Figure It Out: Improve the Frontier of Reasoning with Executable Visual States
This addresses the limitation of purely text-based reasoning in capturing structural constraints for complex mathematical problems, representing a domain-specific advancement.
The paper tackles the problem of complex reasoning involving implicit spatial and geometric relationships by introducing FIGR, which integrates executable visual construction into multi-turn reasoning via reinforcement learning, resulting in improvements of 13.12% on AIME 2025 and 11.00% on BeyondAIME over text-only baselines.
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.