Isn't it just wild how we’ve built these flashy Transformers that can whip up poetry, churn out art, and even chat your ear off, yet they still trip over something as basic as multiplication? Welcome to the AI circus, where failing basic math feels like a trendy quirk rather than a massive oversight.
There's this paper, "Why Can't Transformers Learn Multiplication? Reverse-Engineering Reveals Long-Range Dependency Pitfalls," that dives into this mess. You’d think with all the buzz around these models, they’d have multiplication down pat, but nope! Apparently, while they can keep track of a complex plot twist in a novel, they can’t figure out that 12 times 12 isn’t just an abstract concept. The researchers found that, despite their fancy attention mechanisms and whatnot, these Transformers are like that kid in class who can recite Shakespeare but can’t add two and two without a calculator. They even went so far as to create a graph just to “cache” and “retrieve” partial products. I mean, come on, just count on your fingers!
The paper claims that, theoretically, Transformers could learn multiplication, but they tend to get stuck in a local optimum—think of it like a sports car that refuses to exceed 30 mph because it’s hung up on the wrong gear. They even tossed in an auxiliary loss function to help the model predict running sums, kind of like giving it a cheat sheet for that math test it clearly wasn’t prepared for. Apparently, the right “inductive bias” can work miracles. Who knew math could be so complicated?
They get all technical about how models represent digits using a Fourier basis and implement partial products with Minkowski sums. Sounds super sci-fi, right? But honestly, how ridiculous is it that we need this convoluted approach just for a machine to grasp multiplication? Shouldn’t we have just drilled them on the times tables instead?
In the grand scheme of things, while Transformers are painted as the pinnacle of AI, they’re still fumbling over the basics. Who could have seen this coming? (Oh, wait, literally everyone.) Maybe instead of getting these machines to wrestle with multiplication, we should just let them stick to what they’re decent at—like creating memes or dishing out dad jokes. At least those don’t require a calculator!
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**References**
*(Only the sources actually used in this content are listed below)*
• https://arxiv.org/abs/2510.00184
*Note: This analysis is based on 1 sources. For more comprehensive coverage, additional research from diverse sources would be beneficial.*
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https://arxiv.org/abs/2510.00184