@inproceedings{kang-etal-2026-reactivating,
title = "Reactivating Test-Time Scaling for Plane Geometry Problem Solving",
author = "Kang, Xiaoqiang and
Wu, Shengen and
Ning, Maizhen and
Jin, Xiaobo and
Huang, Kaizhu and
Yue, Yutao and
Huang, Xiaowei and
Wang, Qiufeng",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.487/",
pages = "11193--11211",
ISBN = "979-8-89176-459-0",
abstract = "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 a comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8$\times$. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS."
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<abstract>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 a comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8\times. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.</abstract>
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%0 Conference Proceedings
%T Reactivating Test-Time Scaling for Plane Geometry Problem Solving
%A Kang, Xiaoqiang
%A Wu, Shengen
%A Ning, Maizhen
%A Jin, Xiaobo
%A Huang, Kaizhu
%A Yue, Yutao
%A Huang, Xiaowei
%A Wang, Qiufeng
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F kang-etal-2026-reactivating
%X 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 a comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8\times. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.
%U https://aclanthology.org/2026.emnlp-main.487/
%P 11193-11211
Markdown (Informal)
[Reactivating Test-Time Scaling for Plane Geometry Problem Solving](https://aclanthology.org/2026.emnlp-main.487/) (Kang et al., EMNLP 2026)
ACL
- Xiaoqiang Kang, Shengen Wu, Maizhen Ning, Xiaobo Jin, Kaizhu Huang, Yutao Yue, Xiaowei Huang, and Qiufeng Wang. 2026. Reactivating Test-Time Scaling for Plane Geometry Problem Solving. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 11193–11211, Budapest, Hungary. Association for Computational Linguistics.