Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning

Ruoran Xu, Haoyu Cheng, Bin Dong, Qiufeng Wang

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• By integrating ontology and topological structures, we developed a Multimodal Formalization Parser to enable cross-modal formalization of geometry. Leveraging this foundational integration, we further designed a Reasoning Engine equipped with formal verification mechanisms via Parse2Reason step. The framework implements automatic formal reasoning.

Singularity-aware Optimization via Randomized Geometric Probing: Towards Stable Non-smooth Optimization

Ruoran Xu, Borong She, Xiaobo Jin, Qiufeng Wang

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• Proposed a geometry-aware paradigm for non-smooth optimization, capturing Clarke subdifferential via random finite difference to quantify local instability and suppress updates. Proposed the LGI metric, a rigorous efficient subdifferential diameter proxy built on randomized directional derivatives. Proved S-Adam converges to Clarke stationary points at $O(1/\sqrt{T})$, offering core theoretical support for singularity-aware optimization.

Omni-Geo: Full-Domain Geometry Benchmark with Multimodal Diagram Generation

Ruoran Xu*, Wending Gao*, Haoyu Cheng*, Qiufeng Wang

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• Proposed Omni-Geo, the first unified benchmark for general geometric intelligence spanning plane, analytic, and solid geometry, built on a standardized Geometric Description Language (GDL) and an SDF-based diagram synthesis engine that produces contamination-free data. Comprising ~23K problems evaluated on 11 state-of-the-art LLMs and MLLMs, Omni-Geo highlights the necessity of a comprehensive, unified benchmark for assessing geometric reasoning.

SDF-AnalyticGeo: Multi-Agent for Analytic Geometry Problem Generation

Ruoran Xu*, Wending Gao*, Qiufeng Wang

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• Proposed SDF-AnalyticGeo, a scalable multi-agent pipeline for generating large-scale, high-quality multimodal analytic geometry problems via three collaborative agents covering problem generation, formalization, and SDF-based figure rendering. The resulting dataset—integrating natural language, standardized geometric images, ground-truth answers, and formal annotations—achieves over 90% geometric consistency and provides a unified benchmark for evaluating MLLMs on analytic geometry reasoning.

PhysElite:Olympic physics competition multimodal benchmark

Leader

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• A large Olympic physics competition multimodal benchmark. We tracked the contestants’ daily practice questions, understood the multimodal problem-solving steps, and analyzed and answered them.