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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

#51

Post by throwthrowuknow »

Shrezzing wrote: post #18
josehackernews wrote: post #5

Earlier quoted context omitted.

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…

>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 doing would be either the act of writing or speaking but we obviously process a lot more information and produce a higher volume of information at a much higher rate than we can speak or write. Imagine if you had to verbally direct each motion of your body, it would take an absurd amount of time to do anything depending on the specificity you had to work with.

The work done in this paper is very interesting and your dismissal of “it can’t see a corpus and then generalize to n digits” is not called for. They are training models from scratch in 24 hours per model using only 20 million samples. It’s hard to equate that to an activity a single human could do. It’s as though you had piles of accounting ledgers filled with sums and no other information or knowledge of mathematics, numbers or the world and you discovered how to do addition based on that information alone. There is no textbook or tutor helping them do this either it should be noted.

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#52

Post by mike_hearn »

Havoc wrote: post #43

For things like this where we have computationally cheap, well understood, reliable tools available (aka calculator) it seems better to train the model in tool use. I guess perhaps the techniques could be generalized though?

Generalizable techniques is mostly the point of papers like this one yes. What they show here is that apparently fundamental problems with transformer reasoning can be fixed by encoding data in a more sophisticated manner. This is exciting. I've been thinking for a long time that the tokenization schemes are a low hanging fruit for improving coding LLM performance, this isn't exactly the same thing but it's in the same general area. Smartness and reasoning ability with the current set of algorithmic techniques seems to have topped out around GPT-4 level, which implies that further leaps in mental abilities must come from improving other things beyond training set size.

For example, whilst replacing the need for a calculator isn't very important, one obvious research direction would be to explore adding extra embeddings to code inputs, perhaps that are being computed by an IDE.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#53

Post by tadala »

psychoslave wrote: post #44
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…

> 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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#54

Post by mike_hearn »

Shrezzing wrote: post #18
josehackernews wrote: post #5

Earlier quoted context omitted.

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…

>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…

> Young children take a single textbook & couple of days worth of tuition to achieve generalised understanding of addition

Maybe you did! Most young children cannot actually do bigint arithmetic reliably or at all after a couple days worth of tuition!

Re: Transformers Can Do Arithmetic with the Right Embeddings

#55

Post by weinzierl »

torginus wrote: post #34

I just wonder if numbers were written right to left, llms would be much better at arithmetic. You can 'predict' the least significant digit by reusing the already written digits in the computation, but to generate most significant ones, you generally need to do the entire computation in one go.

This is an interesting idea but probably hard to verify.

A tangent is that positional systems were originally invented with least digit first, I believe.

The Babylonian sexagesimal system was like that as was the Arabic one (where first is on the right).

The most significant digit first convention came when right-to left numbers were used in left-to-right systems without reversing them in writing. To this day we read the more common smaller numbers least significant digit first to varying degrees.

16 = six teen, sech zehn

98 = acht und neunzig, achten negentig, ثمانية وتسعون

Re: Transformers Can Do Arithmetic with the Right Embeddings

#56

Post by mike_hearn »

isaacfung wrote: post #42
Terr_ wrote: post #9

Earlier quoted context omitted.

Isn't it more that they don't have ready access to the much-more-fundamental concept of decimal numbers? My understanding was that they tokenized them into chunks and tried to learn associations between the chunks, the same as if one was breaking apart English words. So "2+2=4" isn't being treated that differently from "all's well that ends well." This might lead to a kind of Benny's Rules [0] situation, where suffic…

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.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#57

Post by vessenes »

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, and there's no reason it shouldn't be made part of standard tokenization.

I'm more interested in the question of how we can find other useful concepts for data -> embedding space like this; can we incept our tokenization inception so it has more inception?

Re: Transformers Can Do Arithmetic with the Right Embeddings

#58

Post by asgeir »

psychoslave wrote: post #38
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.

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."

In my experience, LLMs tend to perform better if you give them instructions before the data to be operated on. At least for the ~13b size models.

So,something like: Please count the number of words in the following sentence. "What is the number of words in the sentence coming before the next one?"

edit: Which might be an artifact of the training data always being in that kind of format.

Re: Transformers Can Do Arithmetic with the Right Embeddings

#59

Post by Thorham »

psychoslave wrote: post #38
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.

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."

14

Re: Transformers Can Do Arithmetic with the Right Embeddings

#60

Post by vessenes »

jiggawatts wrote: post #14

Something I've been thinking about is how the Minds -- the super-human AI hyper-computers that fly the ships in the Culture series of novels are described. The image built up in my head[1] is that they're hybrids blending neural networks and regular compute substrates. They can calculate, simulate, and reason in combination. There have been crude attempts at this already, hooking in Mathematica and Python into ChatGP…

Fellow huge Banks fan here.

I like this idea a lot. Right now we are going the long/hard way round, and post training asking an LLM to know it needs compute, then write a compute request, then feed back the compute answer into a tokenization loop.

It probably does make sense to add a mini CPU as a layer / tool / math primitive. I wonder how you'd train it to use such a thing? In my mind it's not really a layer per-se, but it's a set of function calls a layer could route to when it wants, and weight the response appropriately.

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