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Large Language Models Are Neurosymbolic Reasoners

arxiv.org

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Re: Large Language Models Are Neurosymbolic Reasoners

#71

Post by pistachiopro »

clooper wrote: post #5

I was recently thinking how every neural network is equivalent to a lookup table where the input is all numbers up to what can be expressed within the context window and the output is the result of the arithmetic operations applied to that number. So every neural network is equivalent to T = {(i, f(i)) : i The main practical issue is the size of the table but I don't see any theoretical reasons why this is incorrect.…

Take a relatively simple large language model like Llama 1. It has a context of 2048 tokens and each token can be one of 32,000 values. So the lookup table would need 32,000^2048 entries. That's not just impractically large, that's larger than cosmically large. There are only estimated to be about 10^80 atoms in the visible universe. So while a 32,000^2048 lookup table might be a valid concept mathematically, it's not anything you can intuit physically, and therefore not something you can say is incapable of reason.

Re: Large Language Models Are Neurosymbolic Reasoners

#72

Post by [deleted] »

clooper wrote: post #13
Centigonal wrote: post #9

Earlier quoted context omitted.

It sounds like you're asking whether the output of a neural network is a deterministic function of its input. For many LLMs, you can make that answer yes with the right combination of parameters (temperature = 0) and underlying compute (variance in floating point calculations can still introduce randomness in model outputs even when the model should theoretically return the same answer every time). There are some way…

People can not be reduced to lookup tables even in theory. No one even knows how a single cell does what it does let alone an entire organism like a person. I'm not making an abstract claim about neural networks because all numerical algorithms like neural networks can be reduced to a lookup table given a large enough hard drive. This is not practical because the space required would exceed the number of atoms in the…

[deleted]

Re: Large Language Models Are Neurosymbolic Reasoners

#73

Post by nielsbot »

littlestymaar wrote: post #69
eru wrote: post #68

Earlier quoted context omitted.

Humans also fail much of the time at 'multi jump' reasoning. You have to prod them.

Except no human (non-colorblind at least) past three years old thinks bananas have the same color as the sky (see the example given in the repo, that's a mistake literally no human could make)

Maybe not no human :) But probably 99.99% of them.

Re: Large Language Models Are Neurosymbolic Reasoners

#74

Post by mewpmewp2 »

littlestymaar wrote: post #69
eru wrote: post #68

Earlier quoted context omitted.

Humans also fail much of the time at 'multi jump' reasoning. You have to prod them.

Except no human (non-colorblind at least) past three years old thinks bananas have the same color as the sky (see the example given in the repo, that's a mistake literally no human could make)

For what it's worth, I tried it on ChatGPT and this was its response:

"The color of the daytime sky is commonly blue. The common household fruit that is also blue would be blueberries. Blueberries typically grow in acidic soil. The pH of the soil they grow in is usually between 4.5 and 5.5."

Re: Large Language Models Are Neurosymbolic Reasoners

#75

Post by bubblyworld »

still_grokking wrote: post #70
bubblyworld wrote: post #61

Earlier quoted context omitted.

I'm not sure. I've beaten it a number of times, but only using tons of spoilers as you say. That said, there are players who consistently win almost every game, which is crazy (there's an online nethack server somewhere, can't remember the name offhand, but you can search player stats and some of them are insane). Edit: here's one, a player with a 60% win rate, not as crazy as I initially thought but if you've ever p…

Of course one can beat Nethack. Many people did. That's not the point. The question was more: Without "spoilers" (a.k.a. "hardcoded heuristics and goals")? (I never made progress because I didn't try hard enough. It became very boring after finding out that this game is random and quite nonsensical, and one can't come up with some strategy only by playing it often enough. I'm in general not enjoying dice games. I pre…

Relax, friend, I understand your question =) I'm just pointing out that it's not as random as you think. Mechanics in NetHack are quite predictable for the most part, but they are difficult to _discover_ without dying. Given that AIs can play hundreds of thousands of runs in the time it would take me to play one, I'm a bit more optimistic that they could learn the mechanics eventually.

I think the fundamental problem is that nobody knows how to do exploration-based reward functions effectively. Has Pitfall been solved by modern RL, for instance? As far as I know that's still an open problem (alongside getting to diamonds in minecraft without hardcoded heuristics, and other things along the same line).

(edit: just in terms of evidence for the first claim, once I'd done a run successfully with spoilers I was able to beat the game again without looking anything up. So I think it's more a discovery problem than nethack being inherently random)

Re: Large Language Models Are Neurosymbolic Reasoners

#76

Post by Terretta »

clooper wrote: post #5

I was recently thinking how every neural network is equivalent to a lookup table where the input is all numbers up to what can be expressed within the context window and the output is the result of the arithmetic operations applied to that number. So every neural network is equivalent to T = {(i, f(i)) : i The main practical issue is the size of the table but I don't see any theoretical reasons why this is incorrect.…

> thinking how every neural network is equivalent to a lookup table where the input is all numbers up to what can be expressed within the context window and the output is the result of the arithmetic operations applied to that number... no neural network is actually doing any thinking other than uncompressing the table and looking up the value corresponding to the input number

You're proposing the lookup table as one possible mechanism in Searle's chinese room, then proposing Searle's conclusion?

“Searle argues that, without ‘understanding’ (or ‘intentionality’), we cannot describe what the machine is doing as ‘thinking’ and, since it does not think, it does not have a ‘mind’ in anything like the normal sense of the word. Therefore, he concludes that the ‘strong AI’ hypothesis is false.‘

https://en.wikipedia.org/wiki/Chinese_room

I think you've said Chinese room, run as many times as it takes to get all possible sequences of Chinese characters to cache the results, then using those run it and ask if it's still or yet ‘thinking’.

PS. Where did the arithmetic operations come from? How did they come to be as they are? Is iterating to an algo that does that, ‘learning’? What's the difference between this and lossy or non-lossy compression of information? Could it be said the arithmetic operations are a compression of the lookup table into that which has the ‘right’ response given the inputs? If two different sets of arithmetic operations give by and large the same outputs from inputs, is one of them more ‘reasoning’ than the other depending how it's derived? What do we mean by ‘learning’ and ‘reasoning’ when applying those words to humans? Are teachers telling students to ‘show your work’ searching for explainable intelligence? :-)

Re: Large Language Models Are Neurosymbolic Reasoners

#77

Post by still_grokking »

neurallambda wrote: post #65

I'm trying to tackle this problem more head-on, by outfitting LLMs with lambda calculus, stacks, queues, etc. directly in their internals, operating over their latent space. [1] I'll read your paper, but, LLMs famously fail horribly at "multi jump" reasoning, which to me means they can't reason at all. They can merely output a reflection of the human reasoning that was baked into the training data, and they can also…

May I ask why there are NNs in your project at all? Just to heat up the planet and make Nvidia share holders even more happy? :-)

I mean, what I've seen in the Readme makes sense. But doing basic computer stuff with NNs just makes the resource usage go brr by astronomical factors, for imho no reason, while making the results brittle, random, and often just completely made up.

Also: Do you know about the (already 40 year old!) project Cyc?

https://en.wikipedia.org/wiki/Cyc

This software can indeed "reason". And it does not hallucinate; because it's not based on NNs.

Re: Large Language Models Are Neurosymbolic Reasoners

#78

Post by mjburgess »

bubblyworld wrote: post #51
imtringued wrote: post #49

Earlier quoted context omitted.

How do you lookup quantum mechanics? Please tell the physicists about your breakthroughs.

No need, physicists already do this all the time - any computer simulation of quantum mechanical systems has to come to terms with the same problems (namely quantising the state space and representing the dynamics deterministically).

Physicists simulate on computers only what can be, which is almost nothing. Consider obtaining the dynamics of water by simulating all its parts: proton flow, hydrogen bonding etc. of 10^{PHYSICALLY UNCOMPUTABLE} interactions.

The simulations which do exist fail to model vast amounts. This is why, say, climate change is given as a prediction on temperature -- because it can be obtained as a mean which ignores "basically everything".

And it can be easily show that the assumptions of QM are false if Hilbert space is computable (QM becomes non-linear); and of classical mechanics (which becomes non-deterministic); and so on. ie., that the issue isnt merely 10^{PHYSICALLY UNCOMPUTABLE} but that non-computable functions are essential to the formulation.

The assertion that the world is computable is just that: there are no research projects, no textbooks, no experiments, no formalism to replace physics or anything like it -- nothing. All the basic assumptions of physics would have to be false, and we would have to have good reasons for supposing so.

This is just nonsense. The world is geometrical as described by physics. It is not computational as described by the discrete mathematician whose megalomania and platonism knows no bounds.

Re: Large Language Models Are Neurosymbolic Reasoners

#79

Post by mjburgess »

mewpmewp2 wrote: post #18
mjburgess wrote: post #11

Earlier quoted context omitted.

We're not a lookup table of the things we're, eg., saying, or doing etc. Nor are we looking up, in this sense, when we act. ie., when you compress text into an NN and use it to generate text, the generated text is just a synthesis of the compressed text . Whereas when I type, I am not synthesising text . Rather I have the skill of typing, I have an interior subjectivity of thoughts, I have memories which arent text,…

Typing is just a medium, it is irrelevant. Seeing and all the other senses that you mentioned are input within a context window.

uhuh.. and how do you form the inputs into that context window?

Turns out you need to move (indeed, adapt) the body in order to form the very techinques which become concepts that can be given as inputs.

The eye does not move on its own, it has to be directed to attend to reality as conceptualised -- where do these come from? Somatosenstory representations are built by the sensory-motor system.

Or, simply: in order to first think, we move.

Re: Large Language Models Are Neurosymbolic Reasoners

#80

Post by logifail »

zeroonetwothree wrote: post #25
clooper wrote: post #21

Earlier quoted context omitted.

Then give some concrete numbers for the states of the atoms. My argument is not abstract, it is very concrete. Give me a neural network and I can generate the graph and prove the equivalence between the network and its graph representation as a table of tuples.

You said "even in theory" which is obviously wrong, since the (local) universe is finite and deterministic, hence it is itself a giant lookup table.

> the (local) universe is finite and deterministic

"It is not possible for the Universe being deterministic at any level. Only theories can be deterministic, practical reality is never"[0]

Q: Can you calculate your local universe's past states given its present state?

[0] https://philosophy.stackexchange.com/questions/99163/is-it-p...

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