One neural network. Five mathematical operations. Different learning times.
We trained a small mixture-of-experts transformer on addition, subtraction, multiplication, division, and exponentiation modulo 113.
The operations didn’t generalize together. Multiplication and division reached 90% held-out accuracy first, followed by exponentiation, subtraction, and finally addition.
Multiplication before addition—the reverse of what we expect from a schoolchild.
The accuracy chart in the linked article shows why a single overall accuracy number can hide an interesting learning story.