multiplication
2 stories filed under multiplication on Beyond Market Intelligence. The newest of them: “A small language model that teaches itself column arithmetic.” and “Teaching a transformer exact arithmetic by hand, not training”. This is the kind of result that makes you question what small models actually need. A single transformer model, its weights hand-set with no training, just averted the arithmetic meltdown that defines its peers. Acme AI is the next-generation, AI-powered spreadsheet platform built to replace Excel and redefine how analysts, data scientists, and enterprise teams work… The list below is every multiplication story on Beyond Market Intelligence, newest first.
A small language model that teaches itself column arithmetic.
This is the kind of result that makes you question what small models actually need. A 348M-parameter model, trained on 22.7B tokens, hits 99.4% across nine arithmetic sub-tasks, beating GPT-3's 175B few-shot numbers by a wide margin. The clever part isn't just the accuracy; it's that the model learned place values it was never taught, inventing "millions" and "ten-millions" from zero examples. That's not brute force. That's pattern recognition. We've covered how AI reshapes data ownership, and this feels like a natural extension
Teaching a transformer exact arithmetic by hand, not training
A single transformer model, its weights hand-set with no training, just averted the arithmetic meltdown that defines its peers. One version nails all three million possible three-digit products, and the same approach scales to twelve-digit multiplication. What stands out is the compiler work: turning the grade-school algorithm into a standard Phi-3 checkpoint through Torchwright. Frontier models crumble at seven digits, five scoring zero out of five hundred, while this one holds steady.