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
Neat article. I do wish it mentioned that there are polynomial time algorithms to solve linear programming problems. According to the Google ortools docs it has the option to use those as well (but not with the GLOP solver). Might be good for when simplex is struggling (https://developers.google.com/optimization/lp/lp_advanced)
This might not be the right place for this question but, as someone who has made a couple very modest mps backend contributions, I'm curious why not add metal support to triton (or a fork if openai won't allow it) rather than maintain a whole separate backend?
It's also been a while since I had to flex my math muscles and they are quite flabby. I recommend reading things like this slow, they are written by people who know the field forward and backward and aren't supposed to be trivial. If you aren't in the field you got to be a little bit of an active reader.
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
As noted by the current top comment (https://news.ycombinator.com/item?id=36544024) this is a small part of a dump of all files found during the Bin Laden compound raid that is publicly available on the CIA's website. Check the url to verify that claim. There is no other reason this content is there, it's just a coincidence.
Great analysis, props to these students for taking the time to challenge such a sensational headline. In the conclusion they mention my biggest problem with the paper which is that it appears gpt4 grades the answers as well (see section 2.6 "Automatic Grading").
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.
while nerf.studio is impressive, the parent comment is asking about radiance field free methods. NeRF stands for Neural Radiance Fields and all of the algorithms in that repo use radiance fields
To clarify for people who don't follow NeRF techniques, this research is not prompt based. The algorithm is capturing the 3d scene from real life images. There is some super promising work in mixing NeRF based techniques with various generative models to create 3d objects from prompts but it doesn't seem close to creating anything of this kind of scale / detail yet. I do agree this is a future possibility though.
A few of the comments in this thread seem to be misusing mathematics in order to lend more credence to themselves. At the risk of responding to low quality flamebait here are some problems with your statements.
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.
This analogy does not make sense to me. We do not have equivalence between all of the infinite inputs and outputs here, we have equivalence in a finite number of cases and known cases where the two functions (human output and llm output) diverge drastically. Any mathematician worth their salt would tell you these functions are definitely not equal.
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.
Since this is the comment thread talking about the algorithm I'm gonna add my 2 cents here:
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)
Wow some of these comments seem harsh. The author isn't claiming to have invented these techniques and it's cool to see them being applied in the "real world" to save money.
I would guess combining pieces of two images is a simple place where the graph could become non linear. Agree that if that is the case they should indicate it in their gifs tho
From friends I've had who have made the jump, learn a game engine (unity / unreal / etc), make some small games (can be for a game jam or whatever) to put on a portfolio and mass apply to lots of different companies of many sizes. You may have to take a job title hit (i.e going from senior -> junior) / large pay cut.
Neat post! I'd be curious to see some simple examples of each what the slow queries looked like. It seems to my limited knowledge they attempted to use row based dbs / mongo for column based workloads then saw a large perf boost after switching to Clickhouse.
Generally I find that shallowly learning topics adjacent to the areas I know deeply works best but trying to glean the idea of topics way outside of my understanding (i.e quantum physics) does not end well for me.