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Transformers Can Do Arithmetic with the Right Embeddings

arxiv.org

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Re: Transformers Can Do Arithmetic with the Right Embeddings

#71

Post by Last5Digits »

pmayrgundter wrote: post #63

I'm curious about the framing of research like this.. "The poor performance of transformers on arithmetic tasks" (relative to what?) and how that informs the adjacent conversation on progress towards AGI. Some say AGI has already been achieved, others that it's years or decades away. When I dig into the disagreement, it often partially depends on the perspective of how competent humans are on the tasks in question, w…

Exactly, we need a much more granular approach to evaluating intelligence and generality. Our current conception of intelligence largely works because humans share evolutionary history and partake in the same 10+ years of standardized training. As such, many dimensions of our intelligence correlate quite a bit, and you can likely infer a person's "general" proficiency or education by checking only a subset of those dimensions. If someone can't do arithmetic then it's very unlikely that they'll be able to compute integrals.

LLMs don't share that property, though. Their distribution of proficiency over various dimensions and subfields is highly variable and only slightly correlated. Therefore, it makes no sense to infer the ability or inability to perform some magically global type of reasoning or generalization from just a subset of tasks, the way we do for humans.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#72

Post by matrix2596 »

infogulch wrote: post #2

The other day I was wondering if LLMs are bad at at maths because they don't have readily apparent access to the concept of "columns". Apparently the answer is yes. Vertical alignment across lines is pretty important for humans to learn operations on digits, but the way we encode lines with a \n separator doesn't really help. In a recent codebullet video gpt really struggled with any kind of vertical alignment task.…

wouldnt presenting numbers in reverse order, with the least significant digit on the left and most significant on the right help with the reasoning?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#73

Post by CuriouslyC »

pmayrgundter wrote: post #63

I'm curious about the framing of research like this.. "The poor performance of transformers on arithmetic tasks" (relative to what?) and how that informs the adjacent conversation on progress towards AGI. Some say AGI has already been achieved, others that it's years or decades away. When I dig into the disagreement, it often partially depends on the perspective of how competent humans are on the tasks in question, w…

AGI is like consciousness, 75% of the people in any given conversation are talking about different things.

Truthfully we're going to see that improving language models towards AGI works out the same way self driving cars did - we're going to feel like we're 85% of the way there out of the gate, then we're going to keep tripping over things for the next 15 years.

At least with AGI, we can just throw up our hands, use an easier definition and take the W.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#74

Post by vitus »

logicallee wrote: post #49
sshine wrote: post #19

Earlier quoted context omitted.

> Problem is the current systems can’t reason about things Sounds like the AGI argument trap: They're not able to reason, but we can't succintly define what it is. I don't come with a reasoning chip. Whatever I call reasoning happens as a byproduct of my neural process. I do think that the combination of a transformer network and calls to customized reasoning chips (systems that search and deduce answers, like Wolfra…

>They're not able to reason, but we can't [succinctly] define what it is. People also routinely fail to reason, even programmers often write "obvious" logic bugs they don't notice until it gives an unexpected result at which point it's obvious to them. So both humans and AI don't always reason. But humans reason much better. I myself have observed ChatGPT 4 solving novel problems I invented to my personal satisfactio…

> Today, it fails badly at tasks that require reasoning. A simple example: https://chatgpt.com/share/da95843e-218a-4d69-a161-6aa2d7a3c9...

> The issue is that humans can see its answer is wrong and its "reasoning" is wrong.

I've noticed with LLMs that they're more likely to come to the wrong conclusion if you prime them in that manner. In this case, you posed the follow-up question as "Will always be true?" As a result, it's primed to try to prove that incorrect conclusion.

(That said, ChatGPT further did not answer the posed question, as it also changed "difference" -> "absolute difference"; in fact, the difference will alternate between increasing and decreasing, while the absolute difference is strictly increasing.)

Re: Transformers Can Do Arithmetic with the Right Embeddings

#75

Post by nicklecompte »

YeGoblynQueenne wrote: post #6
josehackernews wrote: post #5

Earlier quoted context omitted.

how do you argue that these models are not able to reason? deductive reasoning is just drawing specific conclusion from general patterns. something I would argue this models can do (of course not always and are still pretty bad in most cases) the point i’m trying to make is that sometimes reasoning is overrated and put on the top of the cognitive ladder, sometimes I have seen it compared to self-awareness or stuff li…

>> deductive reasoning is just drawing specific conclusion from general patterns. This is according to whom, please?

The fundamental argument of "Artificial Intelligence, Natural Stupidity" is that AI researchers constantly abuse terms like "reasoning," "deduction," "understanding," and so on, deluding others and themselves that their machine is almost as intelligent as a human when it's clearly dumber than a dog. My cats don't need "general patterns" to form deductions, they deduce many sophisticated things (on their terms) with n=1 data points.

In the 80s the computers were indisputably dumber than ants. That's probably not true these days. But the decades-long refusal of most AI researchers to accept humility about the limitations of their knowledge (now they describe multiple-choice science trivia as "graduate level reasoning") suggests to me that none of us will live to see an AI that's smarter than a mouse. There's just too much money and ideology, and too little falsifiability.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#76

Post by Havoc »

0-_-0 wrote: post #66
Havoc wrote: post #43

For things like this where we have computationally cheap, well understood, reliable tools available (aka calculator) it seems better to train the model in tool use. I guess perhaps the techniques could be generalized though?

To me this finding shows how transformers don't generalise, since they need specialised embeddings to handle a problem

I'd say the key point here isn't that they "need" specialised embeddings, but rather that it improves things and it can samewhat manage without.

That's a far more surmountable problem. Maybe you need one model for biology and another for coding etc. i.e. Broad split by domain. Still weak AI not true general in AGI sense, but still seems like a good next step

Re: Transformers Can Do Arithmetic with the Right Embeddings

#77

Post by YeGoblynQueenne »

mike_hearn wrote: post #61
YeGoblynQueenne wrote: post #7

What is the point of this work? 99% on 100-digit arithmetic means there's a 0% chance anyone will ever use a Transformer as an ALU or anything of the kind. We already know how to hard-code a (literally) infinitely more accurate addition machine. And not only addition: all four arithmetic operations. The technique proposed in the article -imposing a strong inductive bias for addition- kiind of works for multiplication…

They explain their true goal in the introduction: > With positions resolved, we can study the logical extrapolation ability of transformers They are interested in how well they can make a neural net logically extrapolate outside its training set, once encoding barriers are removed. They show that in fact even quite small language models can do this successfully once we're not confusing them with bad encodings anymore…

>> But this work shows in a controlled environment that the model can learn the principles of addition and extrapolate to much larger numbers.

No, because it's given hand-engineered embeddings that act as a strong inductive bias that is specific to addition. It's like addition is programmed right in.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#78

Post by YeGoblynQueenne »

zarzavat wrote: post #11
YeGoblynQueenne wrote: post #7

What is the point of this work? 99% on 100-digit arithmetic means there's a 0% chance anyone will ever use a Transformer as an ALU or anything of the kind. We already know how to hard-code a (literally) infinitely more accurate addition machine. And not only addition: all four arithmetic operations. The technique proposed in the article -imposing a strong inductive bias for addition- kiind of works for multiplication…

It’s not about arithmetic but about embeddings. The positional embeddings used in transformers are rather simplistic. If they can add this one new capability to transformers by using different embeddings then maybe there are other capabilities that are within reach.

No, because those embeddings only work for addition (very weakly for multiplication and sorting). Imagine needing a specially-crafted bias for every single task. The Deep Learning revolution brought on by Convolutional Neural Nets was supposed to do away with the need to do exactly that.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#79

Post by short_sells_poo »

ekianjo wrote: post #62
short_sells_poo wrote: post #37

Earlier quoted context omitted.

I suppose it's a question whether what we call "reasoning" is an emergent phenomenon from having enough connections in a graph, or whether it's some other special sauce which we simply don't have in our current models yet. E.g. humans follow a deductive process to answer questions which they haven't encountered yet. Do we gain this ability purely from a denser/larger graph of knowledge, or from a completely different…

> humans follow a deductive process to answer questions which they haven't encountered yet nope. most humans fall in various traps such as pattern recognition, confirmation bias, and many others instead of relying on deductive analysis. Even scientists fail at being rigorous.

Of course there are cases like this, nobody is perfect. But we are talking about mathematics here, not everyday subconscious decision making. I agree that 99% of daily life is trivial pattern recognition. That's not what distinguishes humans though is it? Because animals, down to single celled organisms do just fine without higher order mental capabilities. But we are talking about reasoning here - and specifically about structured one like math.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#80

Post by YeGoblynQueenne »

toxik wrote: post #12
YeGoblynQueenne wrote: post #7

What is the point of this work? 99% on 100-digit arithmetic means there's a 0% chance anyone will ever use a Transformer as an ALU or anything of the kind. We already know how to hard-code a (literally) infinitely more accurate addition machine. And not only addition: all four arithmetic operations. The technique proposed in the article -imposing a strong inductive bias for addition- kiind of works for multiplication…

I think there is a good reason to find low-hanging fruits that pay dividends on these types of tasks, not because solving addition with a transformer is a good idea, but because it could improve performance in other parts of the network. Maybe there are other subsequences that could be annotated in this way? Per paragraph, tokens per word, who knows. Obviously, the "best" way to do addition on a computer is by doing…

>> I think there is a good reason to find low-hanging fruits that pay dividends on these types of tasks, not because solving addition with a transformer is a good idea, but because it could improve performance in other parts of the network.

The paper makes this claim but if they could do that, they'd have showed it already: instead their hand-crafted, artisanal embeddings only work well for addition and only weakly for multiplication and sorting, and not at all for other arithmetic operations.

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