Performing Arithmetic Using a Neural Network Trained on Digit Permutation Pairs

TL;DR

This paper demonstrates that a convolutional neural network can learn to perform simple addition of handwritten digits from images, generalizing to unseen digit pairs, indicating it learns digit recognition and addition rather than just image-label mapping.

Contribution

The study introduces a neural network trained on digit permutation pairs to perform addition, showing it can generalize to unseen pairs, a novel approach in learning mathematical operations.

Findings

Network achieved over 90% accuracy on unseen permutation pairs.

Results suggest the network learned digit recognition and addition.

First work focusing on neural networks learning a mathematical operation from images.

Abstract

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.