Tool-Integrated Reasoning (TIR) SFT (ToRA / NuminaMath-TIR)

Supervises interleaved natural-language deduction and executable code/tool blocks: $x \rightarrow r_1 \rightarrow a_1 (\text{Python/SymPy/Bash}) \rightarrow \text{obs}_1 \rightarrow r_2 \rightarrow \dots \rightarrow y$, masking environment execution outputs $\text{obs}_t$ from the cross-entropy loss so the model learns when to offload symbolic/numerical computation and how to interpret stdout/stderr.

Masking tool observation tokens (obs_t) during SFT is mandatory so the model does not learn to hallucinate fake interpreter outputs.