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What's Going on in Machine Learning? Some Minimal Models

writings.stephenwolfram.com

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Re: What's Going on in Machine Learning? Some Minimal Models

#51
post #9

Tsetlin machines have been around for some time: https://en.wikipedia.org/wiki/Tsetlin_machine They are discrete, individually interpretable, and can be configured into complicated architectures.

This looks like it might be interesting or might not, and I wish it said more in the article itself about why it's cool rather than listing technicalities and types of machines. Do you have a favorite pitch in those dozens of references at the end?

Re: What's Going on in Machine Learning? Some Minimal Models

#52

Earlier quoted context omitted.

So, the thing is that linear algebra operations are very cheap already... you just need a lot of them. Any other 'cheap' method is going to have a similar problem: if the unit is small and not terribly expressive, you need a whole lot of them. But it will be compounded by the fact that we don't have decades of investment in making these new atomic operations as fast and cheap as possible. A good take-away from the Wo…

My take is that the neural network is a bit of a red herring -- people poked around in brains to see what was going on and noticed a network structure with many apparently simple computing nodes. So they tried making similar structures in software and quickly discovered they could do some interesting things. But it may turn out that the neural network was just nature's best implementation for "field programmable matr…

I think the point of wolfram's essay is that you don't need the base unit of computation to be a dot product

Re: What's Going on in Machine Learning? Some Minimal Models

#53
post #48
post #33

This article does a good job laying the foundation of why I think homiconic languages are so important, and doing AI in languages that aren't, are doomed to stagnation in the long term. The acrobatics that Wolfram can do with the code and his analysis is awesome, and doing the same without the homoiconicity and metaprogramming makes my poor brain shudder. Do note, Wolfram Language is homoiconic, and I think I remembe…

I'd be curious to see an example of what you are talking about wrt his analysis here.

I don't know how to express my thoughts coherently in such a small space and time, but I will try. There isn't "one" example.

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Almost all the code and its display is some form of meta-programming. Stephen Wolfram is literally brute-forcing/fuzzing all combinations of "code".

    - Permuting all the different rules/functions in a given scope
    - evolutionary adapting/modifying them
    - graphing and analyzing those structures
    - producing the HTML for display
I get that "normal machine learning" is also permuting different programs. But it's more special when you are using the same language for the whole stack. There is a canyon that you have to cross without homoiconicity, (granted I don't know exactly how Wolfram generated and analyzed everything here, but I have used his language before, and I see the hallmarks of it).

I can't really copy and paste an example for you, because plaintext struggles. Here is an excerpt some fanciness in there:

   And as an example, here are the results of the forward and backward methods for the problem of learning the function f[x] =   , for the “breakthrough” configurations that we showed above:
You might see a "just" a small .png interspersed in plain text. The language and runtime itself has deep support for interacting with graphics like this.

The only other systems that I see that can juggle the same computation/patterns around like this are pure object oriented systems like Smalltalk/Pharo. You necessarily need first class functions to come even close to the capability, but as soon as you want to start messing with the rules themselves, you need some sort of term re-writing, lisp macro, or fexpr (or something similar?).

Don't get me wrong, you can do it all "by hand" (with compiler or interpreter help), you can generate the strings or opcodes for a processor or use reflection libraries, generate the graphs and use some HTML generator library to stitch it all together. But in the case of this article, you can clearly see that he has direct command over the contents of these computations in his Wolfram Language compared to other systems, because it's injected right into his prose. The outcome here can look like Jupyter labs or other notebooks. But in homoiconic languages there is a lot more "first-class citizenry" than you get with notebooks. The notebook format is just something that can "pop out" of certain workflows.

If you try to do this with C++ templates, Python Attribute hacking, Java byte-code magic... like... you can, but it's too hard and confusing, so most people don't do it. People just end up creating specific DSLs or libraries for different forms of media/computations, with templating smeared on top. Export to a renderer and call it a day -> remember to have fun designing a tight feedback loop here. /s

Nothing is composable, and it makes for very brittle systems as soon you want to inject some part of a computation into another area of the system. It's way way overspecified.

Taking the importance of homoiconicty further, when I read this article I just start extrapolating, moving past xor or "rule 12", and applying these techniques to the symbolic logic, like Tseltin machine referenced in another part of this thread: https://en.wikipedia.org/wiki/Tsetlin_machine

Or using something like miniKanran: https://en.wikipedia.org/wiki/MiniKanren

It seems to me that training AI on these kinds systems will give them far more capability in producing useful code that is compatible with our systems, because, for starters, you have to dedicate less neuronal connections on syntax parsing with a grammar that is actually fundamentally broken and ad hoc. But I think there are far deeper reasons than just this.

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I think it's so hard to express this idea because it's like trying to explain why having arms and legs is better than not. It's applied to every part of the process of getting from point A to point B.

Also, addendum, I'm not 100% sure homoiconicity it "required" per se. I suppose any structured and reversible form of "upleveling" or "downleveling" logic that remains accessible from all layers of the system would work. Even good ol' Lisp macros have hygiene problems that can be solved, e.g. by Racket's syntax-parse.

Re: What's Going on in Machine Learning? Some Minimal Models

#54

I find it depressing that every time Stephen Wolfram wants to explain something, he slowly gravitates towards these simplistic cellular automata and tries to explain everything through them. It feels like a religious talk. The presentation consists of chunks of hard-to-digest, profound-sounding text followed by a supposedly informative picture with lots of blobs, then the whole pattern is repeated over and over. But…

I think that unless Wolfram is directly contradicting the Church-Turing thesis it is ok to skip over the finite automata sections.

It is a given from Church-Turing that some automata will be equivalent to some turing machines, and while it is a profound result the specific details of the equivalence isn't super important unless, perhaps, it becomes super fast and efficient to run the automata instead of Von Neumann architecture.

Re: What's Going on in Machine Learning? Some Minimal Models

#55
post #28

Say what you will about Wolfram: he's a brilliant writer and teacher. The way he's able to simplify complex topics without dumbing them down is remarkable. His visualizations are not only extremely helpful but usually also beautiful, and if you happen to have Mathematica on hand, you can easily reproduce what he's doing. Anytime someone asks me for a quick introduction to LLMs, I always point them to this article of…

“entropy is the log of the number of states that a system can be in that are consistent with all the information known about that system”. he is amazing at explaining things.

Re: What's Going on in Machine Learning? Some Minimal Models

#56
post #32

Earlier quoted context omitted.

You can see this by giving it broken code and seeing what it can predict. I gave copilot a number of implementations of factorial with the input of 5. When it recognized the correct implementations, it was able to combine the ideas of "factorial", "5", and "correct implementation" to output 120. But when I gave it buggy implementations, it could recognize they were wrong, but the concepts of "factorial", "5", and "in…

This makes very little sense (as a contrast to chatgpt predicted that the likely continuation of factorial and 5 is 120). Perhaps if you are able to share the chat session it's possible to see if you likely confused the issue with various factorial implementations - or got chatgpt to run your code with 5 as input? I mean the code is redundant: https://chatgpt.com/share/be249097-5067-4e3d-93c7-3eebedb510...

Do a google search with 'before:2020' on that code, that is recall from pre-training, not 'calculating'

Re: What's Going on in Machine Learning? Some Minimal Models

#57
post #31

Earlier quoted context omitted.

Computers still aren’t writing essays. They are stringing words together using copied data. If they were writing essays, I would suggest that it wouldn’t be so ridiculously easy to pick out the obviously AI articles everywhere.

> They are stringing words together using copied data. Which is what we will eventually realize is what humans are doing too.

It absolutely is NOT what humans are doing.

When humans write, they are serializing thoughts. Humans (well, most of us. Certainly not AI enthusiasts), are reasoning and thinking.

When AI writes, it is following a mathematical pathway to string words together that it has seen together before in the given context.

Re: What's Going on in Machine Learning? Some Minimal Models

#58
post #57

Earlier quoted context omitted.

> They are stringing words together using copied data. Which is what we will eventually realize is what humans are doing too.

It absolutely is NOT what humans are doing. When humans write, they are serializing thoughts. Humans (well, most of us. Certainly not AI enthusiasts), are reasoning and thinking. When AI writes, it is following a mathematical pathway to string words together that it has seen together before in the given context.

When an LLM solves a novel problem, it's also reasoning, unless you use some contrived definition of the word "reasoning" that doesn't match how the word is actually used in normal conversation. Also I fully expect the human brain to be encoded in a mathematical model.

And if it wasn't obvious, an LLM can string together two words that it had never seen together in the training dataset, it really shows how people tend to simplify the extremely complex dynamics by which these models operate.

Re: What's Going on in Machine Learning? Some Minimal Models

#59
post #8

Is a TL;DR available or at least some of the ideas covered? Because after 3 paragraphs it seems the good old "it is actually something resembling a cellular automata" post by Wolfram.

Wolfram explains the basic concepts of neural networks rather well, I think. He trains and runs a perceptron at the beginning und then a simpler network. Then he dwells into replacing the continuous functions they constitute into discrete binary ones — and ends up with cellular automata he thinks emulate neural networks and their training process. While this surely looks interesting all „insight“ he obtains into the original question of how exactly networks do learn is trained networks do not seem to come up with a simple model they use to produce the output we observe but rather find one combination of parameters in a random state space being able to reproduce a target function. There are multiple possible solutions that equally work well — so perhaps the notion of networks generalizing training data is perhaps not quite accurate (?). Wolfram links this to „his concept“ of „computational irreducibility“ (which I believe is just a consequence of Turing-completeness) but does not give any novel strategies to understand trained machine models or how to do machine learning in any better way using discrete systems. Wolfram presents a fun but at times confusing exercise in discrete automata and unfortunately does not apply the mathematical rigor needed to draw deep conclusions on his subject.

Re: What's Going on in Machine Learning? Some Minimal Models

#60
post #46

Earlier quoted context omitted.

Agree about SpaceX, but I'm not sure how much of that is about Elon. Tesla used to be awesome, its nascency is what I was referring to as the "honeymoon phase," but it definitely feels like it's gone downhill with the Cybertruck goofiness. Like it feels like it has some awesome engineers that do the cool stuff, and then you have Elon interfering from the top and injecting his goofy ass ideas while everyone else is tr…

Maybe "poor emotional intelligence". Like you said, a person can plausibly get lucky on their first business and make it big once. But to do it repeatedly and to such a large degree takes skill. Say what you will about his politics, but his companies deliver. Even Hyperloop, which is basically just a bad subway, still has more buildout than pretty much any subway system in the US in the past decade. That might just b…

I was with ya until the hyperloop example. Hyperloop was pushed for years as a vacuum tube train. Serious prototypes of this were developed. If it had worked out absolutely perfectly, it would still have lacked the throughput to be a good idea, but the prevalence of earthquakes in its target area, the inherent instability of a vacuum tube, the massive intended scale of the system, the economic feasibility of digging a huge tunnel, etc all made it an absolute shitfest of an idea. They then came up with a new idea, which was a one-lane tunnel without a safety walkway, which is utterly useless for passenger transport because it has, at best, the throughput of a two-lane highway. The hyperloop is probably elon’s most embarrassing failure after twitter.
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