Curriculum Learning Shapes the Computation Learned by Arithmetic Transformers

Do transformers learn arithmetic by mirroring digit-wise algorithms, or by exploiting statistical shortcuts? Here we study how an encoder transformer learns to solve addition and find that the most significant digits are learned before the less significant ones, in contrast to how one would compute addition by hand. We exactly solve the learning dynamics of a linear model on the same task and show that it learns a continuous magnitude representation of the sum, despite the task being encoded symbolically. As this representation is learned, it encodes the most significant digits accurately first, since errors in this estimate disproportionately affect less significant digits. Next we apply curriculum learning to the transformer to force it to learn the task in the canonical order, and find that this shifts the model from an estimation-like strategy to digit-wise computation, and improves generalisation performance to tasks with a similar computational structure as addition. These findings demonstrate that different strategies compete inside neural networks, and structuring the training curriculum can fundamentally alter a model's internal strategy.