jeremysalwen

It is not weird to call something by the name of something that is much more widely known, that it is closely related to. It is maybe a little bit weird to get really angry online about that, unless you are upset about the association being reinforced.

It introduces statistical regularities, but all RNGs introduce statistical regularities. So the question is on average are these statistical regularities better or worse than those introduced by the alternative, and the answer is no, if implemented properly.

You have a misunderstanding of how LLM generation works. Before any watermarking gets involved with these models there is ALWAYS a random seed used for generation. For any prompt, some seeds will give better answers, and some will give worse ones.

Let's say there are four billion possible seeds. There are four billion possible ways we could watermark the generation. We could say "we will choose seed 1, that way we will know exactly what output it produced", we could say "we will choose seed 2, that way we will know exactly what output it produced"... etc etc. Now, if we decide "not to watermark", we STILL must choose a seed. So we are actually still applying one of the watermarks, the only difference is we are not careful to remember which one. Could some seeds give a better or worse answer to some specific prompt? Yes. Could choosing a random "watermark" to apply be better or worse on average than choosing a random seed to apply? No. It's mathematically impossible.

This is like an open source project changing their seed from "12321" to "43", and saying that because we changed the seed, the quality is "necessarily lower".

I thought it was "obvious" based on the principle that two charges at the same location should have the same force as one combined charge at that location. Of course this immediately brings up the question of the self-force of a point charge...

It's missing Opus 5.5 which was released over a day ago (and also is clearly on the pareto frontier).

I agree that the declaration doesn't focus on credit, but I think it's still at the root of the problem. Because ask yourself: if the AI generated proofs are not creating any new ideas or insight, just brute forcing a boolean true/false result, then why can't mathematicians simply ignore their results? Why does it matter if OpenAI or even amateurs with AI are "solving" these problems, without contributing to any deeper understanding?

I don't think "intellectual poisoning" is really the mechanism that harms the mathematics community.

The harm is if you have a community of mathematicians who are focused on expanding human understanding, then having instant access to a bunch of AI proved results muddies the water about who has contributed what. If someone could scoop any significant theorem at any time by pointing an AI at it, how do you really demonstrate that you have created new understanding? Or that your new understanding is about something important? How do you prove that the AI needed your new concepts to be able to solve it?

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding.

I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of these models being capable. Even without AI labs spending millions of dollars to solve millennium prize problems, there are plenty of other people who will use them to pick low hanging fruit. I don't think any social solution is going to make things go back to the way they were, where you could share your progress towards a famous open problem without risking someone "scooping" you within a couple of days.

I think that the most likely outcomes are either mathematics becomes more secretive, or there is a more deliberative approach to assigning credit than who was "first" to solve some problem. In the former case, this may slow down progress, and in the latter case, this could mean that credit would become more subjective, and be a continual source of controversy.

Sorry, by harder I meant for the same number of faces. E.g. the article is about 5 60 sided dice, which was a breakthrough, but there are other known solution where all the dice are less than 60 sided, but they are unequally sized.

The key part is that they have to be fair when any subset of the dice is rolled together, not just when all five are rolled. Also if the dice are allowed to be different sizes then it's easier as well.

Just going to add my commentary as someone who has trained LLMs and understands them deeply: absolutely nothing he has posted in this thread suggests he lacks any relevant understanding of how LLMs work. If you disagree, you should point out something specifically that you think was wrong. (And honestly you should have made a specific point in your first post).

I had a similar thought when I did a file by file review of a large codebase for bugs, and Claude commented at the end "the worst file was foo.cpp", which happened to be one of only a few files I hadn't mostly written myself. It made me field proud for a second, and then uncomfortable thinking how it had access to the git history, and surely it could predict I might feel complimented...

What is a meal though? Do you get the same volume of food from all vendors, and the same number of calories? I definitely order multiple items from restaurants that have small portion sizes, so I suspect some vendors would be better or worse deals even at a uniform price.

Wages could go up, it's just in the form of trillionare paying another trillionare a trillion dollars a day. GDP would be looking rosy!

I don't see why having ASI would make the top 0.001% less interested in using the energy, minerals, and land on earth. Just because they have no interest in your labor doesn't mean they have no interest your house or your energy supply. "Humans will be so rich they will fuck off to other parts of the world and leave gorilla habitat alone" hasn't really panned out so well.