[Dejobism]

That would be nice. But I’m not from a great school and don’t have a lot of published research (co-authored a few papers where I wasn’t the main contributor). I thought maybe that would be a better choice in a few years with a better CV.

[shipwright]

That's not necessarily a deterrent :) it really depends where, also would you consider staying in the states for it? Because I know of some reputable places (west coast mostly) where pretty much if you are to the right person's liking and fit their requirements, your admission won't see objections- there's plenty of time to make a decision about it, because the applications (iirc) take place a bit before* the end of the year. Let me know if you need more details!

[Dejobism]

I really should have mentioned that I’m not American, I just want to work there in the future.

Point taken about selection though! I’m thinking I could network with academics while working on implementing papers, etc.

Do you think the selection situation is different for foreigners? Do you know if the same is true about European schools? The 3-year average for PhDs in Europe really looks more attractive to me.

Also would really appreciate if you could tell me more about how these programs select people who aren’t 4.0 students from a top school with famous recommendations. Is practice important, should you know a lot about current SOtA, do you need to show math proficiency?

[shipwright]

Good thinking, and regarding Euro institutions there's lot of regional differences- for instance, brits have steps to take which are pretty set in stone with the Centres for Doctoral Training; basically it's the opposite of the process from the prior comment, it's the system that allocates someone for you. Denmark is free if you're native or from EU- Finland however is free for all (according to peers and the net) and would gauge they're both tad more flexible than UK in terms of requirements. Anyway, there's plenty options! Regarding the selection process, although they're a clear benefit perfect grades aren't a must and it's alright to be from outside of a top ranking school- but you'll have to bring something to the table to make up for it. Whether that is a solid paper, practical achievements along recommendations or whatever again depends on the place. I think there's just so many ways to show something that can be impressive without knowledge about the latest thing or dropping walls of equations for the sake of it haha. Best of luck!