It fascinates me that there's something like this in something as solid and rigid like matrix multiplication. What causes something so rigid to break apart and "leak" at very large scale? Why does the "optimization" appear to be very, very small? Why does galactic algorithm exists? I can't imagine long division suddenly breaking apart after a billion digit, the structure seems very stable? I have heard before that matrix multiplication is apparently optimize-able at very, very large scale.
Does anyone have an intuition to what causes it? What happens at these large scale (or very small)?
One way to think about it is that the classical algorithms are the ones that are fast for small numbers. Galactic algorithms often work for small inputs, it's just that to be faster you need big inputs. A common case of this is a requirement that log(n)<
The other crucial part to this is the ability to actually encode and test the theorem (via Lean).
Otherwise, we would be swarmed with a billion lines of theorems that no one will be able to ever understand and verify anyway.
A majority of these proofs have not been formally verified yet, I think people are overstating how important lean is to the success of LLMs in mathematics.
A paper and a lean proof are always going to be better than just a paper. I think mathematicians generally will not read AI math papers that haven't already been verified, especially since we're about to see a ton more AI math papers. Lean will remain important
Are there any AI generated proofs that are simple enough to be verified quickly by a human, that have not been lean verified? Or are they all basically incomprehensible?
The approximation of edit distance result [1] seems pretty readable to me, but the learn proof is still incomplete [2]. It's certainly much less readable than a good human written proof but it's certainly better than the last generation of AI proofs.
Yeah! They forgot to put a .5 after it! What an idiot! Just imagine if they would have written a 4!?!? We may have had to ban them from the website entirely.
Uhhh, it has always been the case. This libertarian idea of every man for himself is a sickening concept that does not work at scale. You are going to get psychopaths that genuinely does not need other people, then what do you do? He's just exercising his free will and rights after all.
I am having a brain aneurysm trying to understand this
> Regulating gun ownership is exactly regulating the application. In your analogy, the gun is the AI. What you can do with the gun is the application.
From what I can tell, you are arguing that gun laws is reasonable.
> Different actors with different credentials in different contexts will have different requirements and permissions of what they can do with the technology, be it a gun or AI.
But this, is going against that, this is saying, "why should we ban AI or gun when they can be used for both good and bad. What we want is to ban bad, regardless of how it is achieved"
There are levels to it as well. Take alcohol and driving, for example:
Level A: Who can drink it (possession and consumption law)
Level B: What you can do while drunk (DUI law)
Level C: What you can do while drinking (open container law)
All orthogonal to things like reckless driving, endangerment and creating injurious accidents, which are already criminalized without needing additional laws against alcohol use to enforce them.
> From what I can tell, you are arguing that gun laws is reasonable.
Correct.
> But this, is going against that, this is saying, "why should we ban AI or gun when they can be used for both good and bad. What we want is to ban bad, regardless of how it is achieved"
Not at all. I'm saying regulations do that and they are a good thing. Not everybody can own an assault rifle. Some of the people who can, are not allowed to carry it on the streets. Police will have very different regulations towards their gun use. The army, another set of regulations. The list goes on. Even in countries who have lax gun laws, usually not all guns are allowed to everyone in all situations. No one is allowed to carry a nuke into a shopping centre.
Note that regulating and banning are very different things. I don't think you can fully ban guns or AI.
> From what I can tell, you are arguing that gun laws is reasonable.
You aren’t going to repeal the second amendment, so reasonable or not it’s a fact that everyone has to contend with. Do we all want guns? No. Do we all want AI? Also no.
> What we want is to ban bad, regardless of how it is achieved
No, we don’t want to ban bad. Banning doesn’t really work - the effort to reward ratio isn’t great. We want to regulate bad and see if we can minimize the damage it can do.
"Different actors with different credentials in different contexts"
The argument is that the military or police have a need for access to guns, whereas the lunatic on the street corner (or any random citizen) does not. The same argument applies for access to nuclear, biological, or chemical weapons... or autonomous hacking/killing machines...
> I have to disagree here. People who are really into agentic coding like to say/believe this, but come on, it's not rocket science! You literally ask the agent to do something and it does it, that's it. As long as you use a recent model it will do it really well regardless of how fancy your prompt is. There's no moat here, anyone can do it. Your job will be gone and so will mine.
Sure, the skill of writing beautiful for loops and recursive binary search tree is basically worthless, but software is written for a purpose. That purpose is not gone. People will keep wanting POS system, accounting system, lawyers, manufacture stuff, personal assistant, etc etc
If this is true, you would think that companies would be opening shops in the middle of (some shithole country) so they can make money (or someone else would grab it). But they don’t, why is that?
Referring to countries as "shithole countries" does not help in understanding the current dynamic between rich and poor nations. So perhaps it is helpful to understand what that is, without the pejoratives.
Firstly, each country is different. So the relationship between say the USA and Mexico is different to the relationship between the USA and say Ethiopia.
By "richness" we might also be better off thinking as less "spare cash" and more "standard of living". Which includes food, housing etc but also security, safety etc.
In truth much of the US "richness" depends on other nations. If there was no Latin labor the US would have a fresh produce problem. Indeed the very premise of DJT is that the US has a trade deficit with just about everyone. Much of US "richness" is thus dependent on the "poorness" of others.
Yes automation, cheaper energy, AI can reduce the labor content of goods and make them universally cheaper. Yes I believe in a future where the overall standard of living increases.
But it would be a mistake to believe the US is "leading" US there. The US achieved its current position at the barrel of a gun, and uses the military (and threat of military) to interfere with countries and regions either overtly or covertly. The entire premise of the cold war (outside of western europe) was premised on interventions to resist countries switching their political model to something the locals preferred.
And yes, maybe the locals preferred wrong. But the US didn't promote democracy, they promoted "willingness to keep supplying us". Countries which were leaning away from the US had to be punished. (Shah in Iran, Vietnam etc.)
I could go on, but I'll stop there. Suffice to say that an equitable standard of living is not in the (current) interest of most US citizens.
Exactly, it is already priced in. Try setting up shop in the middle of some really bad country and you will soon realize why food is not getting there.
The companies do not do this, because equal distribution of resources is poison to capitalism. The world where everyone are fed, and their basic needs - shelter, medication etc. - are taken care of, does not have trillionaires. Possibly not even billionaires.
It is not profitable to give people humane standards of living. You work a lot harder when you see the homeless on the street on your way to work.
I have this same problem. I am not sure if medication will help but I really don't want to go there. My brain is a scattered mess. Even now, I am doing 3 other things at the same time. Is it a matter of "getting good" and just focus? I just don't think there's a secret technique to this.
Does anyone have an intuition to what causes it? What happens at these large scale (or very small)?
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