For example:
Complex, High performance, Tailwheel as laid out here:
https://www.ecfr.gov/cgi-bin/retrieveECFR?gp&n=14y2.0.1.1.2&r=PART#se14.2.61_131
It is not recurrent, because it doesn't have to happen again. And it includes training in an aircraft.
However some places such as AOPA suggest all of 61.31 is exempt: https://www.aopa.org/advocacy/pilots/alien-flight-training-program/aopas-guide-to-tsas-alien-flight-training-citizenship-validation-rule
He/she is seeking recurrent training, such as a flight review, instrument proficiency check, or flight training listed under 14 CFR 61.31; or
Whereas: https://www.flightschoolcandidates.gov/home Only suggests (g)
High Altitude Training (HAT) 14 CFR Part 61.31(g) - Type rating requirements, additional training, and authorization requirements.
gov references highly appreciated