Loss of MSE always be 0 when keras for topic predict
First, is your output a one-hot vector of predicted classes? i.e: class one is [1, 0, 0, ...] and class two is [0, 1, 0, 0, ...].

If so, then using softmax activation at the output layer is acceptable and you are doing a classification problem. If you are doing a classification problem (one-hot output) you cannot use MSE as the loss, use categorical cross-entropy. 

Softmax scales the output so that the number given is a predicted probability of a certain class. Wikipedia here: https://en.wikipedia.org/wiki/Softmax_function

If you are expecting the output vector to be real numbers then you need to use linear activation on your output neurons.