanity.com/paper/1908.00347/) (2019)
- [Feature Learning based Deep Supervised Hashing with Pairwise Labels](https://mlsanity.com/paper/1511.03855/) (2015)
- [A Survey on Deep Hashing Methods](https://mlsanity.com/paper/2003.03369/) (2020)
- [Simultaneous Feature Learning and Hash Coding with Deep Neural Networks](https://mlsanity.com/paper/1504.03410/) (2015)
- [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)
- [A Survey on Locality Sensitive Hashing Algorithms and their Applications](https://mlsanity.com/paper/2102.08942/) (2021)
- [Deep Supervised Discrete Hashing](https://mlsanity.com/paper/1705.10999/) (2017)
- [Asymmetric Deep Supervised Hashing](https://mlsanity.com/paper/1707.08325/) (2017)
- [Beyond Locality-Sensitive Hashing](https://mlsanity.com/paper/1306.1547/) (2013)
- [One Loss for Quantization: Deep Hashing with Discrete Wasserstein Distributional Matching](https://mlsanity.com/paper/2205.15721/) (2022)
- [What if Neural Networks had SVDs?](https://mlsanity.com/paper/2009.13977/) (2020)
- [Deep Priority Hashing](https://mlsanity.com/paper/1809.01238/) (2018)
- [HyP2 Loss: Beyond Hypersphere Metric Space for Multi-label Image Retrieval](https://mlsanity.com/paper/2208.06866/) (2022)

## Built on by (most cited first, 2 of 2)

- [Leveraging High-Resolution Features for Improved Deep Hashing-based Image Retrieval](https://mlsanity.com/paper/2403.13747/) (2024)
- [Sign-Symmetry Learning Rules are Robust Fine-Tuners](https://mlsanity.com/paper/2502.05925/) (2025)

## Abstract (arXiv)

Hashing is at the heart of large-scale image similarity search, and recent methods have been substantially improved through deep learning techniques. Such algorithms typically learn continuous embeddings of the data. To avoid a subsequent costly binarization step, a common solution is to employ loss functions that combine a similarity learning term (to ensure similar images are grouped to nearby embeddings) and a quantization penalty term (to ensure that the embedding entries are close to binarized entries, e.g., -1 or 1). Still, the interaction between these two terms can make learning harder and the embeddings worse. We propose an alternative quantization strategy that decomposes the learning problem in two stages: first, perform similarity learning over the embedding space with no quantization; second, find an optimal orthogonal transformation of the embeddings so each coordinate of the embedding is close to its sign, and then quantize the transformed embedding through the sign function. In the second step, we parametrize orthogonal transformations using Householder matrices to efficiently leverage stochastic gradient descent. Since similarity measures are usually invariant under orthogonal transformations, this quantization strategy comes at no cost in terms of performance. The resulting algorithm is unsupervised, fast, hyperparameter-free and can be run on top of any existing deep hashing or metric learning algorithm. We provide extensive experimental results showing that this approach leads to state-of-the-art performance on widely used image datasets, and, unlike other quantization strategies, brings consistent improvements in performance to existing deep hashing algorithms.