# Func-R1: Incentivizing Mathematical Function Reasoning in Multimodal Large Language Models

arXiv: https://arxiv.org/abs/2609.14779 · HTML: https://mlsanity.com/paper/2609.14779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 17 of 17)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [InternVL3.5: Advancing Open-Source Multimodal Models in Versatility, Reasoning, and Efficiency](https://mlsanity.com/paper/2508.18265/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [DeepSeek-VL2: Mixture-of-Experts Vision-Language Models for Advanced Multimodal Understanding](https://mlsanity.com/paper/2412.10302/) (2024)
- [GLM-4.5V and GLM-4.1V-Thinking: Towards Versatile Multimodal Reasoning with Scalable Reinforcement Learning](https://mlsanity.com/paper/2507.01006/) (2025)
- [MinerU: An Open-Source Solution for Precise Document Content Extraction](https://mlsanity.com/paper/2409.18839/) (2024)
- [CogVLM2: Visual Language Models for Image and Video Understanding](https://mlsanity.com/paper/2408.16500/) (2024)
- [Soft Adaptive Policy Optimization](https://mlsanity.com/paper/2511.20347/) (2025)
- [WeThink: Toward General-purpose Vision-Language Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2506.07905/) (2025)
- [Math Blind: Failures in Diagram Understanding Undermine Reasoning in MLLMs](https://mlsanity.com/paper/2503.20745/) (2025)
- [Generalizable Geometric Image Caption Synthesis](https://mlsanity.com/paper/2509.15217/) (2025)
- [LiveK12Bench: Have Large Multimodal Models Truly Conquered High School-level Examinations?](https://mlsanity.com/paper/2605.26781/) (2026)

## Abstract (arXiv)

Performing deliberate mathematical reasoning in visual contexts is a hallmark of advanced 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.