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Trace Inversion is fascinating, but it’s more of an independent reconstruction that will give you some coherent-looking generated CoT; but not necessarily anywhere close or related to the underlying model’s CoT.
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I didn't read the paper in details but they claim there is high overlap between the synthetic traces and the ground truth ones (not sure how they confirmed that for blackbox models though, I guess they must have compared to open source models).

They also talk about successful distillation of black box model capabilities with the approach.

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