@inproceedings{wang-etal-2026-geometryzero,
title = "{G}eometry{Z}ero: Advancing Geometry Solving via Group Contrastive Policy Optimization",
author = "Wang, Yikun and
Wang, Yibin and
Wang, Dianyi and
Peng, Zimian and
Guo, Qipeng and
Tao, Dacheng and
Wang, Jiaqi",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-acl.1392/",
pages = "27948--27963",
ISBN = "979-8-89176-395-1",
abstract = "Recent progress in large language models (LLMs) has boosted mathematical reasoning, yet geometry remains challenging where auxiliary construction is often essential. Prior methods either underperform or depend on very large models (e.g., GPT-4o), making them costly. We argue that reinforcement learning with verifiable rewards (e.g., GRPO) can train smaller models to couple auxiliary construction with solid geometric reasoning. However, naively applying GRPO yields unconditional rewards, encouraging indiscriminate and sometimes harmful constructions. We propose Group Contrastive Policy Optimization (GCPO), an RL framework with two components: (1) Group Contrastive Masking, which assigns positive/negative construction rewards based on contextual utility, and (2) a Length Reward that encourages longer reasoning chains. On top of GCPO, we build GeometryZero, an affordable family of geometry reasoning models that selectively use auxiliary construction. Experiments on Geometry3K and MathVista show GeometryZero consistently outperforms RL baselines (e.g., GRPO, ToRL)."
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%0 Conference Proceedings
%T GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimization
%A Wang, Yikun
%A Wang, Yibin
%A Wang, Dianyi
%A Peng, Zimian
%A Guo, Qipeng
%A Tao, Dacheng
%A Wang, Jiaqi
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F wang-etal-2026-geometryzero
%X Recent progress in large language models (LLMs) has boosted mathematical reasoning, yet geometry remains challenging where auxiliary construction is often essential. Prior methods either underperform or depend on very large models (e.g., GPT-4o), making them costly. We argue that reinforcement learning with verifiable rewards (e.g., GRPO) can train smaller models to couple auxiliary construction with solid geometric reasoning. However, naively applying GRPO yields unconditional rewards, encouraging indiscriminate and sometimes harmful constructions. We propose Group Contrastive Policy Optimization (GCPO), an RL framework with two components: (1) Group Contrastive Masking, which assigns positive/negative construction rewards based on contextual utility, and (2) a Length Reward that encourages longer reasoning chains. On top of GCPO, we build GeometryZero, an affordable family of geometry reasoning models that selectively use auxiliary construction. Experiments on Geometry3K and MathVista show GeometryZero consistently outperforms RL baselines (e.g., GRPO, ToRL).
%U https://aclanthology.org/2026.findings-acl.1392/
%P 27948-27963
Markdown (Informal)
[GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimization](https://aclanthology.org/2026.findings-acl.1392/) (Wang et al., Findings 2026)
ACL
- Yikun Wang, Yibin Wang, Dianyi Wang, Zimian Peng, Qipeng Guo, Dacheng Tao, and Jiaqi Wang. 2026. GeometryZero: Advancing Geometry Solving via Group Contrastive Policy Optimization. In Findings of the Association for Computational Linguistics: ACL 2026, pages 27948–27963, San Diego, California, United States. Association for Computational Linguistics.