通过弱监督互学习，让哈希模型同时捕捉局部与全局信息。

Deep hashing has been widely adopted for large-scale image retrieval, with numerous strategies proposed to optimize hash function learning. Pairwise-based methods are effective in learning hash functions that preserve local similarity relationships, whereas center-based methods typically achieve superior performance by more effectively capturing global data distributions. However, the strength of center-based methods in modeling global structures often comes at the expense of underutilizing important local similarity information. To address this limitation, we propose Mutual Learning for Hashing (MLH), a novel weak-to-strong framework that enhances a center-based hashing branch by transferring knowledge from a weaker pairwise-based branch. MLH consists of two branches: a strong center-based branch and a weaker pairwise-based branch. Through an iterative mutual learning process, the center-based branch leverages local similarity cues learned by the pairwise-based branch. Furthermore, inspired by the mixture-of-experts paradigm, we introduce a novel mixture-of-hash-experts module that enables effective cross-branch interaction, further enhancing the performance of both branches. Extensive experiments demonstrate that MLH consistently outperforms state-of-the-art hashing methods across multiple benchmark datasets.