I appreciate the links, but these are all about how to efficiently process an audio sample for a signal of choice.

Your stumbling block seemed to be that you didn’t understand how it was possible, so I was trying to explain that, but I may have done a poor job of emphasizing why the technique I described matters. When you said this in a previous comment:

I do think that they’re not just throwing away the other fish, but putting them into specific baskets.

That was a misunderstanding of how the technology works. With a keyword spotter (KWS), which all smartphone assistants use to detect their activation phrases, they they aren’t catching any “other fish” in the first place, so there’s nothing to put into “specific baskets”.

To borrow your analogy of catching fish, a full speech detection model is like casting a large net and dragging it behind a ship, catching absolutely everything and identifying all the fish/words so you can do things with them. Relative to a KWS, it’s very energy intensive and catches everything. One is not likely to spend that amount of energy just to throw back most of the fish. Smart TVs, cars, Alexa, they can all potentially use this method continuously because the energy usage from constantly listening with a full model is not an issue. For those devices, your concern that they might put everything other than the keyword into different baskets is perfectly valid.

A smartphone, to save battery, will be using a KWS, which is like baiting a trap with pheromones only released by a specific species of fish. When those fish happen to swim nearby, they smell the pheromones and go into the trap. You check the trap periodically, and when you find the fish in there, you pull them out with a very small net. You’ve expended far less effort to catch only the fish you care about without catching anything else.

To use yet another analogy, a KWS is like a tourist in a foreign country where they don’t know the local language and they’ve gotten separated from their guide. They try to ask locals for help but they can’t understand anything, until a local says the name of the tour group, which the tourist recognizes, and is able to follow that person back to their group. That’s exactly what a KWS system experiences, it hears complete nonsense and gibberish until the key phrase pops out of the noise, which they understand clearly.

This is what we mean when we say that yes, your phone is listening constantly for the keyword, but the part that’s listening cannot transcribe your conversations until you or someone says the keyword that wakes up the full assistant.

My question is, how often is audio sampled from the vicinity to allow such processing to happen.

Given the near-immediate response of “Hey Google”, I would guess once or twice a second.

Yes, KWS systems generally keep a rolling buffer of audio a few seconds long, and scan it a few times a second to see if it contains the key phrase.