Yeah it really does seem obvious once it's written up this clearly. And honestly an explanation of LM as taking a Taylor series expansion of the difference in

Yeah it really does seem obvious once it's written up this clearly. And honestly an explanation of LM as taking a Taylor series expansion of the difference in error is so spot on but literally nobody ever told me that's what it's doing. We just derived from minimizing log error and slapped on a bit more gradient for funsies.