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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

#121

Post by zacksiri »

zyklu5 wrote: post #117
zacksiri wrote: post #112

I think the problem here is that 'understanding' is not the same as curve fitting. If all one is doing is giving a model lots of data and fitting curves it's not really 'understanding' but brute forcing it's way (with gradient descent) and then storing the weights and finally approximate the solution when a query is passed in. This is not the same as understanding. Human intelligence can operate deterministically as…

I think you are mixing layers of abstraction. To make a crude but I think not unhelpful analogy: 'Understanding' is a natural language concept that is our way to describe whats happening in our heads, and like most other such concepts is resistant to any clear definition and will exhibit sorites type paradoxes when one is attempted. It belongs to the presentation layer of the stack. While the process of curve fitting…

Thank you for your explanation. It's helpful to see another perspective on 'understanding'.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#122

Post by Chinjut »

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…

Minor point, but Blaise Pascal was centuries earlier than the 1850s.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#123

Post by singularity2001 »

mike_hearn wrote: post #56
isaacfung wrote: post #42

Earlier quoted context omitted.

The current gen llms tokenize numbers digit by digit unlike earlier llms.

No, it doesn't help. Bloomberg tried this and it didn't seem to make much difference.

If someone else is interested in the Bloomberg tokenizer:

https://medium.com/generative-ai-insights-for-business-leade...

Re: Transformers Can Do Arithmetic with the Right Embeddings

#124

Post by YeGoblynQueenne »

nicklecompte wrote: post #91
YeGoblynQueenne wrote: post #84

Earlier quoted context omitted.

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.

I've read McDermot's paper a few times (it's a favourite of mine) and I don't remember that angle. Can you please clarify why you say that's his point?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#125

Post by nprateem »

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.

My calculator manages

Re: Transformers Can Do Arithmetic with the Right Embeddings

#126

Post by shepherdjerred »

nprateem wrote: post #125
naasking wrote: post #95

Earlier quoted context omitted.

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

My calculator manages

Your calculator is deterministic. Humans and AI are not.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#127

Post by jhanschoo »

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.

A basic transformer architecture performs only a bounded amount of computation per generated token, so it can never emulate a machine computing sufficiently hard problems.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#128

Post by jhanschoo »

sshine wrote: post #19
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 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 succintly define what it is.

For transformer-based LLMs, and most LLMs there's an obvious class of problems that they cannot solve. LLMs generally perform bounded computation per token, so they cannot reason about computational problems that are more than linearly complex, for a sufficiently large input instance. If you have a back-and-forth (many shot) your LLM can possibly utilize the context as state to solve harder problems, up to the context window, of course.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#129

Post by math_dandy »

josehackernews wrote: post #5
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.

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…

We have no definition of reasoning that is sufficiently precise to be useful.

But we do have a bunch of benchmark tasks/datasets that test what we intuitively understand to be aspects of reasoning.

For AI models, "being able to reason" means "performing well on these benchmarks tasks/datasets".

Over time, we'll add more benchmarking tasks and datasets that ostensibly test aspects of "reasoning", and people will develop models that succeed on more and more of these simultaneously.

And these models will become more and more useful. And people will still argue over whether they are truly "reasoning".

Re: Transformers Can Do Arithmetic with the Right Embeddings

#130

Post by OtherShrezzing »

throwthrowuknow wrote: post #51
Shrezzing wrote: post #18

Earlier quoted context omitted.

>deductive reasoning is just drawing specific conclusion from general patterns. something I would argue this models can do That the models can't see a corpus of 1-5 digit addition then generalise that out to n-digit addition is an indicator that their reasoning capacities are very poor and inefficient. Young children take a single textbook & couple of days worth of tuition to achieve generalised understanding of addi…

I think the “train for hundreds of years” argument is misleading. It’s based off of parallel compute time and how long it would take to run the same training sequentially on a single GPU. This assumes an equivalence with human thought based on the tokens per second rate of the model which is a bad measurement because it varies depending on hardware and the closest comparison you could draw to what a human brain is do…

>There is no textbook or tutor helping them do this either it should be noted.

For this particular paper there isn't, but all of the large frontier models do have textbooks (we can assume they have almost all modern textbooks). They also have formal proofs of addition in Principia Mathematica, alongside nearly every math paper ever produced. And still, they demonstrate an incapacity to deal with relatively trivial addition - even though they can give you a step-by-step breakdown of how to correctly perform that addition with the columnar-addition approach. This juxtaposition seems transparently at odds with the idea of an underlying understanding & deductive reasoning in this context.

>There is a form of generalization if it can derive an algorithm based on a maximum length of 20 digit operands that also works for 120 digits. Is it the same algorithm we use by limiting ourselves to adding two digits at a time? Probably not but it may emulate some of what we are doing.

The paper is technically interesting, but I think it's reasonable to definitively conclude the model had not created an algorithm that is remotely as effective as columnar addition. If it had, it would be able to perform addition on n-size integers. Instead it has created a relatively predictable result that, when given lots of domain-specific problems, transformers get better at approximating the results of those domain-specific problems, and that when faced with problems significantly beyond its training data, its accuracy degrades.

That's not a useless result. But it's not the deductive reasoning that was being discussed in the thread - at least if you add the (relatively uncontroversial) caveat that deductive reasoning should lead to correct conclusion.

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