Your references show me that it is absolutely task depended.
In many domains it's true that "criticizing is easier than creating".
The best example might be books and movies, where it's trivial to say the characters were shallow, but it's surprisingly hard to create deeply interesting characters.
In Software Engineering, there are similar dynamics. An LLM with a security vuln finding prompt will be able to point out places, where the generated code might be insecure.
But if you want another LLM to find a reasoning mistake in a mathematical proof it basically has to do all the reasoning work as well. In which case I doubt there will be any significant performance gains.
In principle, Math proofs are another relatively easy to verify problem. In the extreme case, you can express any math proof as a computer-verifiable formalism — no intelligence necessary. Step back one step, and you could have a relatively weak model translate a proof into verifiable formalism and then use a tool call to run the verification. Coming up with the proof is an expensive search process, while verifying it is more mechanical. Even if it is not completely trivial to make the proof computer-verifiable, it might still be a vastly easier task compared to finding the proof in the first place.
LLM is a overloaded term now as ML models can do tool calls, or MoE segmentation can have specialized solvers embedded... but people will call all variations LLMs.
The best example might be books and movies, where it's trivial to say the characters were shallow, but it's surprisingly hard to create deeply interesting characters.
In Software Engineering, there are similar dynamics. An LLM with a security vuln finding prompt will be able to point out places, where the generated code might be insecure.
But if you want another LLM to find a reasoning mistake in a mathematical proof it basically has to do all the reasoning work as well. In which case I doubt there will be any significant performance gains.