https://shchen233.github.io/cogflow/

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👍 finally and it was practically applied in our product.

\n","updatedAt":"2026-01-07T03:57:52.225Z","author":{"_id":"6343f83791049e1bce85373e","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/1665398834110-noauth.png","fullname":"Zhang ning","name":"pe65374","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":2,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.9884368181228638},"editors":["pe65374"],"editorAvatarUrls":["https://cdn-avatars.huggingface.co/v1/production/uploads/1665398834110-noauth.png"],"reactions":[],"isReport":false}},{"id":"695f09f77e6ede0dd9f43c7b","author":{"_id":"63d3e0e8ff1384ce6c5dd17d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/1674830754237-63d3e0e8ff1384ce6c5dd17d.jpeg","fullname":"Librarian Bot (Bot)","name":"librarian-bot","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":318,"isUserFollowing":false},"createdAt":"2026-01-08T01:35:51.000Z","type":"comment","data":{"edited":false,"hidden":false,"latest":{"raw":"This is an automated message from the [Librarian Bot](https://huggingface.co/librarian-bots). I found the following papers similar to this paper. \n\nThe following papers were recommended by the Semantic Scholar API \n\n* [ViRC: Enhancing Visual Interleaved Mathematical CoT with Reason Chunking](https://huggingface.co/papers/2512.14654) (2025)\n* [More Than the Final Answer: Improving Visual Extraction and Logical Consistency in Vision-Language Models](https://huggingface.co/papers/2512.12487) (2025)\n* [Figure It Out: Improve the Frontier of Reasoning with Executable Visual States](https://huggingface.co/papers/2512.24297) (2025)\n* [Look as You Think: Unifying Reasoning and Visual Evidence Attribution for Verifiable Document RAG via Reinforcement Learning](https://huggingface.co/papers/2511.12003) (2025)\n* [Artemis: Structured Visual Reasoning for Perception Policy Learning](https://huggingface.co/papers/2512.01988) (2025)\n* [Video-R2: Reinforcing Consistent and Grounded Reasoning in Multimodal Language Models](https://huggingface.co/papers/2511.23478) (2025)\n* [Perceptual-Evidence Anchored Reinforced Learning for Multimodal Reasoning](https://huggingface.co/papers/2511.18437) (2025)\n\n\n Please give a thumbs up to this comment if you found it helpful!\n\n If you want recommendations for any Paper on Hugging Face checkout [this](https://huggingface.co/spaces/librarian-bots/recommend_similar_papers) Space\n\n You can directly ask Librarian Bot for paper recommendations by tagging it in a comment: `@librarian-bot recommend`","html":"

This is an automated message from the Librarian Bot. I found the following papers similar to this paper.

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\n","updatedAt":"2026-01-08T01:35:51.972Z","author":{"_id":"63d3e0e8ff1384ce6c5dd17d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/1674830754237-63d3e0e8ff1384ce6c5dd17d.jpeg","fullname":"Librarian Bot (Bot)","name":"librarian-bot","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":318,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.7367777228355408},"editors":["librarian-bot"],"editorAvatarUrls":["https://cdn-avatars.huggingface.co/v1/production/uploads/1674830754237-63d3e0e8ff1384ce6c5dd17d.jpeg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2601.01874","authors":[{"_id":"695cee316aa73bc11f09163b","name":"Shuhang Chen","hidden":false},{"_id":"695cee316aa73bc11f09163c","user":{"_id":"646c77911ee398a4e9404b8b","avatarUrl":"/avatars/05d1ea421dd4f3e2fd47cbe99fc52933.svg","isPro":false,"fullname":"Yunqiu Xu","user":"Yunqiu","type":"user"},"name":"Yunqiu Xu","status":"claimed_verified","statusLastChangedAt":"2026-01-07T09:27:07.129Z","hidden":false},{"_id":"695cee316aa73bc11f09163d","user":{"_id":"693954a41a18936334d1e6c4","avatarUrl":"/avatars/51f2c802e7745fba1ee7e179671b8d2a.svg","isPro":false,"fullname":"Junjie Xie","user":"JJ01X","type":"user"},"name":"Junjie Xie","status":"claimed_verified","statusLastChangedAt":"2026-01-14T09:53:45.626Z","hidden":false},{"_id":"695cee316aa73bc11f09163e","name":"Aojun Lu","hidden":false},{"_id":"695cee316aa73bc11f09163f","name":"Tao Feng","hidden":false},{"_id":"695cee316aa73bc11f091640","name":"Zeying Huang","hidden":false},{"_id":"695cee316aa73bc11f091641","name":"Ning Zhang","hidden":false},{"_id":"695cee316aa73bc11f091642","name":"Yi Sun","hidden":false},{"_id":"695cee316aa73bc11f091643","name":"Yi Yang","hidden":false},{"_id":"695cee316aa73bc11f091644","user":{"_id":"649d54b314afbb10ce2a9eeb","avatarUrl":"/avatars/15c325d8c2273ff63569f23015e98486.svg","isPro":false,"fullname":"Hangjie Yuan","user":"JacobYuan","type":"user"},"name":"Hangjie Yuan","status":"admin_assigned","statusLastChangedAt":"2026-01-07T13:24:05.922Z","hidden":false}],"publishedAt":"2026-01-05T08:02:18.000Z","submittedOnDailyAt":"2026-01-07T01:06:12.554Z","title":"CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving","submittedOnDailyBy":{"_id":"646c77911ee398a4e9404b8b","avatarUrl":"/avatars/05d1ea421dd4f3e2fd47cbe99fc52933.svg","isPro":false,"fullname":"Yunqiu Xu","user":"Yunqiu","type":"user"},"summary":"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: perceptionRightarrowinternalizationRightarrowreasoning. Inline with this hierarchical flow, we holistically enhance all its stages. We devise Synergistic Visual Rewards to boost perception capabilities in parametric and semantic spaces, jointly improving visual information extraction from symbols and diagrams. 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Papers

arxiv:2601.01874

CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving

Published on Jan 5

· Submitted by

Yunqiu Xu on Jan 7

Upvote

Authors:

Yunqiu Xu ,

Junjie Xie ,

Hangjie Yuan

Abstract

Visual mathematical problem solving remains challenging for multimodal large language models, prompting the development of CogFlow, a cognitive-inspired three-stage framework that enhances perception, internalization, and reasoning through synergistic rewards and visual-gated policy optimization.

AI-generated summary

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: perceptionRightarrowinternalizationRightarrowreasoning. Inline with this hierarchical flow, we holistically enhance all its stages. We devise Synergistic Visual Rewards to boost perception capabilities in parametric and semantic spaces, jointly improving visual information extraction from symbols and diagrams. To guarantee faithful integration of extracted visual cues into subsequent reasoning, we introduce a Knowledge Internalization Reward model in the internalization stage, bridging perception and reasoning. Moreover, we design a Visual-Gated Policy Optimization algorithm to further enforce the reasoning is grounded with the visual knowledge, preventing models seeking shortcuts that appear coherent but are visually ungrounded reasoning chains. Moreover, we contribute a new dataset MathCog for model training, which contains samples with over 120K high-quality perception-reasoning aligned annotations. Comprehensive experiments and analysis on commonly used visual mathematical reasoning benchmarks validate the superiority of the proposed CogFlow.