Length Generalization in Arithmetic Transformers
Samy Jelassi Stéphane d'Ascoli Carles Domingo-Enrich Yuhuai Wu Yuanzhi Li François Charton
We examine how transformers cope with two challenges: learning basic integer
arithmetic, and generalizing to longer sequences than seen during training. We
find that relative position embeddings enable length generalization for simple
tasks, such as addition: models trained on $5$-digit numbers can perform
$15$-digit sums. However, this method fails for multiplication, and we propose
train set priming: adding a few ($10$ to $50$) long sequences to the training
set. We show that priming allows models trained on $5$-digit $\times$ $3$-digit
multiplications to generalize to $35\times 3$ examples. We also show that
models can be primed for different generalization lengths, and that the priming
sample size scales as the logarithm of the training set size. Finally, we
discuss potential applications of priming beyond arithmetic.