Using Convolutional Neural Networks to Analyze Function Properties from Images
Abstract
We propose a system for determining properties of mathematical functions given an image of their graph representation. We demonstrate our approach for two-dimensional graphs (curves of single variable functions) and three-dimensional graphs (surfaces of two variable functions), studying the properties of convexity and symmetry. Our method uses a Convolutional Neural Network which classifies functions according to these properties, without using any hand-crafted features. We propose algorithms for randomly constructing functions with convexity or symmetry properties, and use the images generated by these algorithms to train our network. Our system achieves a high accuracy on this task, even for functions where humans find it difficult to determine the function's properties from its image.
Cite
Text
Lewenberg et al. "Using Convolutional Neural Networks to Analyze Function Properties from Images." AAAI Conference on Artificial Intelligence, 2016. doi:10.1609/AAAI.V30I1.9843Markdown
[Lewenberg et al. "Using Convolutional Neural Networks to Analyze Function Properties from Images." AAAI Conference on Artificial Intelligence, 2016.](https://mlanthology.org/aaai/2016/lewenberg2016aaai-using/) doi:10.1609/AAAI.V30I1.9843BibTeX
@inproceedings{lewenberg2016aaai-using,
title = {{Using Convolutional Neural Networks to Analyze Function Properties from Images}},
author = {Lewenberg, Yoad and Bachrach, Yoram and Kash, Ian A. and Key, Peter B.},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2016},
pages = {4363-4364},
doi = {10.1609/AAAI.V30I1.9843},
url = {https://mlanthology.org/aaai/2016/lewenberg2016aaai-using/}
}