STAGE: Constrained Graph-Phase Refinement for Binary Hashing

Learning binary hash codes for image retrieval requires preserving semantic relationships while enabling independent image encoding. However, jointly refined targets can vary with batch composition or exceed the encoder’s output range, and lower refinement energy does not necessarily yield better retrieval. We propose STAGE, a constrained graph-phase framework that learns an independent hash encoder from jointly refined targets. In its minibatch formulation, a graph-phase teacher combines graph smoothness, semantic supervision, phase separation, and bit decorrelation under a zero-mean constraint. For a fixed graph and energy, learnable per-bit positive-definite spectral operators adapt refinement dynamics while preserving the constrained stationary points. To facilitate target transfer, a fixed-reference extension produces bounded, zero-mean targets, caches them by image identity, and trains the teacher using the student’s ranking loss after a virtual update. We establish mean conservation, conditional energy descent, and a bound relating binary imbalance to quantization error. Experiments on CIFAR-10, CIFAR-100, and VOC 2007 using frozen ResNet-18 features and 8-, 16-, and 32-bit codes show that both formulations achieve the highest mean mAP among the compared methods in all nine settings of their respective protocols. Under the fixed-reference protocol, STAGE improves mean mAP over matched scalar refinement by 0.15–3.91 percentage points. Graph computations are confined to training, retaining independent encoding and standard Hamming search at inference.