发表机构
School of Advanced Technology, Xi’an Jiaotong-Liverpool University; University of Liverpool; The Hong Kong University of Science and Technology (Guangzhou); Hithink Research; Digital Innovation Research Center, Duke Kunshan University（西交利物浦大学先进技术学院; 利物浦大学; 香港科技大学（广州）; 海天瑞声研究院; 昆山杜克大学数字创新研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对平面几何问题求解中测试时缩放失效的问题，提出多轨迹合成、感知增强训练及共识引导多轨迹集成方法，提升了不同模型规模下的几何问题求解性能，且采样成本最高降低8倍。
AI 中文摘要
平面几何问题（PGP）求解已成为多模态推理的关键基准，因为它需要准确的视觉感知和精确的多步骤符号演绎。尽管测试时缩放（TTS）在通用数学推理中表现出显著成功，但它在平面几何的符号程序范式下无法有效缩放。我们确定了两个关键障碍：刚性符号程序导致的推理多样性有限，以及符号演绎前缺乏明确的视觉 grounding。为解决这些问题，我们提出多轨迹合成（MTS），它将每个符号程序转换为异构推理轨迹，包括可执行Python脚本和思维链（CoT）增强变体。我们进一步提出感知增强（PA）训练，它在演绎前将图表解析为结构化语义子句，以及共识引导多轨迹集成（CG-MTE）用于高效自适应推理。在三个几何基准上的实验表明，我们的方法在不同模型规模下始终提升PGP求解性能，且在与通用多模态大语言模型（MLLM）和专用几何求解器的对比中表现强劲。在测试时缩放条件下，CG-MTE达到与高预算自一致性相当的准确率，同时将采样成本降低多达8倍。代码和数据可在本httpsURL公开获取。
英文摘要
Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precise multi-step symbolic deduction. Although test-time scaling (TTS) has demonstrated remarkable success in general mathematical reasoning, it fails to scale effectively under the symbolic-program paradigm for plane geometry. We identify two key obstacles: limited reasoning diversity induced by rigid symbolic programs and insufficient explicit visual grounding before symbolic deduction. To address these issues, we propose Multi-Trace Synthesis (MTS), which converts each symbolic program into heterogeneous reasoning traces, including executable Python scripts and CoT-augmented variants. We further propose Perception-Augmented (PA) training, which parses diagrams into structured semantic clauses before deduction, and Consensus-Guided Multi-Trace Ensemble (CG-MTE) for efficient self-adaptive inference. Experiments on three geometry benchmarks show that our method consistently improves PGP-solving across model scales and achieves strong performance against both general-purpose MLLMs and specialized geometry solvers. Under test-time scaling, CG-MTE achieves comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8x. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.
CommentsAccepted to EMNLP 2026
