Some of the Greeks in Central Asia converted to Buddhism. They were in contact with both China and India and would have been the natural intermediaries for the conduit of culture. The Greek gynmasia or the schools of physical culture existed in Central Asia before Ashoka. We know they existed because the foundations of their cities indicate this and it was a prerquisite for Hellenistic culure. The hypothesis that the Chinese borrowed the idea of martial arts academies remains just that, I suspect that they will contend that ther system was developed independently of foreign cultures.