Confusion about notation in Table 2

[JINAILAB]

While reviewing Table 2, I noticed the notation for "SFT w/ Complex CoT (x̂, ŷ)". However, based on the context and the explanation in the paper, it seems that (x̂, ŷ) might actually refer to (ê, ŷ).

Could you please clarify if this is a typographical error or if I am misunderstanding the notation?

[jymChen]

Hi @JINAILAB,

This is not a typographical error. "ê" represents the model’s internal reasoning, while "ŷ" is the complete answer based on that reasoning. The pair (ê, ŷ) is somewhat analogous to OpenAI-o1's hidden thought process (which you cannot access) and its final response. Therefore, even without ê, ŷ still constitutes a full answer. "SFT w/ Complex CoT (x̂, ŷ)" is more akin to directly distilling o1's response rather than learning its thought process.