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Transformers Can Do Arithmetic with the Right Embeddings

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Re: Transformers Can Do Arithmetic with the Right Embeddings

#81

Post by YeGoblynQueenne »

Xcelerate wrote: post #13
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? Seriously? They say it right in the introduction. The goal is to learn how to infer algorithmic processes directly from data. Much like how MNIST was used in the early days of NNs, you have to start with small toy problems that are representative of the problem domain. Once you have success with that, you can scale up problem complexity. General algorithmic capability is one of the k…

>> Seriously?

Yes, seriously.

>> The goal is to learn how to infer algorithmic processes directly from data.

And they demonstrated nothing like that. An "algorithmic process" is not finding the weights for a function given some carefully designed bias. An algorithm is a sequence of operations that calculates the result of a function. Nothing like that has been demonstrated in the linked paper at all.

>> General algorithmic capability is one of the key traits that we think AGI should have, and it’s currently missing. If you have a better approach for getting there quicker than everyone else in the field, please share it.

It's not missing at all, you just wont' find it in neural nets. And my PhD and post-doc research is exactly on that sort of thing, learning programs, algorithms and, currently, solvers for general planning problems.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#82

Post by r2_pilot »

r2_pilot wrote: post #69

Meanwhile I'm over here using Claude 3 Opus to do trig and calculus problems as well as generate the LaTex representation of the equations. It's not necessary to be 100% in my case (purely for fun) but I follow its reasoning and it's pretty consistent at least enough for "orders of magnitude" and first order effects. I was gonna post some of the chats about physics but probably nobody cares.

I did do some followup research. The math in its complex reasoning "tracks" but when I asked it to do 4 digit x 4 digit multiplication, it got most of it right except for a weird random digit error in the middle (?!) of the correct answer, lol. Now I want to run CLUTTR against Claude since it seems nobody has published that yet.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#83

Post by sshine »

short_sells_poo wrote: post #37
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…

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…

> an emergent phenomenon from having enough connections in a graph, or ... some other special sauce

For humans, it is emergent. But when we reason about reason, we invent special sauce.

If we build our theories of reason into our models, they achieve the strengths and limitations of our models.

If we don't, we're limited by the pace of evolution, because we don't have enough connections in our graph.

So I think we'll have something immediately more useful if we embed ALU special instructions into a neural network.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#84

Post by YeGoblynQueenne »

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…

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#85

Post by YeGoblynQueenne »

golol wrote: post #41
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…

Ok you want the general answer? Consider a discrete time Markov process with memory length N on a finite state space. Train a transformer with context length N on sample trajectories with SGD. Can you expect the transformer to become a good approximation for the dynamics of the Markov process? More specifically, suppose your Markov process is generated by some algorithm/Turing machine couple with some random data. Th…

Is addition a Markov process? I really don't think so. You can certainly model e.g. integer addition by a Markov process, up to some integer k but addition itself is usually formalised by the Peano axioms, that are not quite Markovian. I guess you can see the relation between S(n) and S(S(n)) as some kind of Markov chain. That's really not a standard view though.

In any case, a complete theory of addition must be correct up to inifinity so you won't get that with any Markov process we can train from data. Although you can learn addition with a simple linear regression, by setting the weights appropriately. That's because a function of a line already includes addition, and multiplication, and that's basically not very different to what the team in the paper above is trying to do. Meaning: they're trying to hand-code the concept of addition in embeddings. It's not 100% because they're also at the same time trying to not 100% encode it, but it's a hard balance to strike.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#86

Post by psychoslave »

tadala wrote: post #53
psychoslave wrote: post #44

Earlier quoted context omitted.

> E.g. humans follow a deductive process to answer questions which they haven't encountered yet. Rarely, actually. More generally humans use all kind of inferences where problem at hand is intertwined with all other attention points that is occupying the mental load of the person. Giving a topic full mental attention and finding a path through pure deduction about a circumscribed subject is a rarity, even if you cons…

Not within mathematics, where it is the entire sport, and which is the point of contention.

If there is one space where it shines, sure it’s mathematics. But even there, the most notable mathematicians highly rely on some intuitions far before they manage to prove anything, as well as while selecting/creating their conceptual tools to attempt to build the proof, and rarely go to the point of formalizing their points through Coq/Isabelle or even with meticulous paper craft à la Principia Mathematica from Russel and Whitehead.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#87

Post by psychoslave »

olalonde wrote: post #65
psychoslave wrote: post #38

Earlier quoted context omitted.

I didn’t test with all LLM out there, but all of thus I tested failed with something as basic as "What is the number of words in the sentence coming before the next one? Please answer."

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)_/¯

Re: Transformers Can Do Arithmetic with the Right Embeddings

#88

Post by edflsafoiewq »

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…

I don't understand the framing of your comment. You act like the LLM's feelings are going to be hurt if you say it isn't a real AGI. "Well, you can't do basic math expected of fifth graders, but there are dumb fifth graders too, so here's the 'human-level intelligence' participation trophy anyway."

Re: Transformers Can Do Arithmetic with the Right Embeddings

#89

Post by anon291 »

short_sells_poo wrote: post #37
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…

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#90

Post by ADeerAppeared »

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…

> But this isn't the case.. 5-6% of the population have https://en.wikipedia.org/wiki/Dyscalculia, but can be otherwise normal.

This nitpicking is a red herring.

The issue that separates "AGI" from current AI systems is the lack of generality. (Humour me.)

In particular, the lack of reasoning capability. And what the pessimists argue here is that there is no road to get there for current systems. Transformers are approximation machines, and are generalized for that specific task. But that's also where it stops, they can't do things that aren't such pattern-approximation.

Optimizing a transformer for arithmetic isn't a step towards AGI, because it is not generalizing. You'd need to do this for every conceivable task and subtask. This is the exact reason why imperative-programmed AI architectures were discarded.

Put bluntly, this approach will never get you a transformer that won't shit itself when asked to do novel reasoning tasks, such as novel mathematics. (Which I will remind the reader, anything but the basic programming work counts as)

And critically, the fundamental architecture of these transformer systems doesn't allow the combination of them into other AI systems to acquire generalized capabilities. There's no way to make an LLM hook into a computer-algebra-system, you can only feed 'finished' output of one system into another.

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