normalization of probabilities in predicting a poly-neuron output in neural nets When predicting a poly-neuron output in neural nets, say, predicting multiple handwritten digits and giving an output neuron vector (0.1,...,0.9,0.1,...), many use sth like softmax (or sth like the energy dependent probability exponential formula in statistical mechanics) to normalize the output vector such that all the components of the output vector sum up to 1, and that the normalized output vector becomes a probability vector. I doubt the necessity of this normalization, for without which I can equally well predict as per the biggest vector component. Is there anything I overlooked?
You are correct, but this is not called normalization. You can simply use the highest probability output for category. This is what softmax does for you. For example 2 output neurons can have 0.1 for dog and 0.9 for cat as the loss. Softmax will it just convert it to [0,1] meaning no dog but a cat is on the image.