How does a deep neural network, trained for regression with back propagation, deal with cases when different training pairs have the same input value, but different output values, i.e. the relationship between input and output is not smooth?
In other words, suppose I train a deep neural network for regression from $x$ to $y$, using back propagation. Two of my data pairs have the same $x$ ($x_1 = a$ and $x_2 = a$), but very different $y$'s ($y_1 = b$ and $y_2 = c$). After training the network, what would be the output $y_k$ for an input of $x_k = a$? Would it be $b$, or the average of $b$ and $c$?