Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Figure It Out: Improving the Frontier of Reasoning with Active Visual Thinking

Meiqi Chen, Fandong Meng, Jie Zhou

TL;DR

Pure-text reasoning struggles with global geometric and spatial constraints in complex problems. FigR addresses this by embedding active visual thinking into multi-turn reasoning through end-to-end reinforcement learning, externalizing intermediate visual hypotheses as executable figures, and adaptively regulating when visual reasoning is invoked. The approach yields substantial gains on challenging math benchmarks (e.g., +13.12% on AIME 2025 and +11.00% on BeyondAIME over a strong base), demonstrating improved stability and reliability of multimodal reasoning. These results highlight the practical value of figure-guided reasoning for hard analytical tasks and point to a generalizable direction for interpretable multimodal reasoning systems.

Abstract

Complex reasoning problems often involve implicit spatial, geometric, and structural relationships that are not explicitly encoded in text. While recent reasoning models have achieved strong performance across many domains, purely text-based reasoning struggles to represent global structural constraints in complex settings. In this paper, we introduce FIGR, which integrates active visual thinking into multi-turn reasoning via end-to-end reinforcement learning. FIGR externalizes intermediate structural hypotheses by constructing visual representations during problem solving. By adaptively regulating when and how visual reasoning should be invoked, FIGR enables more stable and coherent reasoning over global structural properties that are difficult to capture from text alone. Experiments on challenging mathematical reasoning benchmarks demonstrate that FIGR outperforms strong text-only chain-of-thought baselines. In particular, FIGR improves the base model by 13.12% on AIME 2025 and 11.00% on BeyondAIME, highlighting the effectiveness of figure-guided multimodal reasoning in enhancing the stability and reliability of complex reasoning.

Figure It Out: Improving the Frontier of Reasoning with Active Visual Thinking

TL;DR

Pure-text reasoning struggles with global geometric and spatial constraints in complex problems. FigR addresses this by embedding active visual thinking into multi-turn reasoning through end-to-end reinforcement learning, externalizing intermediate visual hypotheses as executable figures, and adaptively regulating when visual reasoning is invoked. The approach yields substantial gains on challenging math benchmarks (e.g., +13.12% on AIME 2025 and +11.00% on BeyondAIME over a strong base), demonstrating improved stability and reliability of multimodal reasoning. These results highlight the practical value of figure-guided reasoning for hard analytical tasks and point to a generalizable direction for interpretable multimodal reasoning systems.

Abstract

Complex reasoning problems often involve implicit spatial, geometric, and structural relationships that are not explicitly encoded in text. While recent reasoning models have achieved strong performance across many domains, purely text-based reasoning struggles to represent global structural constraints in complex settings. In this paper, we introduce FIGR, which integrates active visual thinking into multi-turn reasoning via end-to-end reinforcement learning. FIGR externalizes intermediate structural hypotheses by constructing visual representations during problem solving. By adaptively regulating when and how visual reasoning should be invoked, FIGR enables more stable and coherent reasoning over global structural properties that are difficult to capture from text alone. Experiments on challenging mathematical reasoning benchmarks demonstrate that FIGR outperforms strong text-only chain-of-thought baselines. In particular, FIGR improves the base model by 13.12% on AIME 2025 and 11.00% on BeyondAIME, highlighting the effectiveness of figure-guided multimodal reasoning in enhancing the stability and reliability of complex reasoning.
Paper Structure (30 sections, 9 equations, 6 figures, 3 tables)

This paper contains 30 sections, 9 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Text-based Reasoning
  4. Multimodal Reasoning
  5. Methodology
  6. Figure-Steered Reasoning Loop
  7. Reinforcement Learning Procedure
  8. Adaptive Reward Mechanism
  9. Experiments
  10. Experimental Setup
  11. Implementation Details
  12. Training Dataset
  13. Evaluation Datasets
  14. Baselines
  15. Evaluation Metrics
  16. ...and 15 more sections

Figures (6)

  • Figure 2: Overview of our proposed FigR. FigR alternates between textual reasoning and executable drawing steps with visual feedback. An adaptive reward mechanism dynamically regulates visual thinking based on task suitability and execution outcomes.
  • Figure 3: Ablation analysis across training steps. We report average response length, code count, code ratio, average code lines per executable block, and code pass rate under different settings. FigR enables more frequent and structured visual reasoning while preserving stable execution behavior, compared to ablated settings.
  • Figure 4: Case study of reasoning behaviors. FigR demonstrates more effective integration of visual feedback into the reasoning process, resulting in clearer intermediate reasoning and improved final answers, while the baseline models rely primarily on textual reasoning.
  • Figure 5: Prompt template for the figure-steered suitability classifier.
  • Figure 6: Prompt template for multi-turn CoT.
  • ...and 1 more figures