I do actually believe AI will increase productivity. But productivity alone doesn't produce money. In our civilization, money can only be created by the government. When it does this, the value of each dollar decreases.
The fundamental problem is that UBI is at its core, a redistribution of money. It goes *from* those who have it, *to* those who need it. Those who have money, don't make enough to give everyone a UBI, even if *all* of their income goes to fund UBI. So let's say we have the government create more money to make up the shortfall. Now we have an inflation problem. Argentina is a shining example of how this works, experiencing more than 100% inflation per year, when its government tried to pay its obligations by "printing money."
The average per-person income in the US is about $43K per year. Let's say we take all the income over $43K, and give it to people who make less than $43K, to make everything equal. That would be the theoretical limit to what UBI could do, and $43K does seem pretty basic. Now, the problem is, all those people who make more than $43K by busting their butts and doing what it takes to earn more--they will no longer be motivated to bust their butts and earn more. Human nature says they will do exactly how much they are required to do. Or at least, the vast majority will not be motivated to make more money that they cannot keep. Now, that $43K starts to erode, because the rich aren't rich any more and don't care about all that extra effort. Oh, and we're just talking about income, and neglecting to pay for infrastructure or defense, every single dollar is going to redistribution.
No, the math doesn't work out, productivity or not.