@inproceedings{yin-etal-2026-func,
title = "{F}unc-{R}1: Incentivizing Mathematical Function Reasoning in Multimodal Large Language Models",
author = "Yin, Mingze and
Wang, Xiaohan and
Li, Dian and
Haichao, Yao and
Zhao, Yilin and
Chen, Youjun and
Sinbadliu and
Chen, Jintai and
Zhu, Yiheng and
Hsieh, Chang-Yu and
Pan, Aimin",
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.1906/",
pages = "40616--40632",
ISBN = "979-8-89176-462-0",
abstract = "Performing deliberate mathematical reasoning in visual contexts is a hallmark of expert-level Multimodal Large Language Models (MLLMs) and requires a sophisticated synthesis of perceptual grounding and symbolic logic. However, in the realm of mathematical functions, our investigation reveals a critical *modality interference phenomenon*: even advanced models, while performing textual computational reasoning, tend to disregard or misinterpret essential visual cues. To address this challenge, we propose **Func-R1**, which synergistically harmonizes precise visual perception and rigorous logical reasoning. Concretely, built upon an explicitly decoupled architecture, we employ a hierarchical post-training framework to progressively identify critical visual evidence and conduct in-depth theoretical reasoning. Furthermore, the *Perception-Aligned Theoretic Optimization (PATO)* strategy is proposed to steer policy updating towards internalizing fundamental theoretical properties while dynamically rectifying heterogeneous visual information throughout the reasoning process. Extensive experiments across diverse benchmarks demonstrate that Func-R1 delivers the optimal performance among open-source MLLMs, even surpassing GPT-5 with an 8.4{\%} improvement on MathVerse{'}s function-oriented tasks."
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<abstract>Performing deliberate mathematical reasoning in visual contexts is a hallmark of expert-level Multimodal Large Language Models (MLLMs) and requires a sophisticated synthesis of perceptual grounding and symbolic logic. However, in the realm of mathematical functions, our investigation reveals a critical *modality interference phenomenon*: even advanced models, while performing textual computational reasoning, tend to disregard or misinterpret essential visual cues. To address this challenge, we propose **Func-R1**, which synergistically harmonizes precise visual perception and rigorous logical reasoning. Concretely, built upon an explicitly decoupled architecture, we employ a hierarchical post-training framework to progressively identify critical visual evidence and conduct in-depth theoretical reasoning. Furthermore, the *Perception-Aligned Theoretic Optimization (PATO)* strategy is proposed to steer policy updating towards internalizing fundamental theoretical properties while dynamically rectifying heterogeneous visual information throughout the reasoning process. Extensive experiments across diverse benchmarks demonstrate that Func-R1 delivers the optimal performance among open-source MLLMs, even surpassing GPT-5 with an 8.4% improvement on MathVerse’s function-oriented tasks.</abstract>
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%0 Conference Proceedings
%T Func-R1: Incentivizing Mathematical Function Reasoning in Multimodal Large Language Models
%A Yin, Mingze
%A Wang, Xiaohan
%A Li, Dian
%A Haichao, Yao
%A Zhao, Yilin
%A Chen, Youjun
%A Chen, Jintai
%A Zhu, Yiheng
%A Hsieh, Chang-Yu
%A Pan, Aimin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%A Sinbadliu
%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 yin-etal-2026-func
%X Performing deliberate mathematical reasoning in visual contexts is a hallmark of expert-level Multimodal Large Language Models (MLLMs) and requires a sophisticated synthesis of perceptual grounding and symbolic logic. However, in the realm of mathematical functions, our investigation reveals a critical *modality interference phenomenon*: even advanced models, while performing textual computational reasoning, tend to disregard or misinterpret essential visual cues. To address this challenge, we propose **Func-R1**, which synergistically harmonizes precise visual perception and rigorous logical reasoning. Concretely, built upon an explicitly decoupled architecture, we employ a hierarchical post-training framework to progressively identify critical visual evidence and conduct in-depth theoretical reasoning. Furthermore, the *Perception-Aligned Theoretic Optimization (PATO)* strategy is proposed to steer policy updating towards internalizing fundamental theoretical properties while dynamically rectifying heterogeneous visual information throughout the reasoning process. Extensive experiments across diverse benchmarks demonstrate that Func-R1 delivers the optimal performance among open-source MLLMs, even surpassing GPT-5 with an 8.4% improvement on MathVerse’s function-oriented tasks.
%U https://aclanthology.org/2026.findings-emnlp.1906/
%P 40616-40632
Markdown (Informal)
[Func-R1: Incentivizing Mathematical Function Reasoning in Multimodal Large Language Models](https://aclanthology.org/2026.findings-emnlp.1906/) (Yin et al., Findings 2026)
ACL
- Mingze Yin, Xiaohan Wang, Dian Li, Yao Haichao, Yilin Zhao, Youjun Chen, Sinbadliu, Jintai Chen, Yiheng Zhu, Chang-Yu Hsieh, and Aimin Pan. 2026. Func-R1: Incentivizing Mathematical Function Reasoning in Multimodal Large Language Models. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 40616–40632, Budapest, Hungary. Association for Computational Linguistics.