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How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks

This repository is the PyTorch implementation of the experiments in the following paper:

Keyulu Xu, Mozhi Zhang, Jingling Li, Simon S. Du, Ken-ichi Kawarabayashi, Stefanie Jegelka. How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks. ICLR 2021.

arXiv OpenReview

If you make use of the relevant code/experiment/idea in your work, please cite our paper (Bibtex below).

@inproceedings{
xu2021how,
title={How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks},
author={Keyulu Xu and Mozhi Zhang and Jingling Li and Simon Shaolei Du and Ken-Ichi Kawarabayashi and Stefanie Jegelka},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=UH-cmocLJC}
}

Requirements

• This codebase has been tested for python3.7 and pytorch 1.4.0 (with CUDA VERSION 10.0).
• To install necessary python packages, run pip install -r requirements.txt (This installs pytorch).
• The packages networkx and pytorch-geometric need to be installed separately. networkx and geometric versions can be decided based on pytorch and CUDA version.

Instructions

Refer to each folder for instructions to reproduce the experiments. All experiments can be easily reproduced by typing the commands provided.

• Experiments related to feedforward networks may be found in the feedforward folder.
• Experiments on architectures that help extrapolation may be found in the graph_algorithms folder.
• Experiments on representations that help extrapolation may be found in the n_body folder.