My name is pronounced "YOO-ar SKULL-se".
I'm a DPhil Scholar at the Future of Humanity Institute in Oxford.
If a universality statement like the above holds for neural networks, it would tell us that most of the details of the parameter-function map are irrelevant.
I suppose this depends on what you mean by "most". DNNs and CNNs have noticeable and meaningful differences in their (macroscopic) generalisation behaviour, and these differences are due to their parameter-function map. This is also true of LSTMs vs transformers, and so on. I think it's fairly likely that these kinds of differences could have a large impact on the probability that a given type model will learn to exhibit goal-directed behaviour in a given training setup, for example.
The ambitious statement here might be that all the relevant information you might care about (in terms of understanding universality) are already contained in the loss landscape.
Do you mean the loss landscape in the limit of infinite data, or the loss landscape for a "small" amount of data? In the former case, the loss landscape determines the parameter-function map over the data distribution. In the latter case, my guess would be that the statement probably is false (though I'm not sure).
I'm not sure, but I think this example is pathological.
Yes, it's artificial and cherry-picked to make a certain rhetorical point as simply as possible.
This is the more relevant and interesting kind of symmetry, and it's easier to see what this kind of symmetry has to do with functional simplicity: simpler functions have more local degeneracies.¨
This is probably true for neural networks in particular, but mathematically speaking, it completely depends on how you parameterise the functions. You can create a parameterisation in which this is not true.
You can make the same critique of Kolmogorov complexity.
Yes, I have been using "Kolmogorov complexity" in a somewhat loose way here.
Wild conjecture: [...]
Is this not satisfied trivially due to the fact that the RLCT has a certain maximum and minimum value within each model class? (If we stick to the assumption that is compact, etc.)
The assumption that small neural networks are a good match for the actual data generating process of the world, is equivalent to the assumption that neural networks have an inductive bias that gives large weight to the actual data generating process of the world, if we also append the claim that neural networks have an inductive bias that gives large weight to functions which can be described by small neural networks (and this latter claim is not too difficult to justify, I think).
Does this not essentially amount to just assuming that the inductive bias of neural networks in fact matches the prior that we (as humans) have about the world?
This is basically a justification of something like your point 1, but AFAICT it's closer to a proof in the SLT setting than in your setting.
I think it could probably be turned into a proof in either setting, at least if we are allowed to help ourselves to assumptions like "the ground truth function is generated by a small neural net" and "learning is done in a Bayesian way", etc.
That's interesting, thank you for this!
I think the broad strokes are mostly similar, but that a bunch of relevant details are different.
Yes, a large collective of near-human AI that is allowed to interact freely over a (subjectively) long period of time is presumably roughly as hard to understand and control as a Bostrom/Yudkowsky-esque God in a box. However, in this scenario, we have the option to not allow free interaction between multiple instances, while still being able to extract useful work from them. It is also probably much easier to align a system that is not of overwhelming intelligence, and this could be done before the AIs are allowed to interact. We might also be able to significantly influence their collective behaviour by controlling the initial conditions of their interactions (similarly to how institutions and cultural norms have a substantial long-term impact on the trajectory of a country, for example). It is also more plausible that humans (or human simulations or emulations) could be kept in the loop for a long time period in this scenario. Moreover, if intelligence is bottle-necked by external resources (such as memory, data, CPU cycles, etc) rather than internal algorithmic efficiency, then you can exert more control over the resulting intelligence explosion by controlling those resources. Etc etc.
Yes, I agree with this. I mean, even if we assume that the AIs are basically equivalent to human simulations, they still get obvious advantages from the ability to be copy-pasted, the ability to be restored to a checkpoint, the ability to be run at higher clock speeds, and the ability to make credible pre-commitments, etc etc. I therefore certainly don't think there is any plausible scenario in which unchecked AI systems wouldn't end up with most of the power on earth. However, there is a meaningful difference between the scenario where their advantages mainly come from overwhelmingly great intelligence, and the scenario where their advantages mainly (or at least in large part) come from other sources. For example, scaleable oversight is a more realistic possibility in the latter scenario than it is in the former scenario. Boxing methods are also more realistic in the latter scenario than the former scenario, etc.
To clarify, the proposal is not (necessarily) to use an LLM to create an interpretable AI system that is isomorphic to the LLM -- their internal structure could be completely different. The key points are that the generated program is interpretable and trustworthy, and that it can solve some problem we are interested in.
""
The kinds of humans that we are worried about are the kinds of humans that can do original scientific research and autonomously form plans for taking over the world. Human brains learn to take actions and plans that previously led to high rewards (outcomes like eating food when hungry, having sex, etc)*. These two things are fundamentally not the same thing. Why, exactly, would we expect that a system that is good at the latter necessarily would be able to do the former?"
""
This feels like a bit of a digression, but we do have concrete examples of systems that are good at eating food when hungry, having sex, and etc, without being able to do original scientific research and autonomously form plans for taking over the world; animals. And the difference between humans and animals isn't just that humans have more training data (or even that we are that much better at survival and reproduction in the environment of evolutionary adaptation). But I should also note that I consider argument 6 to be one of the weaker arguments I know of.
""
We know, from computer science, that it is very powerful to be able to reason in terms of variables and operations on variables. It seems hard to see how you could have human-level intelligence without this ability. However, humans do not typically have this ability, with most human brains instead being more analogous to Boolean circuits, given their finite size and architecture of neuron connections.
""
The fact that human brains have a finite size and architecture of neuron connections does not mean that they are well-modelled as Boolean circuits. For example, a (real-world) computer is better modelled as a Turing machine than as a finite-state automaton, even though there is a sense in which they actually are finite-state automata.
The brain is made out of neurons, yes, but it matters a great deal how those neurons are connected. Depending on the answer to that question, you could end up with a system that behaves more like Boolean circuits, or more like a Turing machine, or more like something else.
With neural networks, the training algorihtm and the architecture together determine how the neurons end up connected, and therefore, if the resulting system is better thought of as a Boolean circuit, or a Turing machine, or otherwise. If the wiring of the brain is determined by a different mechanism than what determines the wiring of a deep learning system, then the two systems could end up with very different properties, even if they are made out of similar kinds of parts.
With the brain, we don't know what determines the wiring. This makes it difficult to draw strong conclusions about the high-level behaviour of brains from their low-level physiology. With deep learning, it is easier to do this.
""
I find it hard to make the argument here because there is no argument -- it's just flatly asserted that neural networks don't use such representations, so all I can do is flatly assert that humans don't use such representations. If I had to guess, you would say something like "matrix multiplications don't seem like they can be discrete and combinatorial", to which I would say "the strength of brain neuron synapse firings doesn't seem like it can be discrete and combinatorial".
""
What representations you end up with does not just depend on the model space, it also depends on the learning algorithm. Matrix multiplications can be discrete and combinatorial. The question is if those are the kinds of representations that you in fact would end up with when you train a neural network by gradient descent, which to me seems unlikely. The brain does (most likely) not use gradient descent, so the argument does not apply to the brain.
""
Do you perhaps agree that you would have a hard time navigating in a 10-D space? Clearly you have simply memorized a bunch of heuristics that together are barely sufficient for navigating 3-D space, rather than truly understanding the underlying algorithm for navigating spaces.
""
It would obviously be harder for me to do this, and narrow heuristics are obviously an important part of intelligence. But I could do it, which suggests a stronger transfer ability than what would be suggested if I couldn't do this.
""
In some other parts, I feel like in many places you are being one-sidedly skeptical.
""
Yes, as I said, my goal with this post is not to present a balanced view of the issue. Rather, my goal is just to summarise as many arguments as possible for being skeptical of strong scaling. This makes the skepticism one-sided in some places.
You can imagine different types of world models, going from very simple ones to very detailed ones. In a sense, you could perhaps think of the assumption that the input distribution is i.i.d. as a "world model". However, what is imagined is generally something that is much more detailed than this. More useful safety specifications would require world models that (to some extent) describe the physics of the environment of the AI (perhaps including human behaviour, though it would probably be better if this can be avoided). More detail about what the world model would need to do, and how such a world model may be created, is discussed in Section 3.2. My personal opinion is that the creation of such a world model probably would be challenging, but not more challenging than the problems encountered in other alignment research paths (such as mechanistic interpretability, etc). Also note that you can obtain guarantees without assuming that the world model is entirely accurate. For example, consider the guarantees that are derived in cryptography, or the guarantees derived from formal verification of airplane controllers, etc. You could also monitor the environment of the AI at runtime to look for signs that the world model is inaccurate in a certain situation, and if such signs are detected, transition the AI to a safe mode where it can be disabled.