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Length Generalization in Arithmetic Transformers

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arxiv 2306.15400 v1 pith:OKT3MXPA submitted 2023-06-27 cs.LG

Samy Jelassi , Stéphane d'Ascoli , Carles Domingo-Enrich , Yuhuai Wu , Yuanzhi Li , François Charton This is my paper · ORCID
classification cs.LG
keywords digitprimingarithmeticgeneralizationmodelstraininglengthsequences
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abstract

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.

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Forward citations

Cited by 4 Pith papers

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