Geometry problem solving (GPS) poses significant challenges for Multimodal Large Language Models (MLLMs) in diagram comprehension, knowledge application, long-step reasoning, and auxiliary line construction. However, current benchmarks lack fine-grained evaluation for long-step problems necessitating auxiliary construction. To address these limitations, we present GeoLaux, a fine-grained annotated dataset comprising 2186 calculation and proof problems. It features long-step reasoning (with an average solution length of 6.51 steps, maximum of 24 steps) and auxiliary line construction (required in 41.8% of problems). Building on the dataset, we conduct a comprehensive five-dimensional evaluation of 23 leading MLLMs. The evaluation yields three pivotal findings: First, models perform significantly worse on long-step problems compared to short-step ones, with 18 models exhibiting a performance drop of over 50%. Second, it is crucial to enhance models’ understanding, awareness, and proficiency in auxiliary line construction, which is vital for overall geometric reasoning. Third, limited answer hints effectively improve process correctness, whereas explicit answers lead models to neglect intermediate reasoning steps. These findings position GeoLaux both to benchmark MLLMs geometry reasoning abilities and to guide their improvement. Data and code are available at https://github.com/Candice-yu/GeoLaux

Visual Question Generation (VQG) research focuses predominantly on natural images while neglecting the diagram, which is a critical component in educational materials. To meet the needs of pedagogical assessment, we propose the Diagram-Driven Course Questions Generation (DDCQG) task and construct DiagramQG, a comprehensive dataset with 15,720 diagrams and 25,798 questions across 37 subjects and 371 courses. Our approach employs course and input text constraints to generate course-relevant questions about specific diagram elements. We reveal three challenges of DDCQG: domain-specific knowledge requirements across courses, long-tail distribution in course coverage, and high information density in diagrams. To address these, we propose the Hierarchical Knowledge Integration framework (HKI-DDCQG), which utilizes trainable CLIP for identifying relevant diagram patches, leverages frozen vision-language models for knowledge extraction, and generates questions with trainable T5. Experiments demonstrate that HKI-DDCQG outperforms existing models on DiagramQG while maintaining strong generalizability across natural image datasets, establishing a strong baseline for DDCQG.

LLM has achieved impressive performance on multi-modal tasks, which have received ever-increasing research attention. Recent research focuses on improving prediction performance and reliability (e.g., addressing the hallucination problem). They often prepend relevant external knowledge to the input text as an extra prompt. However, these methods would be affected by the noise in the knowledge and the context length limitation of LLM. In our work, we focus on making better use of external knowledge and propose a method to actively extract valuable information in the knowledge to produce the latent vector as a soft prompt, which is then fused with the image embedding to form a knowledge-enhanced context to instruct LLM. The experimental results on knowledge-based VQA benchmarks show that the proposed method enjoys better utilization of external knowledge and helps the model achieve better performance.