If only. Then those CPU cycles would at least have been doing something of value. If you look at crypto mining computations they don't (on the chains I have looked at) actually compute anything meaningful at all. It's literally just generating random numbers and then (almost always) throwing them away.

Like you have Alice who says "Try to guess my number?", and then Bobs around the world go

Bob1: "Is it 13?" Alice: "no" Bob2: "Is it 4672?" Alice: "no" ... Bob175432: "Is it 294762483492643826432862834??" Alice: "Yes. You can do the next block."

Literally that pointless.

This can be used to create the world's largest rainbow table though.

If we're already into unlikely conspiracy uses of crypto, this could have been an NSA Sigint@Home endeavour

Can someone explain why there isn't a blockchain that is powered by users hardware training LLM models all day? Like the worlds best open source trillion parameter model.

Noone has built it and that's because it would be hard to satisfy the needs of a consensus mechanism and also do useful real work.

To understand why that is, you need to understand why they are doing all this generating random numbers nonsense in the first place. They are doing this to establish distributed consensus. You have some chain of blocks b_1... b_2 ... b_3. To make the next block you want to put a bunch of transactions together, calculate their hash and mint it, but there's a problem: In a distributed system, who gets to decide what goes into the block? We all need to agree what b_4 is otherwise the system loses consensus. We can't have me publishing something and calling it b_4 and you publishing something and calling it b_4. The way the "proof of work" mechanism does this is by everyone guessing random numbers until someone chooses the right number at which point that person has the right to mint b_4.[1]. If you wanted that computation (instead of being just choosing random numbers) to do something useful, you'd have to figure out a way to decide what the correct number is without knowing it beforehand. Otherwise you might train your ML model just fine but your computation couldn't be used to establish who gets to mint the next block so wouldn't work in a proof of work consensus algorithm.

People have done this with distributed computations where doing the computation is hard but checking the computation is easy. For example finding large Mersenne primes, is extremely expensive but once you have a big number, checking whether or not it is a Mersenne prime is very cheap. But training an ML model isn't that kind of computation.

[1] Proof of stake just picks who gets to do it randomly from a pool of people who have staked, which is why it is so much more efficient.

Right but making new models costs millions of dollars and weeks of time.

And that's just for a single model.

With distributed users they could be generating those new models all of the time doing highly computational work.

The point isn