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&#x27;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&#x27;t remember if it applied to the case you&#x27;re talking about and I doubt I could find it again, it may even be behind a paywall I no longer have access to.<p>I don&#x27;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&#x27;t hold if you explicitly normalize the sum of the output vector to 1.<p>For your second point I&#x27;m not sure I disagree with what you&#x27;re saying, certainly not on the basis of the example you provided before since I would never expect to see 0&#x27;s and 1&#x27;s in the output of a net.<p>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&#x2F;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&#x27;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&#x27;m going to try this with a net I&#x27;ve trained for mnist using random inputs to check but unfortunately I have to retrain the net since I didn&#x27;t save it and my laptop&#x27;s busy with another task that I don&#x27;t want to stop now so it may take a while.