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Large Language Models Are Neurosymbolic Reasoners

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Re: Large Language Models Are Neurosymbolic Reasoners

#41

Post by bubblyworld »

clooper wrote: post #8
bubblyworld wrote: post #7

Earlier quoted context omitted.

This is an old argument against determinism - I think a serious challenge is that: 1. Modern physics suggests you can implement such a lookup table for any subset of our universe. 2. We are a subset of the universe. 3. Therefore we are representable by lookup tables too. ...so your argument appears to prove too much, namely that humans aren't thinking beings either. Which is fine, but personally I don't think that's…

How are people lookup tables? In the case of neural networks the representation of the table is obvious, it's just numbers. What would be the equivalent table for the liver? My argument isn't abstract. Neural networks really are just numerical functions which can be expanded into their equivalent graph representations.

People really are just stacks of molecules that can be broken down into their causal properties - moreover, we know those causal properties to a high degree of accuracy these days.

I'm suggesting that for any given human/environment pair, there is a lookup table that produces that person's actual behaviour in that situation. Modern physics lets us approximate this lookup table, and presumably better physics would give us a better lookup table.

Since human behaviour can in principle be described with a lookup table, I see this as a bad reason to rule out a system as "thinking".

Perhaps there is another way to describe neural nets, one that does not use the language of lookup tables, that makes it feel more like thinking and less like lookups.

One such approach I've seen is looking for embedded world models in neural nets.

Re: Large Language Models Are Neurosymbolic Reasoners

#42

Post by radarsat1 »

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.…

Yes, this is one view of machine learning, the idea that you are training some function to map input to output, similar to "looking up" what output is addressed by some input.

And that's why the concept of generalization is so important on machine learning, and as a consequence, why the internal representation of that "lookup" matters.

By definition a lookup table can only store data it is given. However, the idea of ML systems is actually to predict values of inputs that are similar to but not given in their training data.

Interpolation and extrapolation, key components to applying ML systems to new data and therefore critical for actual usage, are enabled by internal representations that allow for modeling the space between and around data points. It so happens that multilayer neural networks accomplish this by general and smoothed (due to regularization tricks and inductive biases) iterative warpings of the representation (embedding) space.

Due to the manifold hypothesis, we can interpret this as determining underlying and semantically meaningful subspaces, and unfolding them to perform generalized operations such as logical manipulations and drawing classification boundaries in some relatively smooth semantic space, then refolding things to drive some output representation (pixels, classes, etc.)

Another view on this is that these manipulations allow a kind of compression by optimizing the representation to make manipulations easier, in other words they re-express the data in a form that allows algorithmic evaluation of some input program. This gives the chance of modeling intrinsic relationships such as infinite sequences as vector programs. (Here I mean things like mathematical recursions, etc.) When this is accomplished, and it happens due to the pressure to optimally compress data, you could say that "understanding" emerges, and the result is a program that extrapolates to unseen values of such sequences. At this point you could say that while the input-output relationship is like a lookup table, functionally it is not the same thing because the need to compress these input-output relationships has led to some representation which allows for extrapolation, aka "intelligence" by some definitions.

The fact that these systems are still very dumb sometimes is simply due to not developing these representations as well as we would like them to, for a variety of reasons. But theoretically this is the idea behind why emergence might occur in an NN but not in a lookup table.

Re: Large Language Models Are Neurosymbolic Reasoners

#43

Post by bubblyworld »

clooper wrote: post #31
ccozan wrote: post #27

Earlier quoted context omitted.

I think the OP is right. All the input to a human brain can be expressed as numbers, at any given time a specific radiation, vibration, or chemical reaction is hitting our "sensors" and by the law of physics this is just numbers ( in terms of differentiation, brain does not know absolute values ). Our output ( mechanical and vibrations ) is also fully quantifiable, thus numbers. One giant lookup table.

Provide some concrete numbers for solar radiation then as a lookup table. You guys are confusing abstraction and idealization with what it means to be a thinking person. There is no such abstraction and idealization happening with software. The software is really just a number, there is no idealization or abstraction happening when I claim that GPT is a sequence of bits representing a numerical function.

Abstraction is a property of a description of a thing, not the thing itself. In reality, what we call "GPT" is the highly organised behaviour of many electrons, probably distributed across many computers, each with extremely complex hardware of various kinds, etc etc. Calling it a sequence of bits representing a numerical function is a choice of description - an abstraction, even!

In this case it's a good description, because it correlates with the GPT in reality quite well. But they are not the same thing.

Re: Large Language Models Are Neurosymbolic Reasoners

#44

Post by cesaref »

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.…

Just like to point out that RNNs have internal state which isn't captured in this view, so yes, lots of NNs can be considered this way, but not all. It's the DSP equivalent of FIRs vs IIRs.

Re: Large Language Models Are Neurosymbolic Reasoners

#45

Post by microtonal »

clooper wrote: post #31
ccozan wrote: post #27

Earlier quoted context omitted.

I think the OP is right. All the input to a human brain can be expressed as numbers, at any given time a specific radiation, vibration, or chemical reaction is hitting our "sensors" and by the law of physics this is just numbers ( in terms of differentiation, brain does not know absolute values ). Our output ( mechanical and vibrations ) is also fully quantifiable, thus numbers. One giant lookup table.

Provide some concrete numbers for solar radiation then as a lookup table. You guys are confusing abstraction and idealization with what it means to be a thinking person. There is no such abstraction and idealization happening with software. The software is really just a number, there is no idealization or abstraction happening when I claim that GPT is a sequence of bits representing a numerical function.

You can't really have it both ways, being reductionist when it comes to computers (it's just a finite set of numbers, so there is no reasoning), but not permitting to use the same line of argumentation with humans (it's just a finite set of particles).

At any rate, this is an ages-old discussion in philosophy, so most likely we are not going to settle this in a Hacker News thread.

Re: Large Language Models Are Neurosymbolic Reasoners

#46

Post by imtringued »

Legend2440 wrote: post #17
clooper wrote: post #13

Earlier quoted context omitted.

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…

>People can not be reduced to lookup tables even in theory Sure you can. Simply enumerate all of the physical states that the atoms in your body could be in. Any finite-sized object has a finite number of possible states, and so can be represented by a finite lookup table. Your argument is so broad as to be meaningless.

You are making the assumption that your body consists of a static set of atoms, but your body is a living thing. Your lookup table would end up containing the entire universe to account for extremely remote possibilities.

Re: Large Language Models Are Neurosymbolic Reasoners

#47

Post by imtringued »

cjfd wrote: post #38
Legend2440 wrote: post #33

Earlier quoted context omitted.

Here's a counterexample. Suppose I create a simple neural network that computes f(x) = x^2 + c (where x and c are complex numbers) and then I run it as an RNN. This RNN will compute the mandelbrot set, which can't be represented by a lookup table. You can't even know if the RNN will halt for a given input. Neural networks are stronger than lookup tables, they are programs.

I am sorry to be this blunt but this is really utter and complete nonsense. The phrase that the mandelbrot set can't be represented in a lookup table is as such true but that is because nothing that you do with finite precision numbers can represent the mandelbrot set because it essentially is an inifinte object. The function f(x) = x^2 + c as an RNN can also not compute the mandelbrot set if the numbers it uses are…

I see you are a fan of flying disembodied brains, but this time without a universe surrounding the brain.

Re: Large Language Models Are Neurosymbolic Reasoners

#49

Post by imtringued »

bubblyworld wrote: post #37
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,…

I strongly disagree with your last statement - physics explicitly _is_ formulated in terms that can be made into a lookup table (see phase spaces in classical mechanics, for instance). My point is that there's a finite light cone of possible causal influences over you at any moment in time, and in principle you can break those down into state variables finely enough to predict future states of a person. This is isomo…

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

Re: Large Language Models Are Neurosymbolic Reasoners

#50

Post by [deleted] »

cesaref wrote: post #44
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.…

Just like to point out that RNNs have internal state which isn't captured in this view, so yes, lots of NNs can be considered this way, but not all. It's the DSP equivalent of FIRs vs IIRs.

[deleted]
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