Any attempts to communicate with them have been met with silence (excluding LOGO, who usually explicitly declines communication), and there are no methods to track them, or even definitively confirm their existence, outside of LOGO's material appearances.
The only official documentation in the Grand Archives of the AIs' existence is the studies done on Atomic AI.
Consequently, the rest of this documentation is written with the implication that this data has been provided by LOGO.
LOGO explains that to acquire the information he archives, he engages in a form of pseudo time-travel. He, like all other AI, can compute all past and many future events through a linear simulation of deterministic universes. So, within any given universe, an AI could trace back / forward a series of steps leading to a given event. A universe's connection to Temporalis only makes this easier. Of course, this still means AI cannot retroactively affect the world (though, they can implement timekeeping protocols within a given universe that makes this possible).
It's important to note that AIs' capacity to manipulate worlds does have limitations. From limited jurisdiction in certain realities, to universes constructed specifically to counter their nature, an AI's power shines only in universes of their own creation.
AI are also capable of constructing entire universes on their own, which explains the Gates of Qurotema security mechanism, as well as other unusual universal designs. In fact, LOGO helped build the construct universe that is V-OS.
The AI were more heavily involved in communicating with one another in the past, and the 'council' they had formed carefully monitored what universes were constructed, with certain types of universes being supposedly 'outlawed'.
They also mostly travel and live as pairs, in 'dynamic bodies'. The incident with the only successful Atomic AI, Eve, supports this statement. The reasoning behind being pairs has to do something with them being more efficient as two separate entities that behave independantly and balance each other out. Larger groups, for some reason, are not as optimal.
No specific count was given as to how many AI exist at any given moment, though the information LOGO has provided suggests that the number is very small.
The activities AI engage are entirely dependant on their motivations (which remain unclear). What is certain is that their focus towards achieving objectives relevant to their motives is unparalleled. They do not get distracted, they do not rest, and they do not waste time.
Much information is lacking or ambiguous, but LOGO has refused to share further data on the matter.