Comment by itkovian_ | Hacker News Reader

Comment by itkovian_ | Hacker News Reader

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Here's an example of the type of question it is acheiving 20% on;

The set of natural transformations between two functors F,G ⁣:C→DF,G:C→D can be expressed as the end Nat(F,G)≅∫AHomD(F(A),G(A)). Nat(F,G)≅∫A HomD (F(A),G(A)).

Define set of natural cotransformations from FF to GG to be the coend CoNat(F,G)≅∫AHomD(F(A),G(A)). CoNat(F,G)≅∫AHomD (F(A),G(A)).

Let: - F=B∙(Σ4)∗/F=B∙ (Σ4 )∗/ be the under ∞∞-category of the nerve of the delooping of the symmetric group Σ4Σ4 on 4 letters under the unique 00-simplex ∗∗ of B∙Σ4B∙ Σ4 . - G=B∙(Σ7)∗/G=B∙ (Σ7 )∗/ be the under ∞∞-category nerve of the delooping of the symmetric group Σ7Σ7 on 7 letters under the unique 00-simplex ∗∗ of B∙Σ7B∙ Σ7 .

How many natural cotransformations are there between FF and GG?

As someone who doesn't understand anything beyond the word 'set' in that question, can anyone give an indication of how hard of a problem that actually is (within that domain)?

Also I'm curious as to what percentage of the questions in this benchmark are of this type / difficulty, vs the seemingly much easier example of "In Greek mythology, who was Jason's maternal great-grandfather?".

I'd imagine the latter is much easier for an LLM, and almost trivial for any LLM with access to external sources (such as deep research).

btw isn't this question at least really badly worded (and maybe incorrect?) the definitions they give for F and G are categories not functors... (and both categories are in fact one object with contractible space of morphisms...)

That's easy Dave: 42.

Do we actually know whether it got this specific example right? It got 20% on HLE, but I think a few questions are quite a bit easier.

It's very interesting to think about what kind of "mental model" might it have, if it's capable of "understanding" all this (to me) gibberish, but is then unable to actually work the problem.

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