Asymmetry of verification and verifier's law

https://www.jasonwei.net/blog/asymmetry-of-verification-and-verifiers-law

by polrjoy • 1 year ago

17 8 1 year ago

jasonwei.net

b0gb• 1 year ago

Hmm, no reference to the famous P vs NP problem…?

aleph_minus_one• 1 year ago

Or classes related to NP for which we also don't know the answer, such as TFNP

https://en.wikipedia.org/wiki/TFNP

"TFNP is the class of total function problems which can be solved in nondeterministic polynomial time", i.e. we don't consider decision problems (as for NP), but total functions.

This class contains quite some interesting subclasses, such as PLS (solution can be found via Local Search), PPA (solution exists because of a Parity Argument), PPP (solution exists because of a Pigeonhole Principle), PPAD (solution exists because of a Directed Parity Argument), CLS, ...

In interesting article which explains this topic quite well is https://inference-review.com/article/when-existence-is-ineff...

weinzierl2• 1 year ago

"Interestingly, there are also some tasks that can take way longer to verify than to propose a solution. For example, it might take longer to fact-check all the statements in an essay than to write that essay."

I think this point is odd. If you could really come up with a proper solution (a correct essay in this case) faster than to verify it then why not produce the correct solution directly instead of verifying.

And if you argue, but I don't want a different correct essay but I want this one verified my answer is that the corrected essay without flaws is also a different one.

beart• 1 year ago

I think I might be confused by what you are stating. Are you saying it depends on your definition of "correct"? I think in this case, "verifiable" is what is meant by "correct", and in which case, if you can't verify it, by definition, it can't be correct, right?

weinzierl2• 1 year ago

Verifiable means you can find a proof that a solution is correct. I am stating that the effort to find this proof can never be more effort than constructing the solution in the first place.

I think where the line of argumentation in the article derails is that the author confused finding a solution with coming up with any odd candidate that could be a solution. The former is serious effort, the latter is trivial. Their Sudoku example is the former, their article example the latter

AlotOfReading• 1 year ago

In this essay I propose that P != NP...

jkaptur• 1 year ago

This essay would benefit from results from computational complexity.

P vs NP, of course, but also the halting problem and Rice's theorem: non-trivial semantic properties of programs are undecidable.

In other words, if you say "this is the solution to that sudoku puzzle", that's easy to verify. "This sudoku puzzle has a solution" is almost certainly much harder to verify. "Here's a program that can solve any sudoku puzzle - impossible (in general).

visarga• 1 year ago

The ease of training AI to solve a task is proportional to how verifiable the task is. All tasks that are possible to solve and easy to verify will be solved by AI.

I've been saying this for years. Especially related to predictions like "AGI in N years".. no, it will come a different speeds per domain. All proportional to the scale of verification.

Verifiable domains are usually math and code. Games also fit the bill. But for real world tasks there is the 1B people using AI, we verify, the signal is there implicit in the chat logs.

Asymmetry of verification and verifier's law

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