Emergent properties with repeated examples

Francois Charton, Julia Kempe

Keywords: transformers, learning on repeated examples, emergence

TL;DR: In three controlled experiments with generated data we show that models trained on smaller sets of repeated examples outperform models trained on larger sets of single-use examples and introduce two-set training to show the benefits of repetition.

Abstract: 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 {\em 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.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 3581