Live data from Hacker News

Smallest transformer that can add two 10-digit numbers

github.com

21–30 of 105 posts

Re: Smallest transformer that can add two 10-digit numbers

#21
post #19

I get that this is technically interesting, for certain, but the sheer amount of energy and associated global warming risk needed to do something with >=99% accuracy that we've been able to do easily for decades with a guaranteed 100% accuracy seems to me to be wasteful to the extreme.

You need to recalibrate your sense of scale if you think that this is a geologically relevant usage of energy.

Re: Smallest transformer that can add two 10-digit numbers

#22
post #19

I get that this is technically interesting, for certain, but the sheer amount of energy and associated global warming risk needed to do something with >=99% accuracy that we've been able to do easily for decades with a guaranteed 100% accuracy seems to me to be wasteful to the extreme.

Wait until you see the quantum computer that it takes to factor the integer 15.

Re: Smallest transformer that can add two 10-digit numbers

#23
Very cool, but can I suggest the `add` CPU instruction instead? Supports 64-bit numbers, and it's encoded in hardware, and no need to cross a PCIe interface into a beefy, power-hungry GPU and back again. And chances are it's cross-platform, because basically every ISA since the very first has had `add`.

Re: Smallest transformer that can add two 10-digit numbers

#25

I made a blogpost on my submission (currently the top handwritten one at 36 parameters) https://alexlitzenberger.com/blog/building_a_minimal_transfo...

I ask this question as someone who can't do much more than confirm that your blog post is written in English by someone who knows math.

Does this result suggest that if we had N clever humans manually building an LLM, they might come up with something as smart as a frontier model, but potentially 45 times smaller? (1644 / 36 ~= 45, N = very large, time not specified)

Re: Smallest transformer that can add two 10-digit numbers

#26
post #25

I made a blogpost on my submission (currently the top handwritten one at 36 parameters) https://alexlitzenberger.com/blog/building_a_minimal_transfo...

I ask this question as someone who can't do much more than confirm that your blog post is written in English by someone who knows math. Does this result suggest that if we had N clever humans manually building an LLM, they might come up with something as smart as a frontier model, but potentially 45 times smaller? (1644 / 36 ~= 45, N = very large, time not specified)

I imagine getting things to be polysemantic in a way that does not interfere would lead to sublinear scaling. Also there are smaller ones that were trained so would still be more like 311/36 ~= 8.6.

Re: Smallest transformer that can add two 10-digit numbers

#27
post #25

Earlier quoted context omitted.

I ask this question as someone who can't do much more than confirm that your blog post is written in English by someone who knows math. Does this result suggest that if we had N clever humans manually building an LLM, they might come up with something as smart as a frontier model, but potentially 45 times smaller? (1644 / 36 ~= 45, N = very large, time not specified)

I imagine getting things to be polysemantic in a way that does not interfere would lead to sublinear scaling. Also there are smaller ones that were trained so would still be more like 311/36 ~= 8.6.

Thanks!

(I see the Trained Weights results now, thanks.)

Re: Smallest transformer that can add two 10-digit numbers

#28
post #19

I get that this is technically interesting, for certain, but the sheer amount of energy and associated global warming risk needed to do something with >=99% accuracy that we've been able to do easily for decades with a guaranteed 100% accuracy seems to me to be wasteful to the extreme.

What would be an acceptable amount of energy to spend on something that someone has done in a different manner before? Would you rather we stick with all of the current known ways to do things.

Does this boil down to a condemnation of all scientific endeavours if they use resources?

Would it change things if the people who did it enjoyed themselves? Would they have spent more energy playing a first person shooter to get the same degree of enjoyment?

How do you make the calculation of the worth of a human endeavour? Perhaps the greater question is why are you making a calculation of the worth of a human endeavour.

Re: Smallest transformer that can add two 10-digit numbers

#29
post #11

Earlier quoted context omitted.

From context then, I infer that a transformer is not comprised of matrix multiplications, because it would simply be one that adds two 10-digit numbers.

A transformer tokenizes input, does a bunch of matmul and relu set up in a certain way. It doesn't get to see the raw number (just like you don't when you look at 1+1 you need visual cortex etc. first.)

Notably the difference is that ten digits is not the same thing as a number. One might say that turning it into a number might be the first step, but Neural nets being what they are, they are liable to produce the correct result without bothering to have a representation any more pure than a list of digits.

I guess the analogy there is that a 74ls283 never really has a number either and just manipulates a series of logic levels.

Re: Smallest transformer that can add two 10-digit numbers

#30
post #11

Earlier quoted context omitted.

From context then, I infer that a transformer is not comprised of matrix multiplications, because it would simply be one that adds two 10-digit numbers.

A transformer tokenizes input, does a bunch of matmul and relu set up in a certain way. It doesn't get to see the raw number (just like you don't when you look at 1+1 you need visual cortex etc. first.)

So the question is, why do we tokenise it in such a way that it makes everything harder?
Post reply on HN