When to Trust Tools? Adaptive Tool Trust Calibration For Tool-Integrated Math Reasoning

Tool-integrated reasoning (TIR) offers a direct way to extend thinking models beyond the limits of text-only reasoning. Paradoxically, we observe that tool-enabled evaluation can degrade reasoning performance even when the strong thinking models make almost no actual tool calls. In this paper, we investigate how to inject natural tool-use behavior into a strong thinking model without sacrificing its no-tool reasoning ability, and present a comprehensive TIR recipe. We highlight that (i) the effectiveness of TIR supervised fine-tuning (SFT) hinges on the learnability of teacher trajectories, which should prioritize problems inherently suited for tool-augmented solutions; (ii) controlling the proportion of tool-use trajectories could mitigate the catastrophic forgetting of text-only reasoning capacity; (iii) optimizing for pass@k and response length instead of training loss could maximize TIR SFT gains while preserving headroom for reinforcement learning (RL) exploration; (iv) a stable RL with verifiable rewards (RLVR) stage, built upon suitable SFT initialization and explicit safeguards against mode collapse, provides a simple yet remarkably effective solution. When applied to Qwen3 thinking models at 4B and 30B scales, our recipe yields models that achieve state-of-the-art performance in a wide range of benchmarks among open-source models, such as 96.7% and 99.2% on AIME 2025 for 4B and 30B, respectively.

Tool-integrated reasoning (TIR) has become a key approach for improving large reasoning models (LRMs) on complex problems. Prior work has mainly studied when to invoke tools, while overlooking how tools are applied. We identify two common patterns: a calculator pattern that uses code for direct computation, and an algorithmic pattern that encodes problems as programs. Misaligned choices often cause failures even when reasoning is sound. We propose a two-stage framework that first builds code competence from both patterns and then aligns pattern selection with teacher preferences. Across challenging math datasets, our pattern-aware method substantially improves both code usage and accuracy, for instance raising Code@1 on MATH500 from 64.0% to 70.5% and on AIME24 from 26.7% to 50.0%. These gains highlight the effectiveness of a pattern-aware approach for tool-integrated reasoning.

Tool-integrated reasoning (TIR) enables large language models (LLMs) to enhance their capabilities by interacting with external tools, such as code interpreters (CI). Most recent studies focus on exploring various methods to equip LLMs with the ability to use tools. However, how to further boost the reasoning ability of already tool-capable LLMs at inference time remains underexplored. Improving reasoning at inference time requires no additional training and can help LLMs better leverage tools to solve problems. We observe that, during tool-capable LLM inference, both the number and the proportion of erroneous tool calls are negatively correlated with answer correctness. Moreover, erroneous tool calls are typically resolved successfully within a few subsequent turns. If not, LLMs often struggle to resolve such errors even with many additional turns. Building on the above observations, we propose PruneTIR, a rather effective yet efficient framework that enhances the tool-integrated reasoning at inference time. During LLM inference, PruneTIR prunes trajectories, resamples tool calls, and suspends tool usage through three components: Success-Triggered Pruning, Stuck-Triggered Pruning and Resampling, and Retry-Triggered Tool Suspension. These three components enable PruneTIR to mitigate the negative impact of erroneous tool calls and prevent LLMs from getting stuck in repeated failed resolution attempts, thereby improving overall LLM performance. Extensive experimental results demonstrate the effectiveness of PruneTIR, which significantly improves Pass@1 and efficiency while reducing the working context length for tool-capable LLMs.