Is there a word for a function, f, that has the same critical points as another function, g, albeit with different critical values and where there isn't necessarily equivalence between minimum <-> minimum, maximum <-> maximum, and saddle point <-> saddle point?
I'm mostly thinking out-loud. I think @kldivergence tact will help. Basically, I want my f() to just be g() but it's not. Factoring to make it similar was convoluted. I'd just like to make the hand-wavy argument that under stochastic gradient descent there are *similar* dynamics.