Formalization of informal ideas will not be the hard part. AI will enable not just automated proofs, not just automated conjectures, but also automated formalization of informal intuitions.
This seems both surprising and extremely crux-y to me. I'm curious if you can offer pointers (beyond "read all of Sahil's work") to the best arguments for this.
I'm generally confused by the argument here.
As we examine successively more intelligent agents and their representations, the representation of any particular thing will perhaps be more compressed, but also and importantly, more intelligent agents represent things that less intelligent agents don't represent at all. I'm more intelligent than a mouse, but I wouldn't say I have a more compressed representation of differential calculus than a mouse does. Terry Tao is likely more intelligent than I am, likely has a more compressed representation of differential calculus than I do, but he also has representations of a bunch of other mathematics I can't represent at all, so the overall complexity of his representations in total is plausibly higher.
Why wouldn't the same thing happen for goals? I'm perfectly willing to say I'm smarter than a dog and a dog is smarter than a paramecium, but it sure seems like the dog's goals are more complex than the paramecium's, and mine are more complex than the dog's. Any given fixed goal might have a more compressed representation in the more intelligent animal (I'm not sure it does, but that's the premise so let's accept it), but the set of things being represented is also increasing in complexity across organisms. Driving the point home, Terry Tao seems to have goals of proving theorems I don't even understand the statement of, and these seem like complex goals to me.
So overall I'm not following from the premises to the conclusions. I wish I could make this sharper. Help welcome.
2I feel like a lot of the difficulty here is a punning of the word "problem."
In complexity theory, when we talk about "problems", we generally refer to a formal mathematical question that can be posed as a computational task. Maybe in these kinds of discussions we should start calling these problems_C (for "complexity"). There are plenty of problems_C that are (almost definitely) not in NP, like #SAT ("count the number of satisfying assignments of this Boolean formula"), and it's generally believed that verification is hard for these problems. A problem_C like #SAT that is (believed to be) in #P but not NP will often have a short easy-to-understand algorithm that will be very slow ("try every assignment and count up the ones that satisfy the formula").
On the other hand, "suppose I am shopping for a new fridge, and I want to know which option is best for me (according to my own long-term values)" is a very different sort of beast. I agree it's not in NP in that I can't easily verify a solution, but the issue is that it's not a problem_C, rather than it being a problem_C that's (almost definitely) not in NP. With #SAT, I can easily describe how to solve the task using exponential amounts of compute; for "choose a refrigerator", I can't describe any computational process that will solve at all. If I could (for instance, if I could write down an evaluation function f : fridge -> R (where f was computable in P)), then the problem would be not only in NP but in P (evaluate each fridge, pick the best one).
So it's not wrong to say that "choose a refrigerator" is not (known to be) in NP, but it's important to foreground that that's because the task isn't written as a problem_C, rather than because it needs a lot of compute. So discussions about complexity classes and relative ease of generation and verification seem not especially relevant.
I don't think I'm saying anything non-obvious, but I also think I'm seeing a lot of discussions that don't seem to fully internalize this?
1I feel like this piece is pretty expansive in the specific claims it makes relative to the references given.
- I don't think the small, specific trial in [3] supports the general claim that "Current LLMs reduce the human labor and cognitive costs of programming by about 2x."
- I don't think [10] says anything substantive about the claim "Fine tuning pushes LLMs to superhuman expertise in well-defined fields that use machine readable data sets."
- I don't think [11] strongly supports a general claim that (today's) LLMs can "Recognize complex patterns", and [12] feels like very weak evidence for general claims that today's LLMs can "Recursive troubleshoot to solve problems".
The above are the result of spot-checking and are not meant to be exhaustive.
Thank you, this is helpful.
I think the realization I'm coming to is that folks on this thread have a shared understanding of the basic mechanics (we seem to be agreed on what computations are occurring, we don't seem to be making any different predictions), and we are unsure about interpretation. Do you agree?
For myself, I continue to maintain that viewing the system as a next-word sampler is not misleading, and that saying it has a "plan" is misleading --- but I try to err very on the side of not anthropomorphizing / not taking an intentional stance (I also try to avoid saying the system "knows" or "understands" anything). I do agree that the system's activation cache contain a lot of information that collectively biases the next word predictor towards producing the output it produces; I see how someone might reasonably call that a "plan" although I choose not to.
Suppose we modify the thought experiment so that we ask the LLM to simplify both sides of the "pick a number between 1 and 100" / "ask yes/no questions about the number." Now there is no new variable input from the user, but the yes/no questions still depend on random sampling. Would you now say that the LLM has chosen a number immediately after it prints out "Ready?"
Then wouldn't you believe that in the case of my thought experiment, the number is also smeared through the parameter weights? Or maybe it's merely the intent to pick a number later that's smeared through the parameter weights?
But if I am right and ChatGPT isn't choosing a number before it says "Ready," why do you think that ChatGPT "has a plan?" Is the story situation crucially different in some way?
@Bill Benzon: A thought experiment. Suppose you say to ChatGPT "Think of a number between 1 and 100, but don't tell me what it is. When you've done so, say 'Ready' and nothing else. After that, I will ask you yes / no questions about the number, which you will answer truthfully."
After ChatGPT says "Ready", do you believe a number has been chosen? If so, do you also believe that whatever "yes / no" sequence of questions you ask, they will always be answered consistently with that choice? Put differently, you do not believe that the particular choice of questions you ask can influence what number was chosen?
FWIW, I believe that no number gets chosen when ChatGPT says "Ready," that the number gets chosen during the questions (hopefully consistently) and that, starting ChatGPT from the same random seed and otherwise assuming deterministic execution, different sequences of questions or different temperatures or different random modifications to the "post-Ready seed" (this is vague but I assume comprehensible) could lead to different "chosen numbers."
(The experiment is not-trivial to run since it requires running your LLM multiple times with the same seed or otherwise completely copying the state after the LLM replies "Ready.")
Author here. We were heavily inspired by multiple things, including Demski and Garrabrant, the 1990's work of Kalai and Lehrer, empirical work in our group inspired by neuroscience pointing towards systems that predict their own actions, and the earlier work on reflective oracles by Leike . We were not aware of @Cole Wyeth et al.'s excellent 2025 paper which puts the reflective oracle work on firmer theoretical footing, as our work was (largely but not entirely) done before this paper appeared.