This is not about finding the most effective solution, it’s about showing that they “understand” the problem. Could they write the algorithm if it were not in their training set?
That's an interesting question. It's not the one they are trying to answer, however.
From my personal experience: yes, if you describe a problem without mentioning the name of the algorithm, an LLM will detect and apply the algorithm appropriately.
They behave exactly how a smart human would behave. In all cases.
It's hard. But usually we ask several variations and make them show their work.
But a human also isn't an LLM. It is much harder for them to just memorize a bunch of things, which makes evaluation easier. But they also get tired and hungry, which makes evaluation harder ¯\_(ツ)_/¯
If we're talking about solving an equation, for example, it's not hard to memorize. Actually, that's how most students do it, they memorize the steps and what goes where[1].
But they don't really know why the algorithm works the way it does. That's what I meant by understanding.
[1] In learning psychology there is something called the interleaving effect. What it says is that you solve several problems of the same kind, you start to do it automatically after the 2nd or the 3rd problem, so you stop really learning. That's why you should interleave problems that are solved with different approaches/algorithms, so you don't do things on autopilot.
Yes, tests fail in this method. But I think you can understand why the failure is larger when we're talking about a giant compression machine. It's not even a leap in logic. Maybe a small step
From my personal experience: yes, if you describe a problem without mentioning the name of the algorithm, an LLM will detect and apply the algorithm appropriately.
They behave exactly how a smart human would behave. In all cases.