# Can a neural network classify a new input in the same coordinate of another but have different output label?

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?

• Since the network has to classify that (x, y, z) point one way or another, it can never separately perfectly. See for yourself! Here's a sandbox which lets you add a point right on top of another of the opposite class. cs.stanford.edu/people/karpathy/convnetjs/demo/classify2d.html Commented Jun 28, 2019 at 20:48