US REU programs sometimes accept "self-funded" international students. Such international candidates do not receive any financial assistance from the host university but participate in research.
Would that classify as "independent research", under the B-1/B-2 visa category?
For example, this University of Ohio page mentions:
A visitor conducting independent research. Independent research means the use of University facilities without any affiliation or appointment. NOTE: a visitor with affiliation or appointment should consider coming on a J-1 visa, even if no payment is made to the visitor by the University.
Per the US law, would an international REU candidate be considered affiliated with or appointed by the host university?