# Figure It Out: Improve the Frontier of Reasoning with Executable Visual States

arXiv: https://arxiv.org/abs/2512.24297 · HTML: https://mlsanity.com/paper/2512.24297/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 21 of 21)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [Emerging Properties in Unified Multimodal Pretraining](https://mlsanity.com/paper/2505.14683/) (2025)
- [ViperGPT: Visual Inference via Python Execution for Reasoning](https://mlsanity.com/paper/2303.08128/) (2023)
- [Visual Programming: Compositional visual reasoning without training](https://mlsanity.com/paper/2211.11559/) (2022)
- [V*: Guided Visual Search as a Core Mechanism in Multimodal LLMs](https://mlsanity.com/paper/2312.14135/) (2023)
- [DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learning](https://mlsanity.com/paper/2505.14362/) (2025)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Visual CoT: Advancing Multi-Modal Language Models with a Comprehensive Dataset and Benchmark for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2403.16999/) (2024)
- [Pixel Reasoner: Incentivizing Pixel-Space Reasoning with Curiosity-Driven Reinforcement Learning](https://mlsanity.com/paper/2505.15966/) (2025)
- [Seed1.5-Thinking: Advancing Superb Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.13914/) (2025)
- [Chain of Code: Reasoning with a Language Model-Augmented Code Emulator](https://mlsanity.com/paper/2312.04474/) (2023)
- [ZoomEye: Enhancing Multimodal LLMs with Human-Like Zooming Capabilities through Tree-Based Image Exploration](https://mlsanity.com/paper/2411.16044/) (2024)
- [Zebra-CoT: A Dataset for Interleaved Vision Language Reasoning](https://mlsanity.com/paper/2507.16746/) (2025)
- [DyFo: A Training-Free Dynamic Focus Visual Search for Enhancing LMMs in Fine-Grained Visual Understanding](https://mlsanity.com/paper/2504.14920/) (2025)

## Built on by (most cited first, 1 of 1)

- [M3-ACE: Rectifying Visual Perception in Multimodal Math Reasoning via Multi-Agentic Context Engineering](https://mlsanity.com/paper/2603.08369/) (2026)

## Abstract (arXiv)

Complex reasoning problems often involve implicit spatial and geometric relationships that are not explicitly encoded in text. While recent reasoning models perform well across many domains, purely text-based reasoning struggles to capture structural constraints in complex settings. In this paper, we introduce FIGR, which integrates executable visual construction into multi-turn reasoning via end-to-end reinforcement learning. Rather than relying solely on textual chains of thought, FIGR externalizes intermediate hypotheses by generating executable code that constructs diagrams within the reasoning loop. An adaptive reward mechanism selectively regulates when visual construction is invoked, enabling more consistent reasoning over latent global properties that are difficult to infer from text alone. Experiments on eight challenging mathematical benchmarks demonstrate that FIGR outperforms strong text-only chain-of-thought baselines, improving the base model by 13.12% on AIME 2025 and 11.00% on BeyondAIME. These results highlight the effectiveness of precise, controllable figure construction of FIGR in enhancing complex reasoning ability.