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Computer Science > Machine Learning

arXiv:2405.17399 (cs)
[Submitted on 27 May 2024]

Title:Transformers Can Do Arithmetic with the Right Embeddings

Authors:Sean McLeish, Arpit Bansal, Alex Stein, Neel Jain, John
Kirchenbauer, Brian R. Bartoldson, Bhavya Kailkhura, Abhinav Bhatele,
Jonas Geiping, Avi Schwarzschild, Tom Goldstein
View a PDF of the paper titled Transformers Can Do Arithmetic with
the Right Embeddings, by Sean McLeish and 10 other authors
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    Abstract:The poor performance of transformers on arithmetic tasks
    seems to stem in large part from their inability to keep track of
    the exact position of each digit inside of a large span of
    digits. We mend this problem by adding an embedding to each digit
    that encodes its position relative to the start of the number. In
    addition to the boost these embeddings provide on their own, we
    show that this fix enables architectural modifications such as
    input injection and recurrent layers to improve performance even
    further.
    With positions resolved, we can study the logical extrapolation
    ability of transformers. Can they solve arithmetic problems that
    are larger and more complex than those in their training data? We
    find that training on only 20 digit numbers with a single GPU for
    one day, we can reach state-of-the-art performance, achieving up
    to 99% accuracy on 100 digit addition problems. Finally, we show
    that these gains in numeracy also unlock improvements on other
    multi-step reasoning tasks including sorting and multiplication.

Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as:  arXiv:2405.17399 [cs.LG]
          (or arXiv:2405.17399v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2405.17399
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Sean McLeish [view email]
[v1] Mon, 27 May 2024 17:49:18 UTC (1,221 KB)
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