[wakawaka28]

I don't think you understood what I wrote there. The rules for algebraically computing a derivative are simple and deterministic and essentially captured within AD algorithms. They MUST therefore be correct in an analytical sense, given infinite precision. The video starts off by saying, they are dealing with considerations about how computers actually work. That kind of implies finite precision. Like I said, concerns about stability of the methods are not new. Your original function might not be differentiable at any given point, for example. You have to know about that stuff rather than blindly applying "automatic" techniques. There is a lot of literature about how to use AD and what can go wrong. This is a paper I just found in a basic search, that is a survey of known pitfalls: https://wires.onlinelibrary.wiley.com/doi/full/10.1002/widm....

The entire point of the video is mired in an hour or so of details about how they had trouble using it for solving ODEs. I am familiar with forward and reverse mode but for me to appreciate it I would have to get up to speed with their exact problem and terminology. Anyway, my point is that AD requires you to know what you are doing. This video seems like a valuable contribution to the state of the art but I think you have to recognize that the potential for problems was known to numerical analysis experts for decades, so this is not as groundbreaking as it appears. The title should read, "Automatic differentiation can be tricky to use" to establish that it is in fact a skill issue. The mitigation of these corner cases is valuable, to make them more versatile or foolproof. But the algorithms are not incorrect just because you didn't get it to solve your problem.