When Does Auxiliary Modality Matter in Solving Geometric Problems? A Comprehensive Study of Textual, Formal, and Visual Modalities

Hyuk Namgoong, Jeesu Jung, Yerim Han, Sangkeun Jung


Abstract
Large Language Models (LLMs) face challenges in integrating linguistic and spatial reasoning, which limits their performance on geometry problems. While prior work has attempted to bridge this gap using diagram parsers with multimodal models, a systematic comparison of how various auxiliary modalities and their combinations affect performance has been lacking. To address this, we present a systematic study of four auxiliary modalities—formal diagram facts (CDL), natural language representations (TCDL), diagram descriptions (DES), and image augmentations (IMG)—on a range of open- and closed-source multimodal LLMs. Our analysis reveals a compelling dichotomy in the effectiveness of these modalities. While formal representations like CDL and TCDL offer a modest performance lift, diagram descriptions (DES) cause a dramatic split: they significantly boost the accuracy of open-source LLMs which often struggle with visual parsing, while often misleading more capable closed-source models and causing a performance drop. This highlights a critical trade-off between augmenting input with helpful information and introducing misleading noise, demonstrating that the efficacy of auxiliary modalities is heavily dependent on the inherent capabilities of the underlying model.
Anthology ID:
2026.eacl-short.4
Volume:
Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 2: Short Papers)
Month:
March
Year:
2026
Address:
Rabat, Morocco
Editors:
Vera Demberg, Kentaro Inui, Lluís Marquez
Venue:
EACL
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
76–92
Language:
URL:
https://aclanthology.org/2026.eacl-short.4/
DOI:
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Cite (ACL):
Hyuk Namgoong, Jeesu Jung, Yerim Han, and Sangkeun Jung. 2026. When Does Auxiliary Modality Matter in Solving Geometric Problems? A Comprehensive Study of Textual, Formal, and Visual Modalities. In Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 2: Short Papers), pages 76–92, Rabat, Morocco. Association for Computational Linguistics.
Cite (Informal):
When Does Auxiliary Modality Matter in Solving Geometric Problems? A Comprehensive Study of Textual, Formal, and Visual Modalities (Namgoong et al., EACL 2026)
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https://aclanthology.org/2026.eacl-short.4.pdf
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