Emergent properties with repeated examples
Authors: name: François Charton, name: Julia Kempe

We study the performance of transformers as a function of the number of
repetitions of training examples with algorithmically generated datasets. On
three problems of mathematics: the greatest common divisor, modular
multiplication, and matrix eigenvalues, we show that for a fixed number of
training steps, models trained on smaller sets of repeated examples outperform
models trained on larger sets of single-use examples. We also demonstrate that
two-set training - repeated use of a small random subset of examples, along
normal sampling on the rest of the training set - provides for faster learning
and better performance. This highlights that the benefits of repetition can
outweigh those of data diversity. These datasets and problems provide a
controlled setting to shed light on the still poorly understood interplay
between generalization and memorization in deep learning.