Auxiliary Clues Aware’s Geometry Problem Solving

Geometry Problem Solving (GPS) serves as a rigorous touchstone for evaluating the complex reasoning capabilities of Multimodal Large Language Models (MLLMs), particularly when solutions necessitate auxiliary constructions absent in the visual input. However, current approaches face the following challenges: explicit diagramming methods suffer from unstable image generation quality and error cascading, while existing implicit attention mechanisms are restricted to visible elements, failing to perceive the latent auxiliary structures required for deduction. To bridge this gap, we propose AuxCA (Auxiliary-Clues-Aware GRPO), a novel framework that internalizes the capability of auxiliary construction into the model’s reasoning intuition without relying on external tools. Specifically, we introduce Auxiliary Clues Dependency (ACD) to quantify the causal influence of visual cues and integrate it into GRPO via a fine-grained advantage weighting strategy. Complementing this, we incorporate an auxiliary incentive reward to explicitly encourage the model to actively attend to and utilize these geometric elements during reasoning. Extensive experiments demonstrate that our resulting model, AuxCA-8B, significantly outperforms state-of-the-art explicit plotting methods and achieves performance competitive with top-tier proprietary models. Code is available in \url{https://anonymous.4open.science/r/AuxCA-5510}.