Learning the greatest divisor - Explainable predictions in transformers - Poster

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 $91$.