Effective Automated Geometric Problem Solving (AGP) requires a deep integration of visual perception and textual comprehension. To address this, we propose a dual-stream fusion model that injects deep semantic understanding from a Pre-trained Language Model (PLM) into the geometric diagram parsing pipeline. Our core innovation is a Semantic-Guided Cross-Attention (SGCA) mechanism, which uses the global semantic intent of the problem text to direct attention toward key visual primitives. This yields context-enriched visual representations that serve as inputs to a Graph Neural Network (GNN), enabling relational reasoning that is not only perception-driven but also context-aware. By explicitly bridging the semantic gap between text and diagrams, our approach delivers more robust and accurate predictions. To the best of our knowledge, this is the first study to introduce a semantic-guided cross-attention mechanism into geometric diagram parsing, establishing a new paradigm that effectively addresses the cross-modal semantic gap and achieves state-of-the-art performance. This is particularly effective for parsing problems involving geometric symmetries, where textual cues often clarify or define symmetrical relationships not obvious from the diagram alone.

Geometric relation parsing is a prerequisite for automated geometry problem solving, especially when diagram interpretation depends jointly on visual appearance and textual conditions. In this study, we examine a text-conditioned parsing setting derived from PGDP5K and propose a lightweight parser with atomic cue extraction, iterative visual–semantic feedback, and differentiable logic regularization. Because the active high-level labels are derived through a rule-based weak-supervision protocol, the results should be interpreted as parser-level evidence under Ext-PGDP5K rather than proof of general geometric semantic understanding. The nominal label space contains five candidate relations, while the current evaluation focuses on four active relations with positive instances: Intersect, Parallel, Perpendicular, and Bisect. Compared with text-only, image-only, global-fusion, and shuffled-text controls, the proposed parser improves Edge-F1 and Macro-F1, with the clearest gains for Parallel and Perpendicular. Ablations show that the atomic probe is the main source of improvement, while logic regularization and feedback exhibit non-monotonic interactions. Although limited by weak labels, lexical cues, and the absence of downstream solver validation, this study provides a reproducible protocol-aligned testbed for analyzing text-conditioned relation prediction and low-order logic regularization in geometric diagram parsing.