As far as I'm aware, it's not true for models like DeepSeek or other Chinese open-weight models (at least those that I have seen); their reasoning traces are fully composed from some human language, be it English, Chinese or another one; by the way, most of them can adapt their reasoning based on user language, for example, if user speaks English the reasoning more likely will be in English.

I think that for DeepSeek problem (thinking and replying in Chinese) everything is kinda simpler: in their official chat, they're probably using some kind of system prompt which is (probably) written in Chinese, so that's why model may prefer Chinese in it's output.

Summaries by different smaller models are usually made by closed proprietary models like Claude as a way to combat the distillation of real reasoning traces by competitors. Open weight models show the real reasoning traces. Reasoning traces operate in the same space as the non-reasoning output. It's all just one large text for an LLM. Internally, reasoning is just ordinary chat completion between <think></think> tags.

> summaries generated

Or hallucinated