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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

#91

Post by nicklecompte »

YeGoblynQueenne wrote: post #84
nicklecompte wrote: post #75

Earlier quoted context omitted.

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…

Drew McDermot's warning is well-heeded, but there are established and well-understood definitions of deductive, inductive and abductive reasoning that go back to at least Charles Sanders Pierce (philosopher and pioneer of predicate logic, contemporary of Gotlob Frege) that are widely accepted in AI research, and that even McDermot would have accepted. See sig for intro.

This is completely irrelevant. McDermot's point was that scientifically-plausible definitions of reasoning were not actually being used in practice by AI researchers when they made claims about their systems. That is just as true today.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#92

Post by nprateem »

vessenes wrote: post #57

Wow, a lot of grumpiness in here. If it's true that adding like 20 or so tokens to encode column location / decimal spot triples math performance in out of band tasks, that's a big deal. It's a simple fix, it improves performance A LOT, and they even indicate it's not just a party trick, in that the LLM can use the information to do better on related tasks like sorting and list making. This is basically free to add,…

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#93

Post by naasking »

nicklecompte wrote: post #75
YeGoblynQueenne wrote: post #6

Earlier quoted context omitted.

>> 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…

> My cats don't need "general patterns" to form deductions, they deduce many sophisticated things (on their terms) with n=1 data points.

No they don't. That's just generalization, so they've seen plenty of other data points that are similar enough.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#94

Post by ADeerAppeared »

staunton wrote: post #25
teleforce wrote: post #20

I think understanding mathematics is what LLM really need at the moment far more important than video generation that is just another form of CGI [1]. After deep learning and transformer, understanding mathematics and its proofs not just arithmetic will be the next game changer for LLM and a turning point for humanity. [1] Why LLMs like ChatGPT and Google Bard are bad at math: https://www.xda-developers.com/why-llms-…

> understanding mathematics and its proofs not just arithmetic will be the next game changer for LLM Why? I definitely agree that such capabilities would represent a major advance (and very likely go together with game changing increases of capabilities in other areas). I also think using AI to write formal math proofs in e.g. Lean is very cool. However, by itself, it seems like this capability wouldn't be very usefu…

> However, by itself, it seems like this capability wouldn't be very useful, commercially for example.

Quite the opposite, it's the holy grail of all AI.

Consider various work that isn't (and can't) be done by computers/robots/etc right now.

The intelligence constraint is universally, a required amount of problem solving. Even the "low skill" labour requires it.

And to perform such problem solving, you need advanced logic and reasoning capabilities, which is the same thing as novel mathematics, just applied to a different end.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#95

Post by naasking »

nprateem wrote: post #92
vessenes wrote: post #57

Wow, a lot of grumpiness in here. If it's true that adding like 20 or so tokens to encode column location / decimal spot triples math performance in out of band tasks, that's a big deal. It's a simple fix, it improves performance A LOT, and they even indicate it's not just a party trick, in that the LLM can use the information to do better on related tasks like sorting and list making. This is basically free to add,…

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#96

Post by pmayrgundter »

Last5Digits wrote: post #71
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 d…

Agreed on the first part, but for LLMs not having correlated capabilities, I think we've seen they do. As the GPTs progress, mainly by model size, their scores across a battery of tests goes up, eg OpenAI's paper for ChatGPT 4, showing a leap in performance across a couple dozen tests.

Also found this, a Mensa test for across the top dozen frontier models.

https://www.maximumtruth.org/p/ais-ranked-by-iq-ai-passes-10...

That does seem to me to be demonstrating a global type of reasoning or generalization.

Also see the author's note that at least with Claude, they seem to be releasing about every 20 IQ points.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#97

Post by ADeerAppeared »

Shrezzing wrote: post #24

Since models are very good at writing very short computer programs, and computer programs are very good at mathematical calculations, would it not be considerably more efficient to train them to recognise a "what is x + y" type problem, and respond with the answer to "write and execute a small javascript program to calculate x + y, then share the result"?

This is a cromulent approach, though it would be far more effective to have the LLM generate computer-algebra-system instructions.

The problem is that it's not particularly useful: As the problem complexity increases, the user will need to be increasingly specific in the prompt, rapidly approaching being fully exact. There's simply no point to it if your prompt has to (basically) spell out the entire program.

And at that point, the user might as well use the backing system directly, and we should just write a convenient input DSL for that.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#98

Post by FeepingCreature »

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…

Yes, thank you! This exactly matches my experience. The patterns are in there, they're just not prominent or developed enough to reach our level.

That's why I think of GPT3+ as "subhuman AGI," personally.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#99

Post by lapitopi »

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.

That’s why I am asking a computer.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#100

Post by staunton »

ADeerAppeared wrote: post #94
staunton wrote: post #25

Earlier quoted context omitted.

> understanding mathematics and its proofs not just arithmetic will be the next game changer for LLM Why? I definitely agree that such capabilities would represent a major advance (and very likely go together with game changing increases of capabilities in other areas). I also think using AI to write formal math proofs in e.g. Lean is very cool. However, by itself, it seems like this capability wouldn't be very usefu…

> However, by itself, it seems like this capability wouldn't be very useful, commercially for example. Quite the opposite, it's the holy grail of all AI. Consider various work that isn't (and can't) be done by computers/robots/etc right now. The intelligence constraint is universally, a required amount of problem solving. Even the "low skill" labour requires it. And to perform such problem solving, you need advanced…

Let's be a little more concrete: do you think FormalGeo [1] is a big deal? I think it's very cool but ultimately not useful in and of itself. It's only useful insofar as it shows AI capabilities advancing in general.

Let's suppose we had an AI that works roughly like [1] but for the kind of mathematics done in Lean's Mathlib, and that was on par or better than humans working on it. Would that AI by itself be commercially useful?

Again, of course having such an AI implies a major jump in capabilities and it would most likely mean useful AI can be trained with similar techniques. But that's not what I mean by the system itself being useful. If all you're saying is that such an AI demonstates we can now probably build AIs that do things which we usually say require "logic and reasoning abilities", I completely agree.

Maybe I'm splitting hairs too much here. However, it could well be that such an AI would be useful by itself. I just can't think of much besides a major advance in the formal software verification niche, which still almost nobody would use...

[1]: https://github.com/FormalGeo/FormalGeo

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