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The Emergent Symbolic Structure of Artificial Neural Networks

arxiv.org

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Re: The Emergent Symbolic Structure of Artificial Neural Networks

#41

Post by subsistence234 »

andytratt wrote: post #19

this is an obvious result. for example, this guy has been writing on substack about this for at least a year or two (with code snippets) explaining the phenomenon of grokking and the ghostbasin.com concept - https://richardaragon.substack.com/ their algorithm is even named "DISCOVER" so they set out to discover the connective tissue of why the universe has invariants like math, and lo it was discovered. i guess good…

Post the actual articles that you have in mind. What I've seen is vague slop.

A good example is https://richardaragon.substack.com/p/a-universal-prime-funct... describing a supposed "universal prime function" which is simply a finite approximation using a sum of 50 sines (each applied to a linear term plus a sine-log offset). The 53 parameters are fitted to the first 10^3 or so prime numbers. This is followed by the *absolutely ridiculous* claim that if the function approximates the first 10^3 primes well, it must also fit the remaining prime numbers (of which there are infinitely more than 10^3000000000) equally well.

Then they suggest "A formal proof connecting this function to the RH would involve the following steps" using this great discovery: "1. Correspondence with the Explicit Formula: Demonstrate that the oscillatory correction term in our function corresponds to the sum over zeta zeros in the explicit formula for ψ(x) or π(x). 2. Error Bound: Prove that the error in the prime counting function derived from our function is bounded by O(√x log x). 3. Contradiction: Show that if any non-trivial zero were to lie off the critical line ℜ(s) = 1/2, the error would exceed the bound, leading to a contradiction."

This isn't even midwit math.

It's the kind of naive ideas I had as a high schooler, who was good at high school math and who knew how to code functions and plots in Mathematica, but who had no understanding of higher math. This kind of naive approach to RH signals that one doesn't even understand the problem.

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#42

Post by trnkinju »

Symbolism has tried to strike back repeatedly ever since statistical learning revived with AlexNet. With all the due respect one can have for the names Smolensky and Linzen from the perspective of linguistics, the question about the applicability, generalizability and robustness of the method proposed here should be raised. It seems from section 3.5 of the paper that one cannot be so optimistic about it at least as yet. I get it that the method is still in its infancy, but we've already got the kind of Mech Interp as pushed forward by Neel Nanda and co, among other lines of research. Not that we are forced to make a choice between all interpretability works, or this TPR method is inherently inferior to the other ones, but we can be moderately cautious when looking at such progress.

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#43

Post by gps372 »

As I am going through the article, I was wondering why is this more interesting than having the ability to recover java programs from byte code. So I asked copilot the same question. It told me that - "Honestly this is where the difference between an engineer and researcher shows up!" .

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#45

Post by noduerme »

sigpwned wrote: post #9

The big questions I’m taking away are: (1) they are claiming to produce apparently bijective closed-form symbolic representations/approximations of, among other things, LLMs. Is evaluating these closed-form representations more computationally efficient? The implications of that are potentially huge. It would be essentially analytic distillation. Fable on a chip and not a data center would be important — and disrupti…

Inference is just tokens transformed through a fixed crystalline structure, no? You already could put that on a chip. There's no particular reason it couldn't be represented as some set of symbolic equations instead of a layered process... it's just another kind of quantization.

When symbolic algorithms are that large, they're equally hard to reason with most of the time. The upshot would be a lot more storage required in exchange for more generalized computing, lessening the need for so much GPU in a lot of cases.

I don't see why a model couldn't be represented that way. After all, if you just polled the output of a model, you could evolve genetic algorithms to predict it with fairly high accuracy in a limited domain. Take that out to the Nth degree and you're basically just unspooling the model into a giant set of equations.

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#46

Post by imtringued »

Madmallard wrote: post #37
brabel wrote: post #32

Earlier quoted context omitted.

You are disconnected from reality. The whole industry is already completely dominated by LLMs generating code. Bury your head in the sand all you want. This is not about low expectations or inexperience at all. Your condescending tone doesn't make you look smarter, it makes you look like an Amish who expects the industrial revolution is temporary and soon people will come to their senses and stop using all this nonse…

Yup and the industry is worse than ever. Maybe you forgot that important tidbit? People are using them because they're being shoved down their throats and they're complacent. Software quality, maintainability, exploitability, morale, competency are all at all-time lows and just worsening. It's really bad to defend this.

I spent the last 6 months reviewing all of the AI generated code primarily with gpt 5.3 codex but after I bought the subscription I also used gpt 5.5 and although I was constantly rejecting the bad code and I was mostly happy with the end result.

Then they removed the approve everything manually mode and I thought, maybe I'm the one out of touch, I should try vibe coding. I gave it a big spec of things to implement and I was pretty vague on the details, but I was kind of hoping that the AI would get it right anyway.

I noticed that when you let the AI just do its thing, you spend a lot of time staring at the screen waiting for it to finish. No wonder all these people are obsessed with parallel agents.

Anyway, after a while it produced the end result and it was pretty bad and I don't even mean the code. This was with gpt 5.6 Terra. Definitively not the type of "did a week's worth of work in one hour" type of deal.

Meanwhile if you guide it with your own technical skills the end result is a tireless code generator that operates at 80% of the quality of your own code but is only roughly 1.5x to 2x faster than doing it yourself. The biggest multipliers come from making the AI do things humans don't want to do, like writing a bunch of thorough tests but those don't translate into increased productivity, the opposite in fact. They translate into higher software quality but if you vibe the tests and don't review them, even that disappears.

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#47

Post by philipswood »

hliyan wrote: post #16
profsummergig wrote: post #8

The human mind cannot comprehend the capacity of massively multidimensional space. Just going from 2D to 3D creates massive new positional potential (e.g. surface of the earth, vs. the atmosphere above earth...). Now imagine 1,000 dimensions.

This is nonsense. The human mind cannot visualize more than 3 dimensions. It can perfectly comprehend any number of dimensions as long as they are represented in a vector space. In fact, that's what linear algebra does.

I think it would be fair to say that at least a few people can do a small amount of 4d visualisation.

Agreed, I don't think anyone has a good grasp on, say, 64K D, but we can do a bit better than just 3.

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#48

Post by khalic »

sublinear wrote: post #26
pineaux wrote: post #18

Earlier quoted context omitted.

What about the mathematical advancements?

Doesn't that say more about the massive crumb tray nobody ever bothered to empty at the bottom of mathematics? I'm sure someone will point out something like the 4-color theorem as a counterargument. Where is that kind of theorem proving in this generation of AI? We seem to have hit a dead end rather quickly.

Lol, are you saying the Erdos problems are a "crumb" that nobody bothered to empty? Are you doing a comedy routine?

Re: The Emergent Symbolic Structure of Artificial Neural Networks

#49

Post by imtringued »

suddenlybananas wrote: post #33
colordrops wrote: post #15

"Vectors seem inadequate for capturing the structure of language, logic, and other cognitive domains, yet neural networks achieve impressive performance in these areas". Missing the forest for the trees? Aren't neural networks modeled after biological systems? Our brains are obviously able to contain symbolic structure despite not having a "symbol processing unit".

People really overstate the relationship between ANNs and the brain, they have very different mechanisms and only have a similarity if you squint at 100000 feet. ANNs don't have neurotransmitters or even action potentials.

Correct. Worst of all, even if you do build a spiking neural network, the update rule is kind of a mystery. To have a good update rule, a biological neuron needs to be kind of like a tiny computer in its own right. You might be able to model synapses as weights between neurons, but the neuron carries further internal states within in itself and how the "update rule" uses those internal states is not known at all.
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