Transformers Can Do Arithmetic with the Right Embeddings
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Re: Transformers Can Do Arithmetic with the Right Embeddings
#2The other day I was wondering if LLMs are bad at at maths because they don't have readily apparent access to the concept of "columns". Apparently the answer is yes.
Vertical alignment across lines is pretty important for humans to learn operations on digits, but the way we encode lines with a \n separator doesn't really help. In a recent codebullet video gpt really struggled with any kind of vertical alignment task. I wonder if it would do better on a fixed 80 column width...
Re: Transformers Can Do Arithmetic with the Right Embeddings
#3I think the main problem is the way we turn the raw mathematics symbols or equations into tokens, and these suboptimal tokenization may decreases the performance
Re: Transformers Can Do Arithmetic with the Right Embeddings
#4It 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.
Re: Transformers Can Do Arithmetic with the Right Embeddings
#5It 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 like that. I know that you are not probably saying it in this way, just wanted to let it out.
I believe there is fundamental work still to be done, maybe models that are able to draw patterns comparing experience, but this kind of work can be useful as make us reflect in every step of what these models do, and how much the internal representation learned can be optimized
Re: Transformers Can Do Arithmetic with the Right Embeddings
#6It 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…
>> deductive reasoning is just drawing specific conclusion from general patterns.
This is according to whom, please?
Re: Transformers Can Do Arithmetic with the Right Embeddings
#7What 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, but not for subtraction or division (clearly; I can't even find the words in the paper). As a practical way to build a machine to do arithmetic this is out of the question.
We've known how to mechanise arithmetic since the 1850's with Blaize Pascal and his Pascaline. What is the point in demonstrating it's possible to reinvent a broken, partial, buggy version of an arithmetic machine if one tries really hard and shoehorns the necessary patterns in a neural net? We've known that for a long time, too (every proof that a neural net can simulate this or that Turing machine if you design the network diagram and set the weights by hand, ever).
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?
Re: Transformers Can Do Arithmetic with the Right Embeddings
#8It 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…
> 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.
Re: Transformers Can Do Arithmetic with the Right Embeddings
#9The other day I was wondering if LLMs are bad at at maths because they don't have readily apparent access to the concept of "columns". Apparently the answer is yes. Vertical alignment across lines is pretty important for humans to learn operations on digits, but the way we encode lines with a \n separator doesn't really help. In a recent codebullet video gpt really struggled with any kind of vertical alignment task.…
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 sufficient brute-force can make a collection of overfitted non-arithmetic rules appear to work.
[0] https://blog.mathed.net/2011/07/rysk-erlwangers-bennys-conce...
Re: Transformers Can Do Arithmetic with the Right Embeddings
#10What 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…
There are two sides to this that jump out
One is that research into what the limits of the architecture are is useful. Maths has a nice property of being very easy to verify and you can construct logical processes with it. It's a useful testbed.
Second is there are a lot more places that understanding how to do arithmetic help, outside of just doing sums on their own.