# A Lower Bound of Hash Codes' Performance

arXiv: https://arxiv.org/abs/2210.05899 · HTML: https://mlsanity.com/paper/2210.05899/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 70 references that are in the map.
- First posted on arXiv 12 Oct 2022.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Google Landmarks Dataset v2 -- A Large-Scale Benchmark for Instance-Level Recognition and Retrieval](https://mlsanity.com/paper/2004.01804/) (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)
- [Practical and Optimal LSH for Angular Distance](https://mlsanity.com/paper/1509.02897/) (2015)
- [Central Similarity Quantization for Efficient Image and Video Retrieval](https://mlsanity.com/paper/1908.00347/) (2019)
- [Hash Embeddings for Efficient Word Representations](https://mlsanity.com/paper/1709.03933/) (2017)
- [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)
- [Unified Multivariate Gaussian Mixture for Efficient Neural Image Compression](https://mlsanity.com/paper/2203.10897/) (2022)
- [Supervised Discrete Hashing](https://mlsanity.com/paper/1503.01557/) (2015)
- [Deep Supervised Discrete Hashing](https://mlsanity.com/paper/1705.10999/) (2017)
- [Hashing for Similarity Search: A Survey](https://mlsanity.com/paper/1408.2927/) (2014)
- [Self-Supervised Adversarial Hashing Networks for Cross-Modal Retrieval](https://mlsanity.com/paper/1804.01223/) (2018)
- [DisARM: An Antithetic Gradient Estimator for Binary Latent Variables](https://mlsanity.com/paper/2006.10680/) (2020)
- [Triplet-Based Deep Hashing Network for Cross-Modal Retrieval](https://mlsanity.com/paper/1904.02449/) (2019)
- [Deep Semantic Ranking Based Hashing for Multi-Label Image Retrieval](https://mlsanity.com/paper/1501.06272/) (2015)
- [Stochastic Generative Hashing](https://mlsanity.com/paper/1701.02815/) (2017)
- [Hashing-Accelerated Graph Neural Networks for Link Prediction](https://mlsanity.com/paper/2105.14280/) (2021)
- [One Loss for Quantization: Deep Hashing with Discrete Wasserstein Distributional Matching](https://mlsanity.com/paper/2205.15721/) (2022)
- [Practical Hash Functions for Similarity Estimation and Dimensionality Reduction](https://mlsanity.com/paper/1711.08797/) (2017)
- [Fast Exact Search in Hamming Space with Multi-Index Hashing](https://mlsanity.com/paper/1307.2982/) (2013)
- [Beyond Product Quantization: Deep Progressive Quantization for Image Retrieval](https://mlsanity.com/paper/1906.06698/) (2019)
- [Deep Recurrent Quantization for Generating Sequential Binary Codes](https://mlsanity.com/paper/1906.06699/) (2019)

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

- [COMAE: COMprehensive Attribute Exploration for Zero-shot Hashing](https://mlsanity.com/paper/2402.16424/) (2024)
- [ProS: Prompting-to-simulate Generalized knowledge for Universal Cross-Domain Retrieval](https://mlsanity.com/paper/2312.12478/) (2023)

## Abstract (arXiv)

As a crucial approach for compact representation learning, hashing has achieved great success in effectiveness and efficiency. Numerous heuristic Hamming space metric learning objectives are designed to obtain high-quality hash codes. Nevertheless, a theoretical analysis of criteria for learning good hash codes remains largely unexploited. In this paper, we prove that inter-class distinctiveness and intra-class compactness among hash codes determine the lower bound of hash codes' performance. Promoting these two characteristics could lift the bound and improve hash learning. We then propose a surrogate model to fully exploit the above objective by estimating the posterior of hash codes and controlling it, which results in a low-bias optimization. Extensive experiments reveal the effectiveness of the proposed method. By testing on a series of hash-models, we obtain performance improvements among all of them, with an up to 26.5% increase in mean Average Precision and an up to 20.5% increase in accuracy. Our code is publicly available at https://github.com/VL-Group/LBHash.