They started going off for 2-3 seconds every few minutes (usually 3, has gone from 2 to 10) since 0215. None are in need of new backup batteries (and only the one(s) in need of a new battery beep when needed, and much less annoyingly than a full alarm), they're regularly dusted, and we haven't used the oven in a few days. It stopped after half an hour, then started AGAIN at 0815. Next time they start, I'm going to take the diagonal cutters and dike every last one of them out.
edit 0930: A maintenance guy showed up and reset each of the smoke detectors. It didn't make any difference, but at least he got an earful of the beeping every few minutes.
And Vogon informed me that diking them out would just make the whole system beep, so I am going to locate the speakers. And a hammer.