Note that an AI that does modify its own goals would not be an example of ‘going beyond its programming,’ as it would only modify its goals if it was programmed to. (Barring, of course, freak accidents like a cosmic ray or whatever. However, since that requires no intelligence at all on the part of the AI, I’m fairly confident that you don’t endorse this as an example of a Singularity.)
Note that an AI that does modify its own goals would not be an example of ‘going beyond its programming,’ as it would only modify its goals if it was programmed to. (Barring, of course, freak accidents like a cosmic ray or whatever. However, since that requires no intelligence at all on the part of the AI, I’m fairly confident that you don’t endorse this as an example of a Singularity.)