START: Self-taught Reasoner with Tools
Authors: name: Chengpeng Li, name: Mingfeng Xue, name: Zhenru Zhang, name: Jiaxi Yang, name: Beichen Zhang, name: Xiang Wang, name: Bowen Yu, name: Binyuan Hui, name: Junyang Lin, name: Dayiheng Liu

Large reasoning models (LRMs) like OpenAI-o1 and DeepSeek-R1 have
demonstrated remarkable capabilities in complex reasoning tasks through the
utilization of long Chain-of-thought (CoT). However, these models often suffer
from hallucinations and inefficiencies due to their reliance solely on internal
reasoning processes. In this paper, we introduce START (Self-Taught Reasoner
with Tools), a novel tool-integrated long CoT reasoning LLM that significantly
enhances reasoning capabilities by leveraging external tools. Through code
execution, START is capable of performing complex computations, self-checking,
exploring diverse methods, and self-debugging, thereby addressing the
limitations of LRMs. The core innovation of START lies in its self-learning
framework, which comprises two key techniques: 1) Hint-infer: We demonstrate
that inserting artificially designed hints (e.g., ``Wait, maybe using Python
here is a good idea.'') during the inference process of a LRM effectively
stimulates its ability to utilize external tools without the need for any
demonstration data. Hint-infer can also serve as a simple and effective
sequential test-time scaling method; 2) Hint Rejection Sampling Fine-Tuning
(Hint-RFT): Hint-RFT combines Hint-infer and RFT by scoring, filtering, and
modifying the reasoning trajectories with tool invocation generated by a LRM
via Hint-infer, followed by fine-tuning the LRM. Through this framework, we
have fine-tuned the QwQ-32B model to achieve START. On PhD-level science QA
(GPQA), competition-level math benchmarks (AMC23, AIME24, AIME25), and the
competition-level code benchmark (LiveCodeBench), START achieves accuracy rates
of 63.6%, 95.0%, 66.7%, 47.1%, and 47.3%, respectively. It significantly
outperforms the base QwQ-32B and achieves performance comparable to the
state-of-the-art open-weight model R1-Distill-Qwen-32B and the proprietary
model o1-Preview.