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

ICLR 2026 · Vision-language and multimodal › Multimodal LLMs · approach: Chain-of-thought multimodal reasoning · 0 citations (OpenAlex)

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Proposes CogFlow, a perception→internalization→reasoning framework for visual math that combines synergistic visual rewards, a trained knowledge-internalization reward model, and visual-gated policy optimization, plus a 120K-sample MathCog dataset, reaching 66.0% on FlowVerse with a 7B model.

Problem

Multimodal LLMs struggle with visual math problems; prior perception-enhancing methods improve visual extraction but do not check whether extracted visual cues are faithfully used in subsequent reasoning, causing reasoning drift.

Approach

A three-stage cognitive-inspired pipeline (perception, knowledge internalization, reasoning) with rewards at each stage: parametric and semantic visual rewards for perception, a DPO-trained internalization reward model over five synthetic error types, and a visual gate inside GRPO-style policy optimization that filters perception trajectories before reasoning.

Key results

• CogFlow-7B reaches 66.0% CoT-E on FlowVerse (accuracy 56.2%) and 53.9% on MathVerse testmini, per the tables.
• Adding VSR and VPR together improves MathVerse CoT-E by up to +3.0% and accuracy by +1.7% over the baseline.
• Visual gate used only at inference yields about 0.6-1% accuracy gain even without VGPO training.

Surprising findings

• Gating perception at inference alone gives a consistent gain even for models not trained with VGPO.

Limitations

• Training is computationally demanding, limiting adoption in resource-constrained settings.
• Primitive extraction is tailored to geometric diagrams; generalization to natural scenes is untested.

Experimental setup

Datasets: MAVIS Geo170K LLaVA-CoT

Benchmarks: FlowVerse MathVerse MathVista WeMath LogicVista DynaMath

Metrics: accuracy CoT-E

Baselines: VLM-R1-7B MathFlow SVE-Math-Qwen2.5-7B MultiMath-7B InternVL2.5-8B GPT-4o GPT-5 SophiaVL-R1-7B

Builds on: GRPO Softmax-DPO VLM-R1 MathFlow Qwen2.5-VL

Closest papers by meaning

• MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning (NeurIPS 2025 · similarity 0.92)
• ViRC: Enhancing Visual Interleaved Mathematical CoT with Reason Chunking (CVPR 2026 · similarity 0.90)
• We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning (ICLR 2026 · similarity 0.90)
• Benchmarking Multimodal Mathematical Reasoning with Explicit Visual Dependency (NeurIPS 2026 · similarity 0.90)
• Revisiting the Necessity of Lengthy Chain-of-Thought in Vision-centric Reasoning Generalization (CVPR 2026 · similarity 0.90)
• From Seeing to Thinking: Decoupling Perception and Reasoning Improves Post-Training of Vision-Language Models (ICML 2026 · similarity 0.90)