Billion-Parameter Theories
worldgov.orgTwo handwavey ideas upon reading this:
- Even for billion-parameter theories, a small amount of vectors might dominate the behaviour. A coordinate shift approach (PCA) might surface new concepts that enable us to model that phenomenon. "A change in perspective is worth 80 IQ points", said Alan Kay.
- There is analogue of how we come up with cognitive metaphors of the mind ("our models of the mind resemble our latest technology (abacus, mechanisms, computer, neural network)"), to be applied to other complicated areas of reality.
> Even for billion-parameter theories, a small amount of vectors might dominate the behaviour.
We kinda-sorta already know this is true. The lottery-ticket hypothesis [0] says that every large network contains a randomly initialized small network that performs as well as the overall network, and over the past eight years or so researchers have indeed managed to find small networks inside large networks of many different architectures that demonstrate this phenomenon.
Nobody talks much about the lottery-ticket hypothesis these days because it isn’t practically useful at the moment. (With the pruning algorithms and hardware we have, pruning is more costly than just training a big network.) But the basic idea does suggest that there may be hope for interpretability, at least in the odd application here or there.
That is, the lottery-ticket hypothesis suggests that the training process is a search through a large parameter space for a small network that already (by random initialization) exhibit the overall desired network behavior; updating parameters during the training process is mostly about turning off the irrelevant parts of the network.
For some applications, one would think that the small sub-network hiding in there somewhere might be small enough to be interpretable. I won’t be surprised if some day not too far into the future scientists investigating neural networks start to identify good interpretable models of phenomena of intermediate complexity (those phenomena that are too complex to be amenable to classic scientific techniques, but simple enough that neural networks trained to exhibit the phenomena yield unusually small active sub-networks).
I don't disagree, but neither does the article. It's just talking about the fact that we previously considered anything that can't be easily and tersely written down as nearly or entirely intractable. But, as we have seen, the three body problem is not really a hum-dinger as far as the universe goes, it's not even table stakes. We need to be able to do the same kind of energy arbitrage on n-body problems that we do on 2. And now we have the beginnings of a place to toy with more complicated ideas -- since these won't fit on a blackboard.
Problems with opaque stability boundaries that observe non-liner effects are always great. Chaos theory makes it even more fun as your observation can change the outcome.
Maybe we can come up with smaller models that perform almost as well as the bigger ones. Could that just be pca of some kind?
Gpt nano vs gpt 5 for example.
AI slop DNR
Reminds me of the blog post about Waymo's "World Model". Training on real-world data results in a sufficiently rich model to start simulating novel scenarios that aren't in the training data (like the elephant wandering into the street), which in turn can feed back into training. One could imagine scientific inquiry working the same way.
It strikes me that many of these complex systems have indeterminate boundaries, and a fair amount of distortion might be baked into the choice of training data. Poverty (to take an example from this post) probably has causes at economic, psychological, ecological, physiological, historical, and political levels of description (commenters please note I didn't think too hard about this list). What data we feed into our models, and how those data are understood as operationalizations of the qualitative phenomena we care about, might matter.
> like the elephant wandering into the street
Or a dinosaur that looks like it might:
This "world model" concept has been a big deal in AI research, in LLMs.
He talks about the Santa Fe institute and how they failed to carry their findings into the real world.
They did not.
They showed that for certain problems one could not do more than figure out some invariant and scaling laws. Showing what is impossible is not failure.
For the rest: Modern gene networks and lots of biological modelling is based on their work as well as quite a few other things. That’s also not failure.
I agree that modern AI is alchemy.
True -- I didn't mean to communicate that Santa Fe was a failure writ large. Their contribution was very important!
Though I think it's fair to say that the torch was picked up and carried by others with a different set of strategies.
Clarke's second law:
When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
Also see Minsky's "Perceptrons"
The problem with almost all such proofs is that people (even those who know better) read them as "this can't be done" when in fact they tell you "it can't be done unless you break one of the following assumptions."
I agree that it's unfair to say they failed, but it's likewise unfair to say that their success was in telling us our limits rather than exploring what we need to do to get around the roadblocks.
I disagree with the article. I think it is always possible to come up with reasonably small theories that capture most of the given phenomena. So in a sense, you don't need complex theories in the form of large NNs (models? functions? programs?), other than for more precise prediction.
For example - global warming. It's nice to have AOGCMs that have everything and the carbon sink in them. But if you want to understand, a two layer model of atmosphere with CO2 and water vapor feedback will do a decent job, and gives similar first-order predictions.
I also don't think poverty is a complex problem, but that's a minor point.
> I also don't think poverty is a complex problem, but that's a minor point.
I'm not sure it's a minor point. I don't think poverty is a "complex" problem either, as that term is used in the article, but that doesn't mean I think it fits into one of the other two categories in the article. I think it is in a fourth category that the article doesn't even consider.
For lack of a better term, I'll call that category "political". The key thing with this category of problems is that they are about fundamental conflicts of interest and values, and that's a different kind of problem from the kind the article talks about. We don't have poverty in the world because we lack accurate enough knowledge of how to create the wealth that brings people out of poverty. We have poverty in the world because there are people in positions of power all over the world who literally don't care about ending poverty, and who subvert attempts to do so--who make a living by stealing wealth instead of creating it, and don't care that that means making lots of other people poor.
When all of humanity was hunting and gathering and living at subsistence levels, the was no poverty. It only shows up with wealth.
Pretty simple.
> I think it is always possible to come up with reasonably small theories that capture most of the given phenomena.
I can write a program (call it a simulation of some artificial phenomenon) whose internal logic is arbitrarily complex. The result is irreducible: the entire byzantine program with all of its convoluted logic is the smallest possible theory to describe the phenomenon, and yet the theory is not reasonably small for any reasonable definition.
That's true but I can still approximate what the system does with a simpler model. For example, I can split states of the system into n distinct groups, and measure transition probabilities between them.
Thermodynamics is a classic example of a phenomenological model like that.
Summary: good scientific theories have “reach,” which is not defined in any precise way. Reach has complexity and this can be handled with large parameter neural networks. Assumptions: mechanistic and deterministic worldview; epistemological perfection is the goal (perfect knowledge of facts).
Connectionist models have lots of theory by theoreticians explicitly pissed off about Chomsky's assertion that there is an inbuilt ability for language. Jay McClelland's office had a little corkboard thingy with Chomsky mockery on the side, for example. Putting forth even the implicature that the present direct descendants are intellectual descendants of Chomsky is like saying Protestants are intellectual descendants of Pope Leo X.
Perhaps a failure of communication -- I was indeed attempting to say that Chomsky was wrong and his ideas were interesting, but more or less a dead end.
>Jay McClelland's office had a little corkboard thingy with Chomsky mockery on the side, for example.
I've never understood why the idea of linguistic nativism is so upsetting to people.
Indeed, operating human lips, teeth, tongue, and larynx is far beyond language models.
Give language models 500 million years and lets revisit this. One of the reasons robots are harder to reach parity than higher intelligence, evolution has been cooking it a long time.
Apologies if I'm stepping on a joke, but just in case: Nativism is about cognitive capacities, not sensorimotor ones. All apes could easily communicate just as well as Helen Keller, yet none of them have ever asked a question, much less written a book!
Well that anecdote is referencing the Scruffies v. Neat war[1], within which the nativism debate was merely a somewhat-archaic undercurrent.
IMHO, a lot of the more specifically anti-nativist sentiments of today are based in linguistics itself rather than philosophy, CS, or CogSci, where again it is part of a broader (and much dumber) debate: whether linguistics is the empirical study of languages or the theoretical study of language itself. People get really nasty when they're told that they work in an offshoot field for some reason, which is why I blame them for the ever-too-common misunderstandings of Chomsky -- the most common being "Universal Grammar has been disproven because babies don't speak English in the womb".
If Chomsky weren't so obviously right, this would be a worrying development! Luckily I expect it to be little more than a footnote in history, so it's merely infuriating rather than depressing.
[1] Minsky, 1991: https://ojs.aaai.org/aimagazine/index.php/aimagazine/article...
If we think of spacetime as some sort of cellular automaton, where each state of a given point is a function (with some randomness, because God likes to throw dice) of previous states of the surrounding points, if the rules for a new state generation are extremely complex, there will be some significant overhead in dimensions we don't see, because the rules need to be somehow represented outside the observable reality. Another issue with this idea is that while the rules might be "outside", the parameters themselves have to be somehow encoded in the state of a cell, and can't propagate faster than light, or one cell (an indivisible unit of space) per indivisible unit of time), which limits the number of parameters accessible to any given cell to the ones immediately surrounding it.
Disclaimer: I hope it's obvious, but I'm no physicist. This is just how I would build a universe.
It's an optimistic point of view. Still, when people use large neural nets to model physics, they also have a lot of parameters but they replicate very simple laws. So there's something deeper about this. Something like a simulation of theory.
The deeper may just be the uncertain nature of quantum physics. That is any complex system must be built from redundant and repeatable actions, and/or have a self correction mechanism to fix itself if a bit happens to flip out of the universe. This leads to the evolutionary weeding out of indivisible complex systems as the system gains more components its improbable that a load bearing structure in that system will not fail.
Hence every system we get to see in nature is built from smaller components that generate complexity via repetition.
Our computers don't escape from this either. As the components get smaller you end up with your charge probability field outside of your component traces.
This might be an unkind reading, but to me this just sounds like an attempt to reinvent the very same kind of mysticism that it mentions in the first paragraph.
“No need to study the world around you and wonder about its rules, peasant - it’s far beyond your understanding! Only ~the gods~ computers can ever know the truth!”
I shudder to think about a future where people give up on working to understand complex systems because it’s hard and a machine can do it better, so why bother.
Mark Cubain had a good line, I don't know if he came up with it or who, but he reportedly said:
" There are 2 types of people using AI: Those who use it so they can know everything, and those who use it so they don't have to know anything. " :-
I think probably the sweet spot is using them so you can focus on knowing only the things you care about or need to know about about.
Not the intention at all. The part about mechanistic interpretability was meant to gesture at how building such systems can provide new tool kit for building further intuition and understanding.
Might we ever distinguish what is complex and complicated? Probably not, but I guess the author argues that this gives us a way forward because we can try to distill large models.
> You could capture the behavior of every falling object on Earth in three variables and describe the relationship between matter and energy in five characters.
What we can do is to approximate. Newton had a good approximation some time ago about gravitation (force equals a constant times two masses divided by distance squared. Super readable indeed) But nowadays there's a better one that doesn't look like Newton's theory (Einstein's field equations which look compact but nothing like Newton's). So, what if in a 1000 years we have yet a better approximation to gravity in the universe but it's encoded in millions of variables? (perhaps in the form of a neural network of some futuristic AI model?)
My point is: whatever we know about the universe now doesn't necessarily mean that it has "captured" the underlaying essence of the universe. We approximate. Approximations are useful and handy and will move humanity forward, but let's not forget that "approximations != truth"
If we ever discover the underlaying "truth" of the universe, we would look back and confidently say "Newton was wrong". But I don't think we will ever discover such a thing, thereore sure approximations are our "truth" but sometimes people forget.
Einstein’s equations look like Newton’s in the limit. It would be a little weird if we ended up having to add millions of additional parameters over the next thousand years. At the current rate we seem to get multiple years per parameter, rather than hundreds of parameters per year, right?
This kind of view tends to logically conclude in the idea of a noumenal, unknowable reality. I think it's more reasonable to say that truth itself is gold star we award to descriptions that suit our purposes. After all, descriptions are necessarily approximations (or reductive or "compressions"), since the only model of a thing with 100% fidelity is... the thing itself.
Agreed!
> It's remarkable how much of reality turned out to be modelable by theories that fit in a few symbols.
The admiration for "remarkable" things puts humanity on a dangerous path that is disconnected from the real goals of human progress as a species. You don't need any of this compression of knowledge or truths. Folklore tales about celestial bodies are fine and hood enough. The vulgar pursuit for knowledge is paving the way for extinction of humans as biological creatures.
Right, dinosaurs were perfectly fine, their ignorance worked out well for them.
The universe is uncaring, simply not giving a shit if you have knowledge or not. Knowledge gives you the ability to survive minor conniption fits of cosmic magnitude, and at the same time gives you a gun to shoot your own foot off.
There ain't no such thing as a free lunch.
So you think your tech can help you survive the event that made dinosaurs go bust.
The core of this little essay seems to be this:
Instead of "I understand the causal mechanism and can predict what happens if I change X," you get something more like "I have a sufficiently rich model that I can simulate what happens if I change X, with probabilistic confidence." The answers are distributions, not deterministic outputs. That's a different kind of knowing.
At the beginning this sounded like, "hard problems are complex, machine learning can help us manage complexity, therefore we will be able to solve hard problems with machine learning", which betrays a shallowness of understanding. I think what this essay argues here is a little deeper than that trite tech-bro hype meme.
But I disagree with this conclusion: I don't know that we can begin to build these models to begin with or that our new LLM/transformer-powered tools can help solve these problems. If simulation were the answer to everything, why will new ML tools make a significant difference in ways that existing simulation tools do not?
Stuff like AlphaFold is amazing—I'm not saying that better medical results won't come about from ML—but I feel like there's some substance missing and that even this level of excitement that the author expresses here needs more and better backing.
Very skeptical Adam Curtis hat on while reading this, but it is quite well written. Thanks & kudos!
I think this also creates a vulnerability where, the more time and effort is spent to craft the “correct” solution, it becomes easier to dismiss topics out of hand. Even if our modeling tools have changed, emotions and the human mind have not.
Maybe I missed the point, but this read like Big Think Thought Leadership that would make a good TED talk but not much else. I'll just put it on the big pile over there.
There's a parallel in linguistics. Chomsky showed that all human languages share deep recursive structure. True, and essentially irrelevant to the language modeling that actually learned to do something with language.
Let's gather authors of 15 different world languages together in a room and see if they can collaboratively write a short story. Surely their inability to do so will prove their inadequacy in their native language. /s
Simplicity brings us closer to truth — Occam's razor has underpinned the development of our species for centuries. It's enterprise, empire, and capital that feed off of complexity.
We're entering a period of human history where engineers and businesspeople drive academic discourse, rather than scientists or philosophers. The result is intellectual chicken scratch like this article.