3 ms·

It may genuinely be the case that slower humans are not generally intelligent. But that sounds rather snobbish so it's not an opinion I'd like to express freque

It may genuinely be the case that slower humans are not generally intelligent. But that sounds rather snobbish so it's not an opinion I'd like to express frequently. I think the complaint made by apple is quite logical though and you mischaracterise it here. The question asked in the Apple study was "if I give you the algorithm that solves a puzzle, can you solve that puzzle?" The answer for most humans should be yes. Indeed, the answer is yes for computers which are not generally intelligent. Models failed to execute the algorithm. This suggests that the models are far inferior to the human mind in terms of their computational ability, which precedes general intelligence if you ask me. It seems to indicate that the models are using more of a "guess and check" approach than actually thinking. (A specifically interesting result was that model performance did not substantially improve between a puzzle with the solution algorithm given, and one where no algorithm was given.) You can sort of imagine the human mind as the head of a Turing Machine which operates on language tokens, and the goal of an LLM is to imitate the internal logic of that head. This paper seems to demonstrate that they are not very good at doing that. It makes a lot of sense when you think about it, because the models work by consuming their entire input at once where the human mind operates with only a small working memory. A fundamental architectural difference which I suspect is the cause of the collapse noted in the Apple paper.

GrayShade 1y ago
I think a human will struggle to solve Hanoi using the recursive algorithm for even 6 disks, even given pen and paper. Does that change if you give them the algorithm description? No. Conversely, the LLMs already know the algorithm, so including it in the prompt makes no difference.
- thaumasiotes 1y ago
  > I think a human will struggle to solve Hanoi using the recursive algorithm for even 6 disks, even given pen and paper. Why? The whole point of the recursive algorithm is that it doesn't matter how many discs you're working with. The ordinary children's toys that implement the puzzle are essentially always sold with more than 6 discs. https://www.amazon.com/s?k=towers+of+hanoi https://www.amazon.com/s?k=towers+of+hanoi
  - GrayShade 1y ago
    The recursive solution has a stack depth proportional to the number of disks. That's three pieces (two pegs and how many disks to move) of data for each recursive call, so for 6 disks the "stack" will contain up to around 15 values, which is generally higher than an unaided human will be able to track. In addition, 64-256 moves is quite a lot and I suspect people will generally lose focus before completing them.
    - thaumasiotes 1y ago
      You should try playing with one of the toys. It's not at all difficult to move 7 of them. It's not necessary to use a stack. If you have a goal, you can work "top down", with nothing held in memory. All you need to know to begin the move is whether you're moving an odd number of discs (in which case, the first move will be onto the target peg) or an even number (in which case it will be onto the third peg).
      - GrayShade 1y ago
        Yes, I'm aware of the iterative solution, which is why I explicitly mentioned the recursive one. They tried to give the algorithm description to the LLMs, but they also used the recursive solution (see page 25 of the paper).
        thaumasiotes 1y ago
        What do you think a human using the recursive solution looks like? If you ask someone how the puzzle works, they're overwhelmingly likely to tell you: "To move disc 7, first you move discs 1-6 to the third peg, then you move disc 7[, and then you can put discs 1-6 back on top of it]." This is an explicitly recursive statement of the solution. But the implementation is just that you count down from 7 to 1 while toggling which peg is "the third peg". You can optimize that further by dividing 7 by 2 and taking the remainder, but even if you don't do that, you're using constant space. What would a human be doing (or thinking) differently, if they were using the recursive algorithm?
    - 1y ago

GrayShade 1y ago

I think a human will struggle to solve Hanoi using the recursive algorithm for even 6 disks, even given pen and paper. Does that change if you give them the algorithm description? No. Conversely, the LLMs already know the algorithm, so including it in the prompt makes no difference.

thaumasiotes 1y ago
> I think a human will struggle to solve Hanoi using the recursive algorithm for even 6 disks, even given pen and paper. Why? The whole point of the recursive algorithm is that it doesn't matter how many discs you're working with. The ordinary children's toys that implement the puzzle are essentially always sold with more than 6 discs. https://www.amazon.com/s?k=towers+of+hanoi https://www.amazon.com/s?k=towers+of+hanoi
- GrayShade 1y ago
  The recursive solution has a stack depth proportional to the number of disks. That's three pieces (two pegs and how many disks to move) of data for each recursive call, so for 6 disks the "stack" will contain up to around 15 values, which is generally higher than an unaided human will be able to track. In addition, 64-256 moves is quite a lot and I suspect people will generally lose focus before completing them.
  - thaumasiotes 1y ago
    You should try playing with one of the toys. It's not at all difficult to move 7 of them. It's not necessary to use a stack. If you have a goal, you can work "top down", with nothing held in memory. All you need to know to begin the move is whether you're moving an odd number of discs (in which case, the first move will be onto the target peg) or an even number (in which case it will be onto the third peg).
    - GrayShade 1y ago
      Yes, I'm aware of the iterative solution, which is why I explicitly mentioned the recursive one. They tried to give the algorithm description to the LLMs, but they also used the recursive solution (see page 25 of the paper).
      - thaumasiotes 1y ago
        What do you think a human using the recursive solution looks like? If you ask someone how the puzzle works, they're overwhelmingly likely to tell you: "To move disc 7, first you move discs 1-6 to the third peg, then you move disc 7[, and then you can put discs 1-6 back on top of it]." This is an explicitly recursive statement of the solution. But the implementation is just that you count down from 7 to 1 while toggling which peg is "the third peg". You can optimize that further by dividing 7 by 2 and taking the remainder, but even if you don't do that, you're using constant space. What would a human be doing (or thinking) differently, if they were using the recursive algorithm?
  - 1y ago