The answer to your question depends very much on your network architecture and the parameters used to train it. If you are trying to protect against false alarms, we can set an arbitrary threshold value for the corresponding output nodes.
In general, learning algorithms basically take the form of โclosed setโ recognition, where all testing classes are known during training. However, a more realistic scenario for vision applications is the โopen setโ of recognition, where incomplete knowledge of the world is present during training, and unknown classes can be represented during testing.
This is an ongoing research area - please see this Open Set Recognition web page for a lot of resources on this subject.
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