On your first point in my experience if you use a net with logistic output nodes and you feed it an input that looks nothing like any of the (labeled) training

On your first point in my experience if you use a net with logistic output nodes and you feed it an input that looks nothing like any of the (labeled) training examples I would expect to see low values for all outputs. I would add the caveat that there may be the odd input that is not an example of a class that still provides an erroneous high confidence output but this is not common. These are the types of nets that I have the most experience with. I don't have a link for this, only my recollections from when I was working with these types of nets. I did once see a paper that proved the relationship between P(C|x) and logistic output values trained with the squared error loss but I don't remember if it applied to the case you're talking about and I doubt I could find it again, it may even be behind a paywall I no longer have access to. I don't think this holds with a softmax output layer because I think that provides an output vector that is implicitly normalized across all classes. It also obviously doesn't hold if you explicitly normalize the sum of the output vector to 1. For your second point I'm not sure I disagree with what you're saying, certainly not on the basis of the example you provided before since I would never expect to see 0's and 1's in the output of a net. EDIT: After thinking about this some more I realized that I may have been mistaken in what I said above. It may be that for an unknown input you would expect to see a high entropy output distribution whose sum is close to 1 but where the average output value is about 1/N (ie. the number of output classes). If this is the case then the logistic and softmax cases would be similar. This still indicates a low confidence though, I wouldn't expect to see outputs in the upper quartile, unlike for a cleanly recognized input where you might see 0.8 or 0.9. I'm going to try this with a net I've trained for mnist using random inputs to check but unfortunately I have to retrain the net since I didn't save it and my laptop's busy with another task that I don't want to stop now so it may take a while.