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[2601.01874] CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving
Summary
CogFlow introduces a novel framework for visual mathematical problem solving, enhancing perception and reasoning through knowledge internalization, validated by comprehensive experiments.
Why It Matters
This research addresses the limitations of existing multimodal large language models in visual mathematical reasoning. By proposing a structured approach that integrates perception, internalization, and reasoning, it aims to improve the accuracy and reliability of AI in solving complex visual problems, which is crucial for advancements in AI applications in education and beyond.
Key Takeaways
- CogFlow enhances visual mathematical problem solving through a three-stage framework.
- The framework includes a novel Knowledge Internalization Reward model to improve reasoning.
- A new dataset, MathCog, with over 120K annotations supports model training.
- Experiments validate CogFlow's superiority over existing benchmarks.
- The approach aims to prevent models from relying on visually ungrounded reasoning.
Computer Science > Computer Vision and Pattern Recognition arXiv:2601.01874 (cs) [Submitted on 5 Jan 2026 (v1), last revised 24 Feb 2026 (this version, v3)] Title:CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving Authors:Shuhang Chen, Yunqiu Xu, Junjie Xie, Aojun Lu, Tao Feng, Zeying Huang, Ning Zhang, Yi Sun, Yi Yang, Hangjie Yuan View a PDF of the paper titled CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving, by Shuhang Chen and 9 other authors View PDF HTML (experimental) Abstract:Despite significant progress, multimodal large language models continue to struggle with visual mathematical problem solving. Some recent works recognize that visual perception is a bottleneck in visual mathematical reasoning, but their solutions are limited to improving the extraction and interpretation of visual inputs. Notably, they all ignore the key issue of whether the extracted visual cues are faithfully integrated and properly utilized in subsequent reasoning. Motivated by this, we present CogFlow, a novel cognitive-inspired three-stage framework that incorporates a knowledge internalization stage, explicitly simulating the hierarchical flow of human reasoning: perception$\Rightarrow$internalization$\Rightarrow$reasoning. In line with this hierarchical flow, we holistically enhance all its stages. We devise Synergistic Visual Rewards to boost perception...
