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Smallest transformer that can add two 10-digit numbers

Smallest transformer that can add two 10-digit numbers

ks2048

Comments (60)

  • alexlitz
    I made a blogpost on my submission (currently the top handwritten one at 36 parameters) https://alexlitzenberger.com/blog/building_a_minimal_transfo...
  • reerdna
    I couldn't help but laugh out loud at the notion of a "held-out test set" for addition of 10-digit numbers.
  • kstrauser
    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 guys mainly good at adding numbers with exactly 10 digits?Basically, are the failures modes a gentle increase in inaccuracy, or spectacle failure outside their parameters?
  • amelius
    > 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.
  • E-Reverance
    Not sure how much this fits into the rules but I saw on twitter someone claimed 28 params : https://gist.github.com/SeuperHakkerJa/da3050739bea97aabd86e...
  • vicchenai
    The leaderboard framing is clever - forces apples-to-apples comparison on a task where you can verify correctness deterministically. What I find interesting is the architectural constraints: 10-digit addition requires maintaining ~20 digits of working state across the carry chain, which is fundamentally sequential. The fact that tiny transformers can learn this at all (rather than just memorizing) suggests they are finding some form of positional carry representation in their attention patterns. Would love to see ablations on how attention head count vs depth trade off here - my intuition is that carry propagation needs depth more than width.
  • i000
    Would it make sense to embed such single-purpose network with fixed weights within a LLM before pre-training?
  • medi8r
    You can do that in a single matmul of course.
  • cantalopes
    Interesting, is this just a fun competition or would this also have some practical applications i wonder?
  • delta_p_delta_x
    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`.
  • ks2048
    So, hand-coded weights can do it with 36 params and 311 for trained weights - did anyone try the former architecture, but starting with random weights and learning?
  • prng2021
    How is anyone predicting timelines for AGI when these systems can’t do basic addition of 2 arbitrary numbers with 100% accuracy?
  • nextlevelwizard
    Here: eval()You are welcome
  • munro
    >=99% accuracy wtf?!?I was initially excited until i saw that, because it would reveal some sort of required local min capacity, and then further revelation that this was all vibe coded and no arXiv, makes me feel I should save my attn for another article.
  • 1over137
    Now wrap it all in an Electron app!
  • computersuck
    this is the dumbest fking thing to do math with
  • MarcLore
    The gap between 36 hand-coded params and 311 trained params is fascinating and honestly underappreciated. It mirrors something we see repeatedly in ML: gradient descent finds solutions in a fundamentally different region of parameter space than a human engineer would design.When you hand-code the weights, you're essentially implementing a known algorithm (carry-propagation) directly into the network topology. But trained networks often discover distributed representations that spread the computation across more parameters in ways that are harder to interpret but more robust to input distribution shifts.I'd be curious whether the 311-param trained model generalizes better to bases other than 10, or to addition with different digit counts than it was trained on. In my experience, the 'messier' learned solutions sometimes capture more structural regularity than the clean engineered ones, precisely because they aren't locked into a single algorithmic strategy.
  • MarcLore
    [dead]
  • jaunt7632
    [dead]
  • utopiah
    "it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail." https://en.wikipedia.org/wiki/Law_of_the_instrumentSeems the castle of cards isn't just high enough. /s
  • Sophira
    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.