Understanding Tool-Integrated Reasoning
Authors: name: Heng Lin, name: Zhongwen Xu
Organization: Tencent

We study why Tool-Integrated Reasoning (TIR) makes Large Language Models
(LLMs) more capable. While LLMs integrated with tools like Python code
interpreters show great promise, a principled theory explaining why this
paradigm is effective has been missing. This work provides the first formal
proof that TIR fundamentally expands an LLM's capabilities. We demonstrate that
tools enable a strict expansion of the model's empirical and feasible support,
breaking the capability ceiling of pure-text models by unlocking
problem-solving strategies that are otherwise impossible or intractably
verbose. To guide model behavior without compromising training stability and
performance, we also introduce Advantage Shaping Policy Optimization (ASPO), a
novel algorithm that directly modifies the advantage function to guide the
policy behavior. We conduct comprehensive experiments on challenging
mathematical benchmarks, leveraging a Python interpreter as the external tool.
Our results show that the TIR model decisively outperforms its pure-text
counterpart on the pass@k metric. Crucially, this advantage is not confined to
computationally-intensive problems but extends to those requiring significant
abstract insight. We further identify the emergent cognitive patterns that
illustrate how models learn to think with tools. Finally, we report improved
tool usage behavior with early code invocation and much more interactive turns
with ASPO. Overall, our work provides the first principled explanation for
TIR's success, shifting the focus from the mere fact that tools work to why and
how they enable more powerful reasoning.