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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

#101

Post by uoaei »

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,…

It's also obvious and it's hacky. Frankly I'm stunned this hasn't been tried yet. The people thinking this is a stepping stone to More Intelligence are missing the forest for the trees.

Deep learning is always and only ever about representing data abstractly. The more abstractions you can make irrelevant (why would you have to learn how to do math when the base-10 perspective on ASCII-digits is already provided for you?) the more you've biased your architecture to readily learn and understand the problem space.

Intelligence doesn't exist where Divine Creator gave you access to this or that faculty. It's developing those faculties yourself by reasoning through the process of composing your own mental model about the problem.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#102

Post by catapart »

lapitopi wrote: post #99
naasking wrote: post #95

Earlier quoted context omitted.

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

That’s why I am asking a computer.

I'm with you. I get that this is akin to asking a human, because we're trying to reason, so we will bring along (assumedly) unavoidable deficiencies of human reasoning. But if I were to ask a human genius this question, ne would grab a calculator and employ it as ne did the rest of ner reasoning.

So it seems like we should probably teach LLMs to "use a calculator", rather than try to get them to be more right when doing math 'in their head'.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#103

Post by famouswaffles »

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…

>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 what is the point of this? Transformers are supposed to be the "sparks of AGI" and they can almost do arithmetic if we try very hard to shove it down their heads? Who cares?

You don't need to shove anything down for transformers to get arithmetic. Just changing how numbers are tokenized works. But that requires an entire retrain so why not explore other techniques?

And what does any of this have to do with AGI ? You know how terrible humans are at arithmetic right ?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#104

Post by short_sells_poo »

anon291 wrote: post #89
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…

I must be in the minority here, but I don't think most people exercise any reason. I'd even venture that the vast majority of people haven't reasoned recently at all. In my mind, reasoning is an ability... a willful act to engage in thinking through an abstract problem. Most people don't do this and just use rationalization and learned behavior, which our brains are good at.

Well, 99% of day to day life is mundane for much of living beings on earth. A bee is able to get through it's entire life without showing signs that it deeply ponders about anything.

However, humans have the ability to reason about things (whether most people use this ability is a different question). So then we must ask the question: is this ability just a more advanced form of probabilistic pattern matching, or is it a different architecture altogether? Will current AI models be able to develop this ability, or will we need new models?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#105

Post by wrsh07 »

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,…

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 now have a really good specific example to serve as a baseline for any generalization we seek)

Re: Transformers Can Do Arithmetic with the Right Embeddings

#106

Post by HarHarVeryFunny »

anon291 wrote: post #89
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…

I must be in the minority here, but I don't think most people exercise any reason. I'd even venture that the vast majority of people haven't reasoned recently at all. In my mind, reasoning is an ability... a willful act to engage in thinking through an abstract problem. Most people don't do this and just use rationalization and learned behavior, which our brains are good at.

I think for the most part that's true, but obviously there are things people want to use LLMs for that do require planning/reasoning, and it makes for unexpected failure modes if LLMs don't have this ability.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#107

Post by wrsh07 »

Last5Digits wrote: post #50
msoad wrote: post #8

Earlier quoted context omitted.

> how do you argue that these models are not able to reason? I don't make this argument. Benchmarks like CLUTRR[1] show how poorly LLMs do in reasoning. [1] https://github.com/facebookresearch/clutrr

There is a difference between poor reasoning and no reasoning. SOTA LLMs correctly answer a significant number of these questions correctly. The likelihood of doing so without reasoning is astronomically small. Reasoning in general is not a binary or global property. You aren't surprised when high-schoolers don't, after having learned how to draw 2D shapes, immediately go on to draw 200D hypercubes.

Granting that, the original point was that they're not excited about this particular paper unless (for example) it improves the networks' general reasoning abilities.

The problem was never "my llm can't do addition" - it can write python code!

The problem is "my llm can't solve hard problems that require reasoning"

Re: Transformers Can Do Arithmetic with the Right Embeddings

#108

Post by wrsh07 »

psychoslave wrote: post #87
olalonde wrote: post #65

Earlier quoted context omitted.

GPT-4 (OpenAI): The sentence you're referring to is "What is the number of words in the sentence coming before the next one? Please answer." It contains 14 words.

Thanks. I don’t have access to this engine which for some reason is kept in a closed garden for richer people. ¯\_(ツ)_/¯

You can always use the API which is dirt cheap? Just put $5 on and access via the playground

They have better data policies and your $5 will go way farther than a 1 month subscription

Re: Transformers Can Do Arithmetic with the Right Embeddings

#109

Post by neves »

wrsh07 wrote: post #105
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,…

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#110

Post by grumpopotamus »

msoad wrote: post #4

It seems like a hack to be honest. Problem at hand is not to make transformers do addition of 100 digit numbers. Problem is the current systems can’t reason about things, math included. Optimizing for a certain use case is not gonna take us where we wanna be. We want to have a system that can learn to reason.

>Problem is the current systems can’t reason about things, math included.

Have you tried asking GPT-4 any questions that require reasoning to solve? If so, what did you ask, and what did it get wrong?

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