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

TL;DR

This paper introduces a novel distributional matching approach for deep hashing that improves code balance and reduces quantization error by aligning learned continuous codes with a predefined discrete distribution, enhancing retrieval accuracy.

Contribution

It reformulates quantization as distributional matching, proposing a single loss that effectively balances codes and minimizes quantization error in deep hashing.

Findings

Significant performance improvements over existing hashing methods.

Efficient distributional distance with lower complexity.

Universal applicability to various supervised hashing models.

Abstract

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.