  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.
