@GreyInteresting, but does she have it on, like a flashdrive, her phone, a laptop? Where does one keep an A.I. Also, what is the function of said A.I.? Is it military, or just an advanced version of SIRI?
I'm glad you asked!
So basically in my head, the Sentient AI (I'll call it Sai for convenience) would have been designed by a cape with some kind of intelligence-based power (let's call him "Smartypants", because I can't think of anything better right now) affiliated with The Guardians, and who is - or was, since he died - working for the company Dragoon attacked (AFAIK the company is also protected and supported by Scarborough Enterprises, which is run by Alex's family).
On paper, the intent behind the project was to create an administrative assistant that would support both The Guardians and general law enforcement. Sai's primary function would be to access all the information The Guardians have on capes, and use the data from there to posit theories and predictions, run combat style simulations to determine a path to victory, contact capes, and so on so forth. Off-the-books, Sai would be Smartypants' personal experiment in simulating human consciousness - a test run that would have led up to something bigger.
Of course, there were more functions planned to be appended (like some Ultron-esque robot suit program, probably) if this first iteration succeeded and was determined to have beneficial intentions, but that drawing board was set on fire in the ensuing battle.
Locationwise, I think Sai would be on Smartypants' super-special-awesome-laptop and pending transfer to The Guardians' servers, since Smartypants would probably confess to hijacking the project for his own experiment on his deathbed.
Or at least that's what I imagined.