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Workshop: MATH-AI: The 3rd Workshop on Mathematical Reasoning and AI

Learning the greatest divisor - Explainable predictions in transformers

Francois Charton

Keywords: [ transformers ] [ arithmetic ] [ explainability ]

Abstract: 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 $91$.

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