@inproceedings{wang-etal-2026-binsgps,
title = "{B}i{NSGPS}: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction",
author = "Wang, Qi and
Wang, Peijie and
Yin, Fei and
Liu, Cheng-Lin",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.174/",
pages = "3660--3680",
ISBN = "979-8-89176-462-0",
abstract = "Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions. Experiments show that BiNSGPS achieves state-of-the-art performance, reaching 90.5{\%} completion accuracy on Geometry3K and 90.1{\%} on PGPS9K, while maintaining 96{\%} step-wise logical coherence to balance capability with mathematical rigor."
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<abstract>Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions. Experiments show that BiNSGPS achieves state-of-the-art performance, reaching 90.5% completion accuracy on Geometry3K and 90.1% on PGPS9K, while maintaining 96% step-wise logical coherence to balance capability with mathematical rigor.</abstract>
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%0 Conference Proceedings
%T BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction
%A Wang, Qi
%A Wang, Peijie
%A Yin, Fei
%A Liu, Cheng-Lin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F wang-etal-2026-binsgps
%X Geometry problem solving poses distinct challenges in artificial intelligence. Existing approaches typically fall into two paradigms: symbolic methods, which exhibit limited adaptability, and neural methods, which are prone to hallucinations. Recent neuro-symbolic hybrids predominantly rely on a unidirectional pipeline where neural outputs are fed into solvers without feedback, making system brittle to early-stage errors. To break this unidirectional bottleneck, we propose BiNSGPS, a framework that establishes Bidirectional Neuro-Symbolic Interaction (BiNS) between a MLLM Adviser and a Symbolic Solver. MLLM Adviser actively incorporates feedback from the symbolic solver to dynamically rectify inconsistent formal representations or propose auxiliary hypotheses, resolving symbolic conflicts and facilitating complex deductions. Experiments show that BiNSGPS achieves state-of-the-art performance, reaching 90.5% completion accuracy on Geometry3K and 90.1% on PGPS9K, while maintaining 96% step-wise logical coherence to balance capability with mathematical rigor.
%U https://aclanthology.org/2026.findings-emnlp.174/
%P 3660-3680
Markdown (Informal)
[BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction](https://aclanthology.org/2026.findings-emnlp.174/) (Wang et al., Findings 2026)
ACL