[Question] Importance of backward pass in root finder

Hey @shoyer! I do see this repository has been dormant for quite some time. My name is Ryan and I am interested in implementing this in `Pytorch`. It seems that I have just about everything in place. However, it seems my `x` values become very very large after a first backward pass so leads me to believe that the calculation of the adjoint derivative is actually fairly important.

This is however where my understanding breaks down. If you have a moment to help me understand how that works under the hood I would very much appreciate it or if you have any tips on a `pytorch` implementation (don't know if you have experience with it after all these years) I would appreciate that as well.

Thank you for your time in advance and this is some really neat work!