LIHE: Linguistic Instance-Split Hyperbolic-Euclidean Framework for Generalized Weakly-Supervised Referring Expression Comprehension

Existing Weakly-Supervised Referring Expression Comprehension (WREC) methods, while effective, are fundamentally limited by a one-to-one mapping assumption, hindering their ability to handle expressions corresponding to zero or multiple targets in realistic scenarios. To bridge this gap, we introduce the Weakly-Supervised Generalized Referring Expression Comprehension task (WGREC), a more practical paradigm that handles expressions with variable numbers of referents. However, extending WREC to WGREC presents two fundamental challenges: supervisory signal ambiguity, where weak image-level supervision is insufficient for training a model to infer the correct number and identity of referents, and semantic representation collapse, where standard Euclidean similarity forces hierarchically-related concepts into non-discriminative clusters, blurring categorical boundaries. To tackle these challenges, we propose a novel WGREC framework named Linguistic Instance-Split Hyperbolic-Euclidean (LIHE), which operates in two stages. The first stage, Referential Decoupling, predicts the number of target objects and decomposes the complex expression into simpler sub-expressions. The second stage, Referent Grounding, then localizes these sub-expressions using HEMix, our innovative hybrid similarity module that synergistically combines the precise alignment capabilities of Euclidean proximity with the hierarchical modeling strengths of hyperbolic geometry. This hybrid approach effectively prevents semantic collapse while preserving fine-grained distinctions between related concepts. Extensive experiments demonstrate LIHE establishes the first effective weakly supervised WGREC baseline on gRefCOCO and Ref-ZOM, while HEMix achieves consistent improvements on standard REC benchmarks, improving IoU@0.5 by up to 2.5\%. The code is available at https://anonymous.4open.science/r/LIHE.