Performing arithmetic using a neural network trained on images of digit permutation pairs

Marcus D. Bloice*, Peter M. Roth, Andreas Holzinger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, a neural network is trained to perform simple arithmetic using images of concatenated handwritten digit pairs. A convolutional neural network was trained with images consisting of two side-by-side handwritten digits, where the image’s label is the summation of the two digits contained in the combined image. Crucially, the network was tested on permutation pairs that were not present during training in an effort to see if the network could learn the task of addition, as opposed to simply mapping images to labels. A dataset was generated for all possible permutation pairs of length 2 for the digits 0–9 using MNIST as a basis for the images, with one thousand samples generated for each permutation pair. For testing the network, samples generated from previously unseen permutation pairs were fed into the trained network, and its predictions measured. Results were encouraging, with the network achieving an accuracy of over 90% on some permutation train/test splits. This suggests that the network learned at first digit recognition, and subsequently the further task of addition based on the two recognised digits. As far as the authors are aware, no previous work has concentrated on learning a mathematical operation in this way. This paper is an attempt to demonstrate that a network can learn more than a direct mapping from image to label, but is learning to analyse two separate regions of an image and combining what was recognised to produce the final output label.

Original languageEnglish
Pages (from-to)547-562
Number of pages16
JournalJournal of Intelligent Information Systems
Issue number3
Publication statusPublished - Dec 2021
Externally publishedYes


  • Cognition
  • Neural networks

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Hardware and Architecture
  • Computer Networks and Communications
  • Artificial Intelligence


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