401–410 of 414 posts
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It should be noted that optimization of a convex bounded lipschitz function is exactly what most modern statistical learning (AI) models are based on.
What do you mean by this? A neural network hypothesis space is not typically strictly convex or a lipschitz function.
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It should be noted that optimization of a convex bounded lipschitz function is exactly what most modern statistical learning (AI) models are based on.
Very confused by this comment. The older (poorer) parts of the ML literature focus on models with convex and (gradient-)Lipschitz objectives, but that's not representative of reality, not even close. Modern objectives for AI models are famously nonconvex (catastrophically, from the point of view of classical optimisation theory), and that's where the interesting research is.
So if you dig down a bit it turns out the author had been trying to solve that problem for a year with GPT 5.4 and 5.5 and he fed all that information to the prompt he gave to Sol Pro which may or may not had direct access to the author's chat history. So the claimed "148 minutes" was really "a year plus 148 minutes". Moreover, it seems the prompt included the technique used to solve the problem: https://old.reddit.c…
I (author of the original post and paper) can add a few things here: 1. My previous approaches with GPT 5.5 were really not very sophisticated in terms of my input. I threw the problem at it, and just kept encouraging it to go iterate through ideas without any success. 2. The approaches that are in the prompt, though they will seem cryptic to someone not in the field, are relatively natural ideas. In fact, the constr…
If you, e.g. got an LLM (any one) to one-shot the problem with a prompt that said "solve this problem", then we're much closer to that, than if you spent a year trying with different LLMs and then finally got it to work with a lot of hand-holding and even suggesting the ultimate solution. An autonomous system can't succeed once a year, if it's going to be of any use. It should also be able to identify the right tools on its own, not rely on a human to tell it what to do.
This should also go to address some of the questions you pose on reddit, about the future of mathematics. If LLMs can already do your job fully autonomously (as I would explain the term) then ... you're out of a job. You and all other mathematicians, young or old.
I personally don't think we're there yet.
I hear what you say, btw, about never being able to get there by yourself etc. Maybe you would, maybe you wouldn't. What we know is you used a tool to get there, in fact a series of tools, and it took you many tries before you did. The fact that an earlier LLM tried and failed is interesting, but that may just mean you were capable of crafting a better prompt after your interaction with the earlier LLMs.
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I (author of the original post and paper) can add a few things here: 1. My previous approaches with GPT 5.5 were really not very sophisticated in terms of my input. I threw the problem at it, and just kept encouraging it to go iterate through ideas without any success. 2. The approaches that are in the prompt, though they will seem cryptic to someone not in the field, are relatively natural ideas. In fact, the constr…
There is a firm opinion in some circles that an AI can never do anything but recombine already known things despite a rising number of cases where that very much appears to be an inaccurate view. Any slim possibility that vital information was given to the AI to make the task just one of recombination, rather than coming up with anything original, is grabbed with both hands no matter how tenuous. I can understand why…
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Honestly, i've received a formal MSc education in the hardware aspects, including for designing embedded electronics products. Spent the most part ofy career in the software industry designing enterprise software and feel like i never needed to use them, except maybe early in my career when i was reviewing tech stacks and determined that .NET would be among the winning horses, precisely because it'd take care of that…
> However, having a high affinity with hardware is not a driver / computer science of hiring decisions from what i can see in the enterprise software world I think the way I worded it was maybe a little too close to just being about hardware, because performance do matter a lot in the energy industry. I do think it applies to SWE in general. You mention .NET and I've met C# developers with years of experience who cou…
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Your first two sentences were correct. The last one is already being proven false. It's a threat to everyone. UBI is the only way.
Productivity improvements tend to increase employment. AI will not reduce employment. (Also, the US budget deficit is way too high to afford a UBI.)
It also is not clear workers will be needed. The gain may not be in employment. Perhaps another paradox will arise as the additional gains will be consumed by AI itself. How unique are your prompts? Self prompting is a clear end state.
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Without human verification, an LLM can generate correct or incorrect proofs but it can't tell the difference. A human is necessary to be able to tell one from the other. Saying that's a solution "done autonomously by an automated AI pipeline" is like saying that a self driving car that can only take you to the nearest train station after which you have to ride the rain to where you're going is "autonomously" driving…
The automated AI pipeline also had an automatic grading model to try to reduce false positives. But anyway, my point was that in that case the prompt involved was indeed pretty much "hey, ChatGPT, solve an unsolved problem, thanks."
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Nature has no language. Language is a human tool to imperfectly describe nature. Putting language before nature is magical thinking (also known as Platonism).
Yes, of course mathematics is a tool to model nature as accurately as we could. That still doesn't mean mathematics is as trivial or frivolous as manipulating symbols.
Genuine question: If you still or did think LLMs are just stochastic parrots that just summarize everything and have no form of creativity, what do you think after seeing results like this? I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.
I hold my stance that LLMs are stochastic parrots. Making the parrots ever more complex and training on ever more data produced by intelligent, creative beings may make them more useful or convincing but does at no point give rise to intelligence or creativity.
Genuine question: If you still or did think LLMs are just stochastic parrots that just summarize everything and have no form of creativity, what do you think after seeing results like this? I'm very curious how people reconcile their fear/hatred of AI with actual objective reality. This is actually what interests me most about the whole AI thing. How we tell ourselves what we tell ourselves.
They aren’t really stochastic parrots, they’re next token prediction machines. They aren’t intelligent nor creative imo. However they are quite useful at some tasks. Why would you assume people who don’t kneel at the alter of AI are somehow fearful or hate AI? Most of the hate I’ve seen have been for the people and companies involved with AI not the technology itself.
Like, this is just so silly. Come with me for a little thought experiment.
Picture in front of you a Kibana dashboard. It displays, say, latencies.
Now apply some statistic functions. Let's find the time ranges where we had outlier tail latencies, for example.
You pin down some patterns, cool. But this is post-incident. We want to alert on-incident.
So you begin writing some rules. And then some more rules. And then even more rules. All of a sudden you captured the entire logic of the program emitting these metrics, along with the surrounding dependencies'.
See where I'm going with this? To do sufficiently well at prediction, you'll need to model the entire constitution of the thing you're trying to predict, along with the stuff going through it. Locally, all predictions will be unlikely. But globally, you'll be right.
But if you do that, you quite literally "understand" and simulate the entire thing. That's the whole point, and this is why "just predicting the next token", "stochastic parrot" and other anti-AI dogwhistles are so flagrantly asinine. They imply some sort of rudimentary Markov process, or at best some sort of dozen or so variable statistics research paper type prediction. It's a laughable proposition, given the quite literally trillions of parameters actually in use, and all the research that has already went into identifying countless semantically interpretable latent spaces and activation patterns.
> Most of the hate I’ve seen have been for the people and companies involved with AI not the technology itself.
Anecdotes are fun! Visit any Reddit thread where AI is brought up and watch that ratio shift very rapidly. The hate and cope train is incessant there.