I think "are the failures of a simple linear regression on the METR graph relevant" is a much better framing than "does seeing a line if you squint extrapolate forever." As I said, I'd much rather frame the discussion around the actual material conditions of AI progress, but if you are going to be drawing lines I'd at least want to start by acknowledging that no such model will be perfect.

This is the part I find very strange. Let's table the problems with METR [1], just noting that benchmarking AI is extremely hard and METR's methodology is not gospel just because METR's "sole purpose is to study AI capabilities". (That is not a good way to evaluate research!)

Taking whatever idealized metric you want, at some point it has to level off. That's almost trivially true: everyone should agree that unrestricted exponential growth forever is impossible, if only for the eventual heat death of the universe. That makes the question when, and not if. When do external forces dominate whatever positive feedback loops were causing the original growth? In AI, those positive feedback loops include increased funding, increased research attention and human capital, increased focus on AI-friendly hardware, and many others, including perhaps some small element of AI itself assisting the research process that could become more relevant in the future.

These positive feedback loops have happened many times, and they often do experience quite sharp level-offs as some external factor kicks in. Commercial aircraft speeds experienced a very sharp increase until they leveled off. Many companies grow very rapidly at first and then level off. Pandemics grow exponentially at first before revealing their logistic behavior. Scientific progress often follows a similar trajectory: a promising field emerges, significant increased attention brings a bevy of discoveries, and as the low-hanging fruit is picked the cost of additional breakthroughs surges and whatever fundamental limitations the approach has reveal themselves.

It's not "extremely surprising" that COVID did not infect a trillion people, even though there are some extremely sharp exponentials you can find looking at the first spread in new areas. It isn't extremely surprising that I don't book flights at Mach 3, or that Moore's Law was not an ironclad law of the universe.

Does that mean the entire field will stop making any sort of progress? Of course not. But any analysis that fundamentally boils down to taking a (deeply flawed) graph and drawing a line through it and simplifying the whole field of AI research to "line go up" is not going to give you well-founded predictions for the future.

A much more fruitful line of analysis, in my view, is to focus on the actual conditions and build a reasonable model of AI progress that includes current data while building in estimations of sigmoidal behavior. Does training scaling continue forever? Probably not, given the problems with e.g., GPT-4.5 and the limited amount of quality non-synthetic training data. It's reasonable to expect synthetic training data to work better over time, and it's also reasonable to expect the next generation of hardware to also enable an additional couple orders of magnitude. Beyond that, especially if the money runs out, it seems like scaling will hit a pretty hard wall barring exceptional progress. Is inference hardware going to get better enough that drastically increased token outputs and parallelism won't matter? Probably not, but you can definitely forecast continued hardware improvements to some degree. What might a new architectural paradigm be for AI, and would that have significant improvements over current methodology? To what degree is existing AI deployment increasing the amount of useful data for AI training? What parts of the AI improvement cycle rely on real-world tasks that might fundamentally limit progress?

That's what the discussion should be, not reposting METR for the millionth time and saying "line go up" the way people do about Bitcoin.

[1] https://www.transformernews.ai/p/against-the-metr-graph-codi...

AI can be used in ways that lead to deeper understanding. If a student wants AI to give them practice problems, or essay feedback, or a different explanation of something that they struggle with, all of those methods of learning should translate to actual knowledge that can be the foundation of future learning or work and can be evaluated without access to AI.

That actual knowledge is really important. Literacy and numeracy are not the same thing as mental arithmetic. Someone who can't read literature in their field (whether that's a Nature paper or a business proposal or a marketing tweet) shouldn't rely on AI to think for them, and certainly universities shouldn't be encouraging that and endorsing it through a degree.

I think the most important thing about that kind of deeper knowledge is that it's "frictional", as the original essay says. The highest-rated professors aren't necessarily the ones I've learned the most from, because deep learning is hard and exhausting. Students, by definition, don't know what's important and what isn't. If someone has done that intellectual labor and then finds AI works well enough, great. But that's a far cry from being reliant on AI output and incapable of understanding its limitations.

It's basically a variation on the multiple comparisons, but sneakier: it's easy to spend an hour going through data and, over that time, test dozens of different hypotheses. At that point, whatever p-value you'd compute for a single comparison isn't relevant, because after that many comparisons you'd expect at least one to have uncorrected p = 0.05 by random chance.

I think you also have to consider that AI with superpowers is not going to materialize overnight. If superintelligent AI is on the horizon, the first such AI will be comparable to very capable humans (who do not have the ability to talk their way into nuclear launch codes or out of decades-long prison sentences at will). Energy costs will still be tremendous, and just keeping the system going will require enormous levels of human cooperation. The world will change a lot in that kind of scenario, and I don't know how reasonable it is to claim anything more than the observation of potential risks in a world so different from the one we know.

Is it possible that search ends up doing as much for persuasion as it does for chess, superintelligent AI happens relatively soon, and it doesn't have prohibitive energy costs such that escape is a realistic scenario? I suppose? Is any of that obvious or even likely? I wouldn't say so.

AI that's as good as a persuasive human at persuasion is clearly impactful, but I certainly don't see it as self-evident that you can just keep drawing the line out until you end up with 200 IQ AI that is so easily able to manipulate the environment it's not worth elaborating how exactly a chatbot is supposed to manipulate the world through extremely limited interfaces with the outside world.

I certainly think it's possible to imagine that an AI that says the exactly correct thing in any situation would be much more persuasive than any human. (Is that actually possible given the limitations of hardware and information? Probably not, but it's at least not on its face impossible.) Where I think most of these arguments break down is the automatic "superintelligence = superpowers" analogy.

For every genius who became a world-famous scientist, there are ten who died in poverty or war. Intelligence doesn't correlate with the ability to actually impact our world as strongly as people would like to think, so I don't think it's reasonable to extrapolate that outwards to a kind of intelligence we've never seen before.

- It's elementary to the point that you can introduce it whenever you want.

- It automatically gives a sense of scale: larger than 2, but not by a lot.

- At least to me, it confers some sense of importance. You can get the sense that this number e has some deep connection to infinity and infinitesimal change and deserves further study even if you haven't seen calculus before.

- It directly suggests a way of calculating e, which "the base of the exponential function with derivative equal to itself" doesn't suggest as cleanly.

I don't know of any calculus course that relies on this definition for much: that's not its purpose. The goal is just to give students a fairly natural introduction to the constant before you show that e^x and ln x have their own unique properties that will be more useful for further manipulation.

I suppose my question is why you think TCS people would do this analysis and development better than non-TCS people. Once you leave the warm cocoon of big-O, the actual practical value of an algorithm depends hugely on specific hardware details. Similarly, once you stop dealing with worst-case or naive average-case complexity, you have to try and define a data distribution relevant for specific real-world problems. My (relatively uninformed) sense is that the skill set required to, say, implement transformer attention customizing to the specific hierarchical memory layout of NVIDIA datacenter GPUs, or evaluate evolutionary optimization algorithms on a specific real-world problem domain, isn't necessarily something you gain in TCS itself.

When you can connect theory to the real world, it's fantastic, but my sense is that such connections are often desired and rarely found. At the very least, I'd expect that to often be a response to applied CS and not coming first from TCS: it's observed empirically that the simplex algorithm works well in practice, and then that encourages people to revisit the asymptotic analysis and refine it. I'd worry that TCS work trying to project onto applications from the blackboard would lead to less rigorous presentations and a lot of work that's only good on paper.

What's meant by "it’s already too much to ask for a closed form for fibonacci numbers"? Binet's formula is usually called a closed form in my experience. Is "closed form" here supposed to mean "closed form we can evaluate without needing arbitrary-precision arithmetic"?

Compare the automobile. Automobiles today are a lot nicer than they were 50 years ago, and a lot more efficient. Does that mean cars that never need fuel or recharging are coming soon, just because the trend has been higher efficiency? No, because the fundamental physical realities of drag still limit efficiency. Moreover, it turns out that making 100% efficient engines with 100% efficient regenerative brakes is really hard, and "just throw more research at it" isn't a silver bullet. That's not "there won't be many future improvements", but it is "those future improvements probably won't be any bigger than the jump from GPT-3 to o1, which does not extrapolate to what OP claims their models will do in 2027."

AI in 2027 might be the metaphorical brand-new Lexus to today's beat-up Kia. That doesn't mean it will drive ten times faster, or take ten times less fuel. Even if high-end cars can be significantly more efficient than what average people drive, that doesn't mean the extra expense is actually worth it.