Asymmetry of verification and verifier's law

Summary

Asymmetry of verification is the idea that some tasks are much easier to verify than to solve. With reinforcement learning (RL) that finally works in a general sense, asymmetry of verification is becoming one of the most important ideas in AI. Understanding asymmetry of verification through examplesAsymmetry of verification is everywhere, if you look for it. Some prime examples:Sudoku and crossword puzzles take a lot of time to solve because you have to try many candidates against various constraints, but it is trivial to check if any given solution is correct.Writing the code to operate a website like instagram takes a team of engineers many years, but verifying whether the website is working properly can be done quickly by any layperson.Solving BrowseComp problems often requires browsing hundreds of websites, but verifying any given answer can often be done much more quickly because you can directly search if the answer meets the constraints.Some tasks have near-symmetry of verification: they take a similar amount of time to verify as to write a solution. For example, verifying the answer to some math problems (e.g., adding two 900-digit numbers) often takes the same amount of work as solving the problem yourself. Another example is some data processing programs; following someone else’s code and verifying that it works takes just as long as writing the solution yourself.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 (cue Brandolini's law: “The amount of energy needed to refute bullshit is an order of magnitude bigger than that needed to produce it.”). Many scientific hypotheses are also harder to verify than to come up with. For example, it is easy to state a novel diet (“Eat only bison and broccoli”) but it would take years to verify whether the diet is beneficial for a general population.Improving asymm...