I've reached for this solution many times too; it's certainly convenient.
What I don't like is that all the resulting pages look the same. It's so easy to tell when a page is authored by Claude, and by now, I get the same “ugh another one” feeling as Dall-E generated images would give when they were completely overdone.
Maybe it's just be, but if not, maybe HTML generated outputs will also end up being dialed down from where they're at now.
But maybe not, since it's obviously a useful thing to be able to do. I wonder if there's a way out. To be able to introduce some natural entropy so not everything ends up looking the same. I guess not, since we're using machines whose natural mode of behavior is regression toward the mean. And maybe having it be harder to tell the author wouldn't even be desirable anyway.
It would be very helpful to know in understanding the capabilities of the models; and in getting intuition about where they are best applicable.
If the reason it was able to output the proof is that it happened to be included in an in-house university report written in Georgian, then that would make it less useful for research than if it's new entirely.
The XOR swap trick also features in the compilation/synthesis of quantum algorithms, where the XOR instruction (in the form of a CNOT gate) is fundamental in many architectures, and where native swapping need not be available.
One extension that I ran into, and which I think forms a nice problem is the following:
Just like the XOR swap trick can be used to swap to variables (and let's just say that they're bools), it can be extended to implement any permutation of the variables: suppose that the permutation is written as a composition of n transpositions (i.e., swaps of pairs), and that is the minimal number of transpositions that let's you do that. Each transposition can be implemented by 3 XORs, by the XOR swap trick for pairs, and so the full permutation can be implemented by 3n XORs. Now here's the question: Is it possible to come up with a way of doing it with less than 3n, or can we find a permutation that has a shortcut through XOR-land (not allowing any other kinds of instructions)? In other words, is XOR-swapping XOR-optimal?
I'm not going to spoil it, but only last year a paper was published in the quantum information literature that contains an answer [0]. I ended up making a little game where you get to play around with XOR-optimizing not only permutations, but general linear reversible circuits. [1]
I don't remember if it's ever explicitly stated, but I certainly took that to be the implication. Maybe it's actually funnier if they're doing it pro bono, now I am suddenly unsure.
Just to not feed the witch hunt further, note that human 30 second solve times can be entirely possible for the easiest puzzles, with enough experience, practice, and a bit of risk-taking; see e.g. https://adventofcode.com/2021/leaderboard/day/1 part 1. But the 4 second solution times we saw last year are not, no matter how you look at it.
What I don't like is that all the resulting pages look the same. It's so easy to tell when a page is authored by Claude, and by now, I get the same “ugh another one” feeling as Dall-E generated images would give when they were completely overdone.
Maybe it's just be, but if not, maybe HTML generated outputs will also end up being dialed down from where they're at now.
But maybe not, since it's obviously a useful thing to be able to do. I wonder if there's a way out. To be able to introduce some natural entropy so not everything ends up looking the same. I guess not, since we're using machines whose natural mode of behavior is regression toward the mean. And maybe having it be harder to tell the author wouldn't even be desirable anyway.
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