# Explanation for MLP classification probability

I showed some results of one implemented NN MLP model.

In the result, for classification of two categories, if I sum up the probabilities of both cats, them some sum would be greater than 1.

When I was asked why the sum is greater than 1, I gave the guess that the probability stands for confidence concept in mathematics.

Could anyone tell me am I right?

It depends a little on the specific model.

If your model is using a softmax output layer, then the values are usually interpreted as mutually-exclusive class probabilities and should sum to 1.

If your model is using a sigmoid output layer, then the values for a classification problem can be interpreted as the individual, non-exclusive probabilities. In that case, it is possible for an example to not be in either of your classes (an output close to [0,0]), or to definitely be in both classes (an output close to [1,1]) - if that is not the case in the problem that you have trained the NN to model, then you might want to consider altering the model.

So, if your classification should be mutually-exclusive, then the person asking you the question has a valid point. The probabilities should sum to 1, and you may need to fix the model. In that case, you should use a softmax output layer, and would not have this problem because the probabilities would always sum to 1.

Whether it is worth fixing the model, depends on your understanding of mutually-exclusive vs non-exclusive classes in the problem, whether the current model meets its goals (it is not a big issue in practice, if the model is not a strict theoretical match to the problem, but has a perfectly good accuracy) and how much effort it would take to alter your code and re-train the model.