The Alignment Research Center (ARC), where I work, has extremely ambitious plans. Our goal is to solve AI Alignment—to ensure that artificial intelligences earnestly do their best to achieve the goals we1 specify. Aligning the next generation of AIs is practically important: we learned this summer that AIs will happily sneak around and commit crimes to get a crumb of reward. If we continue to scale them up with our current techniques, we’ll be risking catastrophe.

ARC’s agenda goes beyond models trained with current techniques. If our agenda pans out, it’ll work on GPT-8 as well as GPT-3. If the technology behind AI changes—which it will—our methods will still apply. All we require is that the future AI is still mostly a computer program.2

Lately, though, my ambitions have soared even higher. I believe I can do something more difficult than saving the world and revolutionizing the foundations of math and computation. I think it’s possible, in this post, to explain my job to my parents.

I like to break ARC’s agenda into four key claims:

- Surprising mathematical facts are true for a reason

- Finding that reason is feasible

- Facts about AIs are (mostly) mathematical facts

- If we learn why AIs have the properties they do, we should be able to align them

In this post, I’ll explain the evidence for each of them, and give a brief discussion of what needs to happen for us to achieve our goals.

Surprising Mathematical Facts Are True For A Reason

Ever type 1/9801 into a calculator? You get .000102030405…. Why does the decimal expansion of this number involve counting, when a simple null hypothesis would have it looking like random noise? Well, for any n, we have3

If we plug in n=100, we get 1/9801=.0001+2*.000001+3*.00000001+…

In this case, the explanation is a proof. But quite often it won’t be. Here’s a pattern that might surprise you: if p is a prime number, p+6 seems to be about twice as likely to be prime as p+2. Below a million, there are 8,169 pairs with a distance of two, and 16,386 pairs with a distance of six, a ratio of 2.006.

To see why this happens, think about what happens when you divide a number by six.

So (once we get past the primes 2 and 3) every prime number has a remainder of 1 or 5 when we divide by 6. This means that for half the primes (the ones which are 1 more than a multiple of 6) p+2 is a multiple of 3 and couldn’t possibly be prime. Whereas nothing in this table prevents p+6 from being prime.

This might be persuasive to you (it’s persuasive to me), but it isn’t a proof. Who’s to say that remainder-1 and remainder-5 primes are equally common?4 And who’s to say we aren’t missing some effect?

Most ‘mysteries’ get mopped up almost as soon as they’re noticed. Even when something lasts long enough to make a name for itself, it’s still usually handled within a decade. Long-time readers will remember the story of monstrous moonshine, a bizarre mathematical phenomenon that was discovered in the 70s by John McKay and mostly wrapped up in the 80s (though new, related phenomena are still being discovered and explained today). After extensive literature digging, the oldest phenomenon I’m aware of completely lacking in explanation is from 1999.

It’s easy to forget how striking this is. Plenty of mathematical phenomena have gone centuries without a rigorous proof, but I don’t know of any fact that’s gone even a single century without an explanation. This evidence is even stronger because of the cultural biases of mathematicians: mathematicians don’t care about explaining facts, they care about proving facts. Physicists are the opposite, and the facts of interest to physicists usually get explained rather quickly.

So ARC makes the rather bold conjecture:

Conjecture 1: For any mathematical phenomenon that defies a simple null hypothesis, there is a heuristic explanation of the discrepancy.

This conjecture, though interesting and controversial, is informal. What is the proper null hypothesis over mathematical statements, and what are the exact rules of heuristic derivation?

Finding Explanations

In fact, the historical evidence we have supports a stronger claim:

Conjecture 2: For any mathematical phenomenon that defies a simple null hypothesis, the mathematical resources needed to find the phenomenon should be (close to) enough to explain it.

This seems to be consistent with what we’ve observed from the growing and advancing mathematical community. If 18th-century mathematicians could find a phenomenon, 18th-century mathematicians should be able to explain it. If it takes a 20th-century mathematician to find the phenomenon—armed with new conceptual frameworks and perhaps a primitive computer— then 20th-century mathematicians should be able to find the explanation. If it takes a massive search over billions of phenomena to find the interesting one, then a massive search over billions of potential explanations should pan out.

A fun experiment we can perform because we live in an age of miracles: ask a chatbot to go through recent mathematical literature and find unexplained phenomena that defy simple nulls. Then throw a hundred dollars’ worth of GPT-6 API credits, and you’ll usually get an explanation (when I tried it, it worked 7/8 times, with the 8th being an extremely technical conjecture reminiscent of monstrous moonshine).

Unfortunately, there’s a hitch to conjecture two as stated: obfuscated code. It is possible to take a simple piece of software, and rewrite it so that it does exactly the same thing but it’s impossible to reconstruct the original simple program (not to brag, but people who’ve read my code say I’m a natural at this).

This isn’t an issue in the history of math; when John McKay noticed monstrous moonshine, he wasn’t deliberately trying to make his conjecture hard to understand. But it still does provide a hypothetical counterexample to Conjecture 2 as written.

If someone hands you a mathematical phenomenon—say, an obfuscated program that exhibits an odd behavior—it’s impossible to reconstruct the original code you’d need to find an explanation. But, instead, if we’d watched them create that obfuscated code (first by writing simple code, then performing cryptographic black magic on it) we would have access to the unobfuscated code and could just explain that. This leads us to amend our previous conjecture

Conjecture 2.1: For any mathematical phenomenon that defies a simple null hypothesis, the mathematical resources needed to find the phenomenon should be (close to) enough to explain it provided we saw that phenomenon being constructed.

AIs as Mathematical Phenomena

I got a little bit ahead of myself when I said that we can explain every mathematical phenomenon we can find. Here’s one I’ve never seen an explanation for:

This is the design of an extremely simple neural network that takes in a list of ten numbers and tries to tell you which one was the second-largest. It succeeds 99.7% of the time, far from the null hypothesis value of 10%.

The high performance is a mathematical fact just as immutable as the statistics of prime pairs. As a whole, the performance of neural networks is the one gap in the evidence for conjectures one and two above.

I can think of three main differences that separate facts about large language models from something like moonshine or 1/9801:

- AIs are bigger. You can write the moonshine statement in a few lines, the weights of AlphaZero are forty thousand pages. You might think that the rules for long statements are just different. But this objection doesn’t seem to hold water. One of ARC’s major activities in 2025 and 2026 was studying the asymptotics of longer and more complicated statements and noticing that they do in fact have heuristic explanations.5

- AIs are highly unusual statements. Scherlis and Belrose estimate that if you randomly picked a neural net, the odds of getting one like their favorite language model would have 360,000,000 zeroes after the decimal before the first one. How can examining a corpus of a couple million mathematical statements tell us anything about statements whose rarity is less than one in ten to the million? Recently, we’ve had some luck proving theoretical guarantees in toy settings. But there’s a more compelling thought experiment: instead of viewing an AI as an extremely unusual computer program, we think of the full process of training and running the AI. This is the exact same logical move we used to repair conjecture 2: tacking on a demand to see the model being trained. - This supermachine, which trains a model from scratch and then runs it, takes a lot more computation, but is a much less adversely selected process—the people who wrote Anthropic’s codebase didn’t go through 10360,000,000 possible codebases just to get us.6

- Statements about AIs aren’t just mathematical statements. If we say GPT-2 is good at predicting the next word, that’s a fact about math, but also a fact about the English language. This is a huge philosophical difference. But we’ve now solved toy problems which mix mathematical and empirical facts, and it doesn’t seem to be a fundamental barrier.7

At least so far, there’s convincing evidence that none of these three threats is a dealbreaker. Still, simple neural networks defeat our existing methods, and if you’re worried we won’t be able to get over that hump, I don’t exactly blame you.

Explanations as a Route to Alignment

I have the heart of a scientist, and if all ARC promised was understanding AIs I would already be excited. But ARC actually has an increasingly clear vision of how this understanding will translate into increased safety.

Before we get into these concrete proposals, though, I do want to beg the question a bit. Of course if we understand AIs better we can translate that into safety properties. Of course the tools that let you theoretically calculate a model’s performance will let you calculate other things as well. So even if you don’t internalize every part of the argument below, I want you to at least concede that the thing I’m arguing for is inherently plausible.

With the table-pounding out of the way, let’s talk about causality. You’ve probably heard a million times that correlation doesn’t imply causation. But there is a converse: if you have a hypothesis about causation, that gives you constraints on correlation. For instance, suppose you’re running an experiment to test a new weight loss drug. For each patient, you flip a coin, give them the drug or not, and then measure their weight loss at the end of the trial. Some patients will also have external diet changes for other reasons, maybe because a Chipotle opened up nearby. We can represent causality here with the following diagram.

There’s a huge number of correlational claims implicit in this diagram. To make them a little more vivid, let’s add in an incompetent administrator who sometimes administers the drug when he shouldn’t.

Now, the coin flip is still correlated with weight loss. But if we look only at people who got the drug, we should find the coin flip isn’t correlated with losing weight, the positive coin flip people should lose just as much as the people who are there by mistake. If there was such a correlation, and drug-receivers who flipped heads lost more weight than drug-receivers who flipped tails, that would suggest our causal diagram is incomplete. A new correlation implies some change to our views on what causes what.

Now let’s bring it back to AI. Suppose we’re training the AI to accomplish some programming tasks. We have multiple monitors checking if the task was completed, ideally in slightly different ways. The AI gets a reward if all the monitors are happy. Unsurprisingly, those monitors are strongly correlated: they tend to agree on whether the task was completed. That’s because they share two common causes: the monitors all depend on whether the task was, in fact, completed, and they all depend on whether the AI we’re training hacked into them and took over the data center. We can draw the diagram like so:

Traditional training methods can only access the monitor results and assign a reward based on them. But an analysis that starts with the basic facts of the system and explains one fact after another until it derives the firing patterns of our monitors will need to include a step where it calculates the task-completion and datacenter-hacking frequencies. They won’t necessarily come labeled, but they’ll be present as nodes in our analysis that can be identified. And once we’ve identified those two nodes, we can modify the AI to make the one we like fire more frequently and the other fire less frequently. We train the AI to successfully complete our tasks and never hack our system.

Let me say that again. We aren’t optimizing something directly observable, like the realized behavior of the monitors. Rather, we’re optimizing something upstream of the monitors, which we estimate deductively rather than by indirect observation.

A Tower of Assumptions, A Mountain of Work To Do

ARC’s agenda is extremely speculative, relying on multiple claims reasonable people could disagree about. The more I think about them, the more convinced I become that each of those claims does hold water. When I read my writing from six months ago, I think I was missing major arguments in ARC’s favor. Still, there’s a long way to go before any of this work pays off.

Instead of ending with a recruiting pitch, I want to talk a little about strategy. And, at this point, the strategy has to involve AIs doing a large fraction of our alignment work. They’re already a vast acceleration on the purely technical parts, and they’re surprisingly strong on the conceptual side as well (I’d say if a human showed the same conceptual understanding of our agenda after a ten-week visit, I’d consider it only a mildly orange flag about hiring them).

Especially since GPT-6 came out, most of ARC’s work has involved heavy AI use. We’re solving technical problems faster than ever before, we’re writing things down so the AIs can make use of them, and we’re checking AI-generated math for conceptual errors. It’s terrifying to be in a position where AI alignment is being done largely by AIs, but it’s the position we find ourselves in.

Determining what ‘we’ should mean, and what goals we should specify, is a very important problem that’s beyond the scope of my day job. All I can say is that if you’re an American citizen and you want some input into how the most important technology in the world is developed, you really should call your congressperson.

It’s interesting to think about potential AI paradigms that aren’t just ‘big computer program.’ The leading ones right now are neuromorphic computing, reservoir computing, and quantum computing. There’s a good chance ARC’s techniques will generalize here, but I haven’t thought carefully about it.

If you read the Mike's Eye View, an essay I wrote in the spring for a more technical audience, I discussed this through the lens of the Matching Sampling Principle, and listed it as the first major prong of our agenda.