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We don’t know o1 thinks in English. What we see is a summary of the thinking process.

My guess is it “thinks” in non-eligible tokens

The o1 release blog post contains 8 full examples of o1 chains of thought (not the summarized versions visible to users). They're English.

I have seen the summaries dip into completely random languages like Thai, so it might switch between languages occasionally.

Did you mean to write "non-legible" ?