Wouldn&#x27;t it still be likely to settle on a local minima when the deciding factors for the existence of a local minima are limited to those that contribute to the likelihood of a single output category, and not whether all functions are curving up?<p>An example I can think of would be an absurd million input neural network, where one of the inputs only has a pronounced effect on one of the outputs. It seems like it would be possible for the path of the input to output to be dragged downhill in the context of all outputs, but uphill in the context of the single output it affects.<p>Is what I&#x27;ve described not likely, or am I just completely off base?