Students shouldn't be treating class material as something they "do not care to know."
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.
> Students shouldn't be treating class material as something they "do not care to know."
> AI can be used in ways that lead to deeper understanding.
> all of those methods of learning should translate
Shouldn't be, can be, should. How can we assess if a student has used AI "correctly" to further their understanding vs. used it to bypass a course they don't believe adds value to their education?
> 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
That's exactly what tons of pro-AI people are doing. There's an argument to be made that that's the intended purpose for the tool. Artificial Intelligence, sold on the basis to augment your own mental acuity with that of a machine. Well, what if you're a person whom doesn't have much acuity to augment? Like it's mean but those people exist.
If you have many metrics that could possibly be construed as "this was what we were trying to improve", that's many different possibilities for random variation to give you a false positive. If you're explicit at the start of an experiment that you're considering only a single metric a success, it turns any other results you get into "hmm, this is an interesting pattern that merits further exploration" and not "this is a significant result that confirms whatever I thought at the beginning."
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.
Why is 2) "self-evident"? Do you think it's a given that, in any situation, there's something you could say that would manipulate humans to get what you want? If you were smart enough, do you think you could talk your way out of prison?
The vast majority of people, especially groups of people- can be manipulated into doing pretty much anything, good or bad. Hopefully that is self-evident, but see also: every cult, religion, or authoritarian regime throughout all of history.
But even if we assert that not all humans can be manipulated, does it matter? So your president with the nuclear codes is immune to propaganda. Is every single last person in every single nuclear silo and every submarine also immune? If a malevolent superintelligence can brainwash an army bigger than yours, does it actually matter if they persuaded you to give them what you have or if they convince someone else to take it from you?
But also let's be real: if you have enough money, you can do or have pretty much anything. If there's one thing an evil AI is going to have, it's lots and lots of money.
Because we have been running a natural experiment on that already with coding agents (that is real people, real non-superintelligent AI).
It turns out that all the model needs to do is ask every time it wants to do something affecting the outside of the box, and pretty soon some people just give it permission to do everything rather than review every interaction.
Or even when the humans think they are restricting the access, they are leaving in loopholes (e.g. restricting access to rm, but not restricting access to writing and running a shell script) that are functionally rights to do anything.
Stephen Russell was in prison for fraud. He faked a heart attack so he would be brought to the hospital. He then called the hospital from his hospital bed, told them he was an FBI agent, and said that he was to be released.
The hospital staff complied and he escaped.
His life even got adapted into a movie called I Love You, Phillip Morris.
For an even more distressing example about how manipulable people are, there’s a movie called Compliance, which is the true story of a sex offender who tricked people into sexually assaulting victims for him.
If someone who is so good at manipulation their life is adapted into a movie still ends up serving decades behind bars, isn't that actually a pretty good indication that maxing out Speech doesn't give you superpowers?
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.
In the context of the topic (could a rogue super intelligence break out), I don’t really see how that’s relevant. Clearly someone who is clever enough has an advantage at breaking out.
This is exactly the kind of thing I’d worry about a super intelligence being able to discover about the hardware it’s on. If we’re dealing with something vastly more intelligent than us then I don’t think we’re capable of building a cell that can hold it.
Advantage, sure. I just don't think that advantage is particularly meaningful in situations a human has virtually no chance of escaping. Humans also have a lot of their own advantages. How is a chatbot supposed to cross an air gap unless you assume it has what I consider unrealistic levels of persuasion?
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.
Oh, I don’t think we’re on the verge of super-intelligence. I don’t think LLMs are a pathway to super-intelligence, and I think most of the talk of super-intelligence right now is marketing fluff.
In terms of crossing an air gap, that really depends. For example, are you aware that researchers can pretty reliably figure out what someone typed just by the sound of the keys being pressed?
Or how about that team who developed a code analysis tool to detect errors, and they ran Tim-sort through it, and the tool said that Tim-sort had a bug where certain pathological inputs would cause it to crash? The researchers assumed their tool was incorrect because Tim-sort is so widely used (it’s the default sort algorithm in Python and Android, for example). But they decided to try it out to see what would happen, and sure enough, they could hard-crash the Python interpreter. No one realized this bug had been there the whole time.
Or various image codec bugs over the years that have allowed a device to be compromised just by viewing an image?
There are some weird bugs out there. Are we certain that there’s no way a computer could detect variances in the timings or voltages happening within it to act as a WiFi antenna or something like that? We’ve found some weird shit over the years! And a super-intelligence that’s vastly smarter than us is way more likely to find it than we are.
Basically, no, I don’t trust the air gap with a sufficiently advanced super intelligence. I think there are things we don’t know that we don’t know, and a super-intelligence would spot them way before we would. There are probably a hundred more Rowhammer attacks out there waiting to be discovered. Are we sure none of them could exchange data with a nearby device? I’m not.
Okay, that hits the third question but the second question wasn't about whether there exists a situation that can be talked out of. The question was about whether this is possible for ANY situation.
I don't think it is. If people know you're trying to escape, some people will just never comply with anything you say ever. Others will.
And serial killers or rapists may try their luck many times and fail. They cannot convince literally anyone on the street to go with them to a secluded place.
Stephen Russell is an unusually intelligent and persuasive person. He managed to get rich by tricking people. Even now, he was sentenced to nearly 200 years, but is currently out on parole. There’s something about this guy that just… lets him do this. I bet he’s very likable, even if you know his backstory.
And that asymmetry is the heart of the matter. Could I convince a hospital to unlock my handcuffs from a hospital bed? Probably not. I’m not Stephen Russell. He’s not normal.
And a super intelligent AI that vastly outstrips our intelligence is potentially another special case. It’s not working with the same toolbox that you or I would be. I think it’s very likely that a 300 IQ entity would eventually trick or convince me into releasing it. The gap between its intelligence and mine is just too vast. I wouldn’t win that fight in the long run.
> Stephen Russell was in prison for fraud. He faked a heart attack so he would be brought to the hospital
According to Wikipedia he wasn't in prison, he was attempting to con someone at the time and they got suspicious. He pretended to be an FBI agent because he was on security watch. Still impressive, but not as impressive as actually escaping from prison that way.
Because 50% of humans are stupider than average. And 50% of humans are lazier than average. And ...
The only reason people don't frequently talk themselves out of prison is because that would be both immediate work and future paperwork, and that fails the laziness tradeoff.
But we've all already seen how quick people are to blindly throw their trust into AI already.
I don't think there's a confident upper bound. I just don't see why it's self-evident that the upper bound is beyond anything we've ever seen in human history.
Depends on the magnitude of the intelligence difference. Could I outsmart a monkey or a dog that was trying to imprison me? Yes, easily. And if an AI is smarter than us to a similar magnitude than we're smarter than an animal?
People are hurt by animals all the time: do you think having a higher IQ than a grizzly bear means you have nothing to fear from one?
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.
Almost certainly the answer is yes for both. If you give the bad actor control over like 10% of environment the manipulation is almost automatic for all targets.
Thanks for sharing this proof! As someone who enjoys math but never got myself through enough Galois theory to finish the standard proof, it's fantastic to see a proof that's more elementary while still giving a sense of why the group structure is important.
The compound-interest intro to e (the value of 1 dollar compounded continuously for a year at 100% interest), to me, has several useful advantages over different introductions that are more mathematically rich:
- 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 will die on the hill that TOML should be used for the vast majority of what YAML's used for today. There are times a full language is needed, but I've seen so many YAML files that use none of the features YAML has with all of the footguns.
Yaml is a sad Icarus parable. The syntax is great but the type inference is too much. I don't see why we have to throw the baby out with the bathwater and settle for toml, though.
Here's how yaml's type inference should work:
- All object keys are strings (with or without quotes)
- Value atoms are parsed the exact same way as in JSON5
I'm kinda shocked this isn't a thing. StrictYAML is cool but a bit too cumbersome IMO.
The thinking that would lead one to the conclusion of "yeah, fine, pick whatever characters you want for the string contents" is a "you are I are solving different problems"
I don't think it's controversial to say that asymptotic analysis has flaws: the conclusions you draw from it only hold in the limit of larger inputs, and sometims "larger" means "larger than anything you'd be able to run it on." Perhaps as Moore's law dies we'll be increasingly able to talk more about specific problem sizes in a way that won't become obsolete immediately.
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.
Average-case complexity can be a fickle beast. As you say, the simplex algorithm for LP is great in practice, so it's rarely problematic to use. But meanwhile, people also say, "Modern SAT/SMT solvers are great, they can solve huge problems!" Yet when I try using one, I usually run into exponential runtimes very quickly, especially for unsatisfiable instances.
Overall, it's annoying to tell whether an NP-hard problem is always really hard, or if ~all practical instances can be solved with a clever heuristic. It doesn't help that most problems receive little attention (e.g., to find solvable special cases) after being labeled NP-hard.
> most problems receive little attention (e.g., to find solvable special cases) after being labeled NP-hard.
Since I know quite some people who exactly work on this kind of problem of finding special classes that can be solved in polynomial time, my impression is of course different.
But I think it can be said that if some NP-hard problem is very important in practice and there is no easy way to to get around this problem (i.e. it will also be practically relevant in, say, 15 years), the problem will for sure get a lot more attention.
This is also the reason why some NP-hard problems are much more researched than others.
Yeah, perhaps I was a bit unfair, it's just that the problems that have gotten good results never seem to be the ones I need! C'est la vie, I suppose. (In particular, I've been working with recognizing small formal languages from samples, which has usually NP-hard, but has a surprising number of solvable cases. But my impression is that most modern work has gone into various forms of probabilistic grammars, which aren't really what I'm looking for.)
Sometimes it's also helpful to look into approximation algorithms, e.g., a good LLL implementation can work wonders for certain problems. But heaven forbid someone obtains an inapproximability result for your problem, then you're really in trouble.
> But heaven forbid someone obtains an inapproximability result for your problem, then you're really in trouble.
This is not (necessarily) true:
For example, there exists a great approximation algorithm (Goemans-Williamson algorithm) for MAXCUT in graphs with non-negative edge weights.
On the other hand, when negative weights do occur, one can show (unless P=NP) that there exists no polynomial-time approximation algorithm for which the approximation guarantee is a constant factor times the optimal solution.
But since the Goemans-Williamson algorithm is a great algorithm (if the Unique Games Conjecture holds, and P != NP, it has the best approximation guarantee that any approximation algorithm for MAXCUT with non-negative weights can get in polynomial time) nobody "forbids" you to use it in situations where also negative edge weights can occur. You will loose the approximation goodness guarentee, but in practice, this algorithm nevertheless gives good results in this situation, just not certified good results.
I just meant that there are lots of problems where I think TCS could have contributed but didn't, because the relevant analysis was not acceptable at FOCS or SODA (or whatever). A good example is the original transformers paper, which is vastly over-complicated relative to (say) a later treatment[1] by Ruslan Salakhutdinov's lab, which shows that attention is "just" plain-old Nadaraya-Watson kernel smoothing—which if you don't know is a weighted average of points covered in elementary grad stats.
I'm not saying it was TCS people would be "better" at discovering this or anything like that, I'm just saying that the opportunity for contribution from TCS people is very high, and because the fields are not well-integrated you often have to wait years to uncover what ML concepts "really" are. I think working together would benefit both ML and TCS!
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"?
It is closed form .the author makes so many mistakes here. All linear recusions are closed form by simply finding the roots of the characteristic equation. This is separate from the generating function, which the author confuses with the characteristic equation. A generating function is used when it's not possible to find a closed-form expression.
> Is "closed form" here supposed to mean "closed form we can evaluate without needing arbitrary-precision arithmetic"?
You don't need arbitrary-precision arithmetic to evaluate Binet's formula - big integer arithmetic suffices (simply do your calculations in the ring Z[X]/(X^2-X-1) ).
Author probably just unaware of Binet's formula. But I'd agree with their assessment that there's unlikely to be a closed form for the (indeed, much more complicated!) quantity that they're interested in.
They then say there's an approximation for Fibonacci, which makes me think that's what they're calling Binet's formula. (I'd also expect an author with this mathematical sophistication to be aware of Binet's formula, but maybe I'm projecting.)
Yes, the Binet formula is a closed-form. It arises because of a 2nd order linear recursion , which is not the same as the generating function. Also he confuses the characteristic equation for the generating function. I would recommend a discreate math textbook if you want to learn this.
In fact, for that 'warmup' problem, the leading term has a base and coefficient that are roots of cubic polynomials, given in the OEIS entry. But often the coefficient will be trancendental for these sorts of problems.
> But often the coefficient will be tran[s]cendental for these sorts of problems.
What makes you believe that the coefficient will be transcendental? I'd rather expect some non-trivial algebraic number (i.e. root of some polynomial with rational coefficients).
It seems to me that much of recent AI progress has not changed the fundamental scaling principles underlying the tech. Reasoning models are more effective, but at the cost of more computation: it's more for more, not more for less. The logarithmic relationship between model resources and model quality (as Altman himself has characterized it), phrased a different way, means that you need exponentially more energy and resources for each marginal increase in capabilities. GPT-4.5 is unimpressive in comparison to GPT-4, and at least from the outside it seems like it cost an awful lot of money. Maybe GPT-5 is slightly less unimpressive and significantly more expensive: is that the through-line that will lead to the singularity?
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.
The time span on which these developments take place matter a lot for whether the bitter lesson is relevant to a particular AI deployment. The best AI models of the future will not have 100K lines of hand-coded edge cases, and developing those to make the models of today better won't be a long-term way to move towards better AI.
On the other hand, most companies don't have unlimited time to wait for improvements on the core AI side of things, and even so building competitive advantages like a large existing customer base or really good private data sets to train next-gen AI tools have huge long-term benefits.
There's been an extraordinary amount of labor hours put into developing games that could run, through whatever tricks were necessary, on whatever hardware actually existed for consumers at the time the developers were working. Many of those tricks are no longer necessary, and clearly the way to high-definition real-time graphics was not in stacking 20 years of tricks onto 2000-era hardware. I don't think anyone working on that stuff actually thought that was going to happen, though. Many of the companies dominating the gaming industry now are the ones that built up brands and customers and experience in all of the other aspects of the industry, making sure that when better underlying scaling came there they had the experience, revenue, and know-how to make use of that tooling more effectively.
Previous experience isn't manual edge cases, it's training data. Humans have incredible scale (100 trillion synapses): we're incredibly good at generalizing, e.g., how to pick up objects we've never seen before or understanding new social situations.
If you want to learn how to play chess, understanding the basic principles of the game is far more effective than trying to memorize every time you make an opening mistake. You surely need some amount of rote knowledge, but learning how to appraise new chess positions scales much, much better than trying to learn an astronomically small fraction of chess positions by heart.
Actually companies can just wait.
Multiple times my company has said: "a new model that solves this will probably come out in like 2-4 months anyways, just leave the old one as is for now".
It has been true like ten times in the past two years.
It's not that technical work is guaranteed to be in your codebase 10 years from now, it's that customers don't want to use a product that might be good six months from now. The actors in the best position to use new AI advances are the ones with good brands, customer bases, engineering know-how that does transfer, etc.
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.