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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

#171

Post by short_sells_poo »

hollerith wrote: post #138
short_sells_poo wrote: post #137

Earlier quoted context omitted.

Oh I'm very much with you. In fact I get irked by people here breathlessly parroting that human level AGI is upon us any day now. I'd be impressed if an AI had mouse level capabilities any time soon. I think the current models are very impressive, but they are parlor tricks compared to what a true AGI should be capable of.

>if an AI had mouse level capabilities any time soon That's why nobody has gotten any traction selling access to AIs for $20 a month whereas selling access to mouse labor is such a thriving business.

This is such a strawman. Do you have to really stoop to this level? There are a billion useless things people pay for, is that a measure of the intelligence behind it? People routinely pay $1000 dollars for a dog, does that mean a dog is 50x more intelligent than ChatGPT? All I'm saying is that we should be a bit more humble about intelligence when we understand so little about it.

Just because LLMs are useful, it doesn't mean they exhibit more intelligence than a mouse. A mouse probably also doesn't reason about anything, but it is an agent capable of independent behavior, something that is still very far removed from current AI models.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#172

Post by krapp »

naasking wrote: post #95
nprateem wrote: post #92

Earlier quoted context omitted.

But I don't want tricks. I want to know that it knows so I don't have to continually guess whether it's right or not.

That's simply not possible. Human understanding is still unreliable, even for geniuses.

It's entirely possible. Don't use LLMs for math. Use the computers we already have that have been capable of doing math accurately for a century. Right tool, right job.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#173

Post by Tycho »

TeMPOraL wrote: post #168
jayd16 wrote: post #151

Earlier quoted context omitted.

LLMs are deterministic. We just sample the results, no? Also, no reason AI needs not be deterministic.

> LLMs are deterministic. In theory, yes. In practice, parallelism combined with floating point math make current implementations fundamentally non-deterministic.

Can you elaborate more on the parallelism aspect?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#174

Post by Jensson »

gmerc wrote: post #145
traverseda wrote: post #30

Earlier quoted context omitted.

It's probably on-par or better than humans get unaided. Hell, I'd bet due to transcription errors it's better than what humans get in a lot of settings, even when aided by a calculator.

I guarantee you professionals using math at work - for example in finance - not have a 1% error quota. They use tools. We have tools. Nobody in any serious role (money, etc) works unaided. Math inference is a palor trick as is the whole “world model” bullshit - physics doesn’t work with 99% accuracy. It’s the same reason agents are bullshit right now - error compounding at 95% reliability per step murders them and cu…

People didn't have 1% error before computers either, they just practiced enough to barely ever make errors.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#175

Post by andoando »

CamperBob2 wrote: post #166
andoando wrote: post #132

Earlier quoted context omitted.

I disagree that daily life is "trivial pattern recognition". Just our visual object recognition is immensely powerful and far beyond and current AI. A simple task like walking to the fridge requires a ton of pattern recognition and spatial reasoning. Recognizing people's moods/predicting behaviors is also incredibly involved imo. Ive said this many times but perhaps we should focus on achieving dog level intelligence…

Just our visual object recognition is immensely powerful and far beyond and current AI. That's a point you'll likely have to revisit pretty soon. Radiology, for instance, probably won't exist as a profession 20-30 years from now. Captchas are already pretty much done for.

Well 1. Radiology is an insanely niche subject not indiciative of general intelligence, and 2. AI being at good radiology isn't about object recognition or spatial reasoning, its data analysis connecting features to outcomes.

Lastly, check out the ARC challenge or any other spatial reasoning tests for AI. Humans get ~80% on these challenges whereas the best AI is still at 25%

Re: Transformers Can Do Arithmetic with the Right Embeddings

#176

Post by [deleted] »

TeMPOraL wrote: post #168
jayd16 wrote: post #151

Earlier quoted context omitted.

LLMs are deterministic. We just sample the results, no? Also, no reason AI needs not be deterministic.

> LLMs are deterministic. In theory, yes. In practice, parallelism combined with floating point math make current implementations fundamentally non-deterministic.

[deleted]

Re: Transformers Can Do Arithmetic with the Right Embeddings

#177

Post by hollerith »

short_sells_poo wrote: post #171
hollerith wrote: post #138

Earlier quoted context omitted.

>if an AI had mouse level capabilities any time soon That's why nobody has gotten any traction selling access to AIs for $20 a month whereas selling access to mouse labor is such a thriving business.

This is such a strawman. Do you have to really stoop to this level? There are a billion useless things people pay for, is that a measure of the intelligence behind it? People routinely pay $1000 dollars for a dog, does that mean a dog is 50x more intelligent than ChatGPT? All I'm saying is that we should be a bit more humble about intelligence when we understand so little about it. Just because LLMs are useful, it do…

>All I'm saying is that we should be a bit more humble about intelligence when we understand so little about it.

OK, as long as we're are being humble, how about we refrain from confidently proclaiming that there is a mouse level and a dog level that AI hasn't reached yet and that researchers will have to spend a long time getting past, so there's plenty of time before we have to worry about the possibility of AI's becoming dangerous or transformative to society?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#178

Post by wrsh07 »

neves wrote: post #109
wrsh07 wrote: post #105

Earlier quoted context omitted.

This is cool, but special casing digits is unsatisfying. It makes me think that the authors have correctly identified an issue (positional embeddings) but don't propose a general solution. I'm not sure if such a thing is possible, but if it is, it would feel more complete. (Fwiw, positional embeddings have had issues for a long time! So a general solution to this would benefit more than just arithmetic. Helpfully, we…

but it makes sense to have a different encoding. Mathematics is a completely different language. Maybe we should have more than one class of encodings.

I would only find that satisfying (from a snobbish and impractical perspective) if we were able to have the model decide: 1) what encoding should this section use? 2) how should I train this encoding?

A mixture of experts but for encodings is interesting, though!

Maybe there's a clean way to implement

Re: Transformers Can Do Arithmetic with the Right Embeddings

#179

Post by famouswaffles »

YeGoblynQueenne wrote: post #150
famouswaffles wrote: post #103

Earlier quoted context omitted.

>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. Nobody's going to be replacing calculators with transformers sure but many are and will be using transformers to solve problems arithmetic is a necessary component of. >So w…

Yes, but humans invented arithmetic. And then we invented computers that are much better than us at arithmetic calculations. That's a pattern we can observe all over the place: we're pretty damn good at inventing rich models of complex environments and processes but we're not very good at calculating the results of such models when that requires a lot of computation. E.g., take chess. Modelling a game of chess as a g…

>Yes, but humans invented arithmetic.

I think most would argue Mathematics is a discipline that is discovered more than invented. That said, this isn't really the point I think.

A few humans invented/discovered arithmetic. Most humans will be born, live and die inventing absolutely nothing, even those with the opportunity and resources to do so.

It doesn't make sense to me that a bar most humans can't reach is the bar for General Intelligence of the Artificial kind. You can't eat your cake and have it.

Don't get me wrong. It's a fine goal to have. Of course we want machines that can invent things and push the frontier of science! It is still however a logical fallacy that an inability to do such would disqualify machines of general intelligence when it does not do so for Humans.

>The challenge is to get computers to create their own models. And that's a grand, open challenge that is not even close to be solved, certainly not by LLMs.

LLMs have fairly complex models of the world made manifest by the data they're trained on.

https://transformer-circuits.pub/2024/scaling-monosemanticit...

Lecun may disagree but some others like Hinton, Ilya and Norvig don't.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#180

Post by vidarh »

chowells wrote: post #160
vidarh wrote: post #147

Earlier quoted context omitted.

The point is don't ask an LLM to do tasks that a calculator can do. Ask if to use the calculator, just like most humans would.

The point is that you shouldn't need to ask. If it's actually a general-purpose system it will do it automatically.

An LLM in isolation is not a general purpose system, but with ChatGPT at least, most of the time you don't need to ask. In fact, it's increasingly difficult to force it to do "manual" maths, as it's strongly predisposed to do things like write and evaluate Python code instead of doing it "manually".

E.g. I verified just now and asked it to multiply two huge numbers, and it immediately spat out Python code, then evaluated it and gave me the result, rather than try to add the numbers itself.

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