Billion-Parameter Theories

Two 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.

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.

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.

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.

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.

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.

> 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.

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.

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.

> 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.

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.

...this is so absurdly and blatantly wrong that it's hard to move past. Has the author ever heard of programming languages??

[dead]

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.