SEGA: Shaping Semantic Geometry for Robust Hashing under Noisy Supervision
Yiyang Gu, Bohan Wu, Qinghua Ran, Rong-Cheng Tu, Xiao Luo, Zhiping Xiao, Wei Ju, Dacheng Tao, Ming Zhang
Learning from noisy multi-label supervision remains a central challenge in hashing, where labels are unreliable and outputs are discrete. Prior methods often focus on label denoising or prediction regularization, but pay limited attention to the geometric organization of the representation space, which is especially crucial given the structured nature of hash codes. We introduce  Semantic Geometry Shaping (SEGA), a framework that learns robust hash functions by explicitly sculpting semantic geometry under noise. SEGA organizes embeddings around dynamic class prototypes that serve as semantic anchors and quantify structural consistency. It estimates uncertainty from both energy and structural divergence, then calibrates label supervision using uncertainty-weighted soft targets. To reinforce continuity in sparse or ambiguous regions, SEGA performs MixUp only between semantically similar instances with contrasting uncertainty levels, generating smooth interpolation paths that expand and regularize class boundaries. This closed-loop process aligns supervision, uncertainty, and representation geometry throughout training. We provide theoretical guarantees showing that SEGA reduces semantic misalignment and improves boundary smoothness. Experiments on noisy multi-label hashing benchmarks confirm state-of-the-art robustness, highlighting the importance of semantic geometry refinement in robust hashing.