Hi @orashi,
thank you for the credit. I might be among the first to discuss this in detail in this specific context and with a pytorch implementation, but certainly the identification of 1-Lipschitz (in the classical definition) with unit sphere in $W_{1,\infty}$ in the Sobolev scale (which is the fancy mathematician talk for the gradient being bounded by 1) is very standard just as the approximation of the derivative by finite differences (actually, one could fancy-talk that into a different norm, but let’s not), so I would expect many other people to have the same idea independently, so I’d go for coincidence. (Actually sampling two points is a bit different to sampling the center and using the two side points as I did, too.)
What struck me as particularly curious in this case is why the authors of Improved Training chose to do a point-wise derivative test instead of testing the Lipschitz constant directly, but I have not asked them yet, so I don’t know.
Best regards
Thomas