arxiv:2406.00075

Arbitrary Length Generalization for Addition

Published on May 31, 2024

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Abstract

A novel autoregressive generation technique enables a small Transformer model to generalize addition to numbers with unseen lengths of digits.

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This paper introduces a novel training methodology that enables a small Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at: https://github.com/AGPatriota/ALGA-R/.

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AGPatriota

Jun 7, 2024

In order to test for random numbers with 100 digits run the following inside your R session opened in the main folder:
source('Testing-Digits.R')

Change the seed by commenting set.seed(10) in the file Testing-Digits.R

If you want to test the algorithm for variable digit numbers, replace
x = paste0(sample(0:9,n0, replace=TRUE), collapse="")
and y = paste0(sample(0:9,n0, replace=TRUE), collapse="")
with
x = paste0(sample(0:9,sample(1:n0,1), replace=TRUE), collapse="")
and y = paste0(sample(0:9,sample(1:n0,1), replace=TRUE), collapse=""):

Best regards,
Alexandre G. Patriota,
Department of Statistics,
Institute of Mathematics and Statistics,
University of São Paulo, Brazil.

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