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In my research internship report, I'm mentioning a successful deep learning experiment. I performed it because another researcher told me it gave them good results for a similar problem.

I need to justify why I tried this, but I can't cite something un-published like this conversation. Is it appropriate to mention it in a footnote, like "according to other researchers, [...]"? Should I search for a citable source that says the same thing, or just drop the justification?

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You can cite it as a "private communication" but it's more common (at least in my field, which is physics) to mention the person in the acknowledgements, for example, "We thank A. Smith and B. Jones for useful discussions". You can make the phrasing more specific if you want, for example, "We thank C. Davies for an insighful discussion about deep learning that inspired our approach to this work".

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