Learning the greatest divisor - Explainable predictions in transformers

We train small transformers to calculate the greatest common divisor (GCD) of two positive integers, and show that their predictions are fully explainable. During training, models learn a list $\mathcal D$ of divisors, and predict the largest element of $\mathcal D$ that divides both inputs. We also show that training distributions have a large impact on performance. Models trained from uniform operands only learn a handful of GCD (up to $38$ out of $100$). Training from log-uniform operands boosts performance to $73$ correct GCD, and training from a log-uniform distribution of GCD to $91$.