In a 3D model, say we have the following input:
x---y---z---Label
0---0---0---A
1---0---0---A
1---1---0---A
0---1---1---A
1---0---1---B
1---1---1---B
Now, there's a new input that we want to add to the previous data with the (0,1,1) coordinates. If the new input is labeled "A", a NN can easily separate perfectly the data in two classes (a simple regression would do it).
However, if it is labeled "B", we will have two data that have the same coordinates but different labels. How does a NN with, say one hidden layer, deal with this kind of problem?
My guess is that the problem becomes not linearly separable (NN are good with that) however, they are at the same spot so we would not be able to separate perfectly the data between A and B. Am I correct?