You can definitely do arbitrary work as a sort of proof of work. Not quite the same mathematically, but pragmatically similar. The key is building in some redundancy/error-correction and ensuring that a single node can't by itself define "correctness" of a solution. You do that by duplicating work across nodes, distributing chunks randomly and rejecting/rerunning disagreeing results. It's also pretty easy to spot bad actors trying to cheat on their computational work in this scenario.
I don't think it's that easy at all. The work function must be cheap and canonical to check, and the consensus algorithm has to be rigorous, or else it's too easy to attack the security of the network. DoS, Sybil, 51%, social takeover via hard fork, the list goes on...
It has a well define loss function with a numerical value. The improvement of this value can be a type of difficulty. Check some other comments I’ve made on this post for how it might work.
It's an interesting idea for sure, but loss doesn't go down forever. I think this ends with a highly overfitted network that grinds to a halt as the loss function hits local minima.
Even if you get past that, there's no consensus mechanism or finalization as it stands, and validating solutions is relatively expensive.
We only just started thinking about this and I suspect these issues are solvable in a protocol. For instance using cross validation there must be a distributed protocol to control over fitting.
I’m not sure validation is so expensive if the data is small enough. Actually maybe that’s a way to approach this, two type of block that are paired and share the rewards in some way. One that proposes better a better splice of weights and another that proves they are better out of sample.
Give it a few weeks and with GPT-4s help I think we can find some promising approaches.
