Very interesting! Thanks for the reply. I wonder if they tried these other solvers and decided they were either too slow b/c their problems were too small or the answers were too inaccurate
679 karma · joined September 16, 2019
For example, I also didn't remember why you needed a determinant in the equation you linked so I made a simple example and saw the determinant was there to keep the density normalized, (i.e the indefinite integral of the density = 1).
In this case, the simple example I used was a distribution q0(x) = 1 where x>=0 and x <= 1 (zero elsewhere) and scaling transformation y = ax
In a way it makes perfect sense that gpt4 can score 100% on a test gpt4 also grades. To be clear the grading gpt4 has the answers so it does have more information but it still might overlook important subtleties in how the real answer differs from the generated answer due to it's own failure to understand the material.
Regardless this answer does not responded to the parent comment's question at all since all of these papers are about radiance fields.
1. P = NP refers to a two very specific sets of problems (which might actually be the same set) not any general question. There are problems that we know don't fall into P or NP, (for example the Halting Problem). Also whether or not P=NP is an open question almost the opposite of a fact.
2. You claim: "Evaluating if an answer is correct or not is easier than coming up with a correct answer from scratch." This is the right idea but not quite correct.
The correct statement is as follows: "Evaluating if an answer is correct is not harder than the difficulty of coming up with a correct answer from scratch."
This is because evaluating some answer can still be just as hard as the original problem. In fact sometimes it's uncomputable (if the original problem is also uncomputable). To use an example from above consider the question: "Does a program x halt?" If I tell you "no" it could be impossible to verify my answer unless you have solved the halting problem.
To bring this back to reality, again if GPT-4 is wrong about some complex medical question it doesn't mean it's mathematically easier to figure that out than solving the problem from scratch.
Now you could make the argument that these functions are close enough most of the time so it won't matter but unless you want to get really rigorous that's more of a stats / engineering perceptive not mathematics. Any more importantly that's very up for debate, especially in a high pressure situation like medicine.
Of course these models are wild and I'm quite impressed with them. I still can be worried about the damage someone who doesn't think things through could cause by assuming GPT-4 has human or super human level intelligence in a niche, high impact field.
Here's the problem statement as far as I see it: Each tile has a number of move points to spend to go through it (1 for regular and 2 for water). Each tile also has a cost associated with it. Given a max number of move points find the lowest cost path between two tiles or return none if no such path exists.
I'm gonna say this is still modified dijkstra with a small twist. The fire has cost 1, the other tiles have cost 0. However instead of pathing on a 2d grid (x, y) we path on a 3d grid (x, y, moves). All "goal" tiles within (goal_x, goal_y, moves < total_move_points) have a 0 cost edge which brings them to the true goal node. The implementation difference is that the get neighbors function queries neighbors in later grid layers (x+..., y+..., moves + 1 or 2)