How to choose the non-linear activation function for the output layer, if the most of the value of the target are negative numbers?

I try to use MLP to solve a regression problem, and most of the target numbers are negative, but there is a very small part of them are positive numbers. For now, I choose a LogSigmoid function as the non-linear function of the output layer, but the MSE loss can’t get down to a low level. Should I choose a better non-linear function?
the histogram of the target value is attached below.
Many thank!