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Smallest transformer that can add two 10-digit numbers

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

#71

Post by Lerc »

qsera wrote: post #68
Lerc wrote: post #65

Earlier quoted context omitted.

That's a counterargument to a different thing. Iteratively measuring loss is a way to reconstruct values. That's trivial to show for a single value If 5 gives you a loss of 2 and 9 gives you a loss of 2 then you know the missing value is 7. A model with enough parameters can memorise the training set in a similar manner. Technically the model hasn't seen that data by direct input either, but the mechanism provides th…

Yea, because "seeing" is also tweaking the parameters. Which this example is doing manually. So I don't understand how any one can make the claim that the model as not seen it. Because the internal transformation is similar.

You are going to have to be more specific, because that reads like nonsense.

By what mechanism do you propose the model observed the test set?

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

#72

Post by tovej »

ACCount37 wrote: post #50
delta_p_delta_x wrote: post #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`.

No. You cannot. It's the wrong tool for the problem. That little "add" of yours has the overhead of: having an LLM emit it as a tool call, having to pause the LLM inference while waiting for it to resolve, then having to encode the result as a token to feed it back. At the same time, a "transformer-native" addition circuit? Can be executed within a single forward pass at a trivial cost, generate transformer-native re…

giggle

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

#73

Post by sambapa »

famouswaffles wrote: post #54
prng2021 wrote: post #46

How is anyone predicting timelines for AGI when these systems can’t do basic addition of 2 arbitrary numbers with 100% accuracy?

Can you do basic addition of 2 arbitrary numbers with 100% accuracy (no tools) ? No you can't. You will make mistakes for a sufficiently large N even with pen and paper, and a very small N without. Are you no longer generally intelligent ?

No, but I can develop methods to eventually do it.

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

#74

Post by tovej »

mapontosevenths wrote: post #41
Sophira wrote: 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.

> the sheer amount of energy and associated global warming risk I think that's one very good reason to make them more efficient, and that's part of the point of contests like this one.

Making things more efficient in a market setting just means they're used more. Which means we eventually use more resources with efficient methods, not less.

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

#75

Post by qsera »

Lerc wrote: post #71
qsera wrote: post #68

Earlier quoted context omitted.

Yea, because "seeing" is also tweaking the parameters. Which this example is doing manually. So I don't understand how any one can make the claim that the model as not seen it. Because the internal transformation is similar.

You are going to have to be more specific, because that reads like nonsense. By what mechanism do you propose the model observed the test set?

>By what mechanism do you propose the model observed the test set..

By explicitly setting the model parameters.

What happens when a model is trained? We tweak the model parameters by some feed back.

In both cases, you affect the model parameters. Only the method is different. So both are eqvialent to "model observing the test set".

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

#77

Post by qayxc »

akoboldfrying wrote: post #60
computersuck wrote: post #36

this is the dumbest fking thing to do math with

Yes, but it's interesting that you can teach it to do arithmetic, don't you think? Most things can't be taught to do arithmetic, making this "transformer" thing slightly magical. And so then it seems interesting to investigate exactly how much magic is needed to achieve this.

> Most things can't be taught to do arithmetic, making this "transformer" thing slightly magical.

Yep, for people who don't have know the fundamentals (i.e. maths). To people who don't know the universal approximation theorem, this may seem like "magic", but it's just as much magic as making a dark room bright by flipping a light switch.

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

#79

Post by SlinkyOnStairs »

kstrauser wrote: post #56

So, what happens when you test it on 11 digit numbers? I don’t mean that as a gotcha or “LOL dumb transformer” snark. More like, does the accuracy start to drop as you add digits? Or instead, maybe it’s the transformer equivalent of a stack overflow and it outputs a picture of a burning spoon or something? And for that matter, what’s it do with 9 digit numbers? Like, is it more accurate with them, or are these little…

One major limitation of the LLM architecture is that even the failure mode varies unpredictably between inputs.

The set of 11-digit numbers with any given failure mode (or even successful output) has no discernable pattern, merely whatever randomness the training process baked into the model.

You can't predict ahead of time when they will fail spectacularly, nor draw a clear boundary around the failure cases. And early major example of this were the "glitch tokens" introduced into most LLMs by training on reddit data.

But there is an "in general"/"average failure rate across all inputs of a given size" answer: LLMs performance drops off a cliff once the input reaches too much complexity. (A "┐" shaped curve) In contrast to humans, where you can ask a child to add two N-digit numbers and the error rate will be approximately linear to N.

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

#80

Post by freakynit »

vasco wrote: post #58
amelius wrote: post #2

> In short: if you can swap in a different set of weights and use the exact same inference code for a different task, your setup is legitimate. If the inference code is inseparable from the algorithm, it's not. I wonder why they don't just write the code themselves, so by design the focus can be on the model.

Writing code by hand, what is this, 6 months ago??

Time do be running real fast these days
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