Train neural network for regression with negative samples
An option might be to tinker with the cost function: Usually one uses the difference between the target output ($out_{t}$) and the actual output ($out_{a}$) as a part as the cost function. Let's say

$$
J = \sum_{i=1}^N (out_{t,i} - out_{a,i})^2
$$

is the cost function, where N is the number of samples. Now we can adjust this to the cost function

$$
J = \sum_{i=1}^N type_i \cdot (out_{t,i} - out_{a,i})^2
$$

where $type_i$ is 1 for normal samples and -1 for "negative samples". Alternative one might also use

$$
J = \left( \sum_{i=1}^M (out_{t,i} - out_{a,i})^2 \right) + \left( \sum_{i=M+1}^N \frac1{(out_{t,i} - out_{a,i})^2} \right)
$$

as the cost function where the samples up to $M$ are the normal ones and from $M+1$ to $N$ are the negative samples.