LPisGood

I’m not sure if this counts as a nitpick, but the definition of frontier automatically includes the cheapest models

That is a very interesting idea that I have never heard anyone say. It would certainly help from a liability standpoint I assume.

Is open data just not possible because it is almost all copyright infringement? I wonder why Chinese labs haven’t dumped it at least.

Half a million dollars is a rounding error to the defense industry. If the risks were evaluated to be a national security problem, it would be trivial to do.

> But you never heard someone say "you should still code in assembly so you can understand what your compiler is doing

Any quality CS program will have you do that for a year or so, plus theory.

The minimum is achieved at a vertex, it is just also achieved elsewhere!

A linear program is a fundamental type of constrained optimization problem. It is made of two things: linear inequalities and a linear objective function.

The linear inequalities are referred to as the constraints and the set of points which simultaneously obey all inequalities is called the feasible region. The goal of the game is to find a point in the feasible region which minimizes the linear objective function. That means when you plug the coordinates of that point into the linear objective, you get the smallest value of any point in the feasible region.

A fun fact which is not so difficult to prove in 2 dimensions is that if a linear program has an optimal point (guaranteed when the constraints define a convex polytope), then the minimum objective value will be achieved at one of the vertices of the polytope.

This website lets you change the shape of the feasible region and the direction of the objective function (it is a linear function, so it’s behavior for optimization purposes is fully defined by that direction vector). It then gives you multiple famous algorithms for solving the linear program:

Simplex, for example starts at an exterior point and moves toward optimality. Dual simplex will start at a point with optimal objective and move towards feasibility, etc.

This is very cool. I wish there was a little more information while running each algorithm. Saying the update rule and being able to tick “next iteration” or something would be interesting.

Simplex is there.

Minor updates can provide substantial improvements sometimes, it really depends on the specifics.

What if those “cost implications” are just asking Opus 6.7 to fix whatever issue cropped up?

Yes. This is how this works.

Any proof which is correct can be formalized. That is what is means for a proof to be correct.

I’m not sure why you are restricting the scope of our discussion to what _Lean_ can(not) formalize. Even if we do choose to do that for some reason, Lean is not a formal system of fixed axioms; it supports optional additional axioms.

If a theorem has a published proof, it is either formalizable or incorrect.

My assumption is that it is there to make the process less convenient so people only use it if they really need to.

That’s why it makes sense. It’s not evidence though. I was looking for investment numbers, papers, blog posts, etc.

This makes sense, but what evidence is there that this is true?

You can be linear in the bit length of the input number, but exponential in the magnitude.

This is a common thing in complexity, and I think even the abstract says it is talking about “length n” and not “magnitude n”

Turing machines are good for computability but not great for complexity.

Sometimes I think about the infrastructure projects that could’ve been done instead of a war in Afghanistan and Iraq and Iran.

It’s shocking really how wasteful the leaders of the United States can be.

That would not be without precedent. When we decided that certain internet platforms were too big to moderate, we let them get away with hosting all kinds of illegal content.

I really don’t think that’s true. When I get a 50% off coupon in the mail, I am expecting it to work as stated and it pretty much always does.

It is definitely self-motivated. People want to read and interpret these results.

That is exactly what I’m trying to say. The findings are of such such a quality that it would not make sense to ignore them wholesale.

That’s why it doesn’t make sense to present AI companies as dumping or burdening the scientific community into doing labor for them; the scientific community is self motivated to do so.

They should certainly be allowed to share their findings. No one is forcing scientists and mathematicians to review the findings in general. It’s just the case that the findings are of such such a quality that it would not make sense to ignore them wholesale

The money he got came from the same shared pool that the other artists get money from.

That may be true by itself. However, misleading and inauthentic speech to make money is fraudulent and illegal.

He was doing it fraudulently to make money.

Claude, and other American models, are heavily subsidized by investors (and the United States government).

I think we’re no where near a physical information theoretic limit.

A signature for the purpose of displaying a signature or for parody/as part of the art is different from the purpose of a signature for attribution.