This repository contains the offical implementation of the paper "Frame Averaging for Invariant and Equivariant Network Design" (ICLR 2022).
Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.
For more details, see: https://arxiv.org/abs/2110.03336.
The code is compatible with python 3.8 and pytorch 1.7. Conda environment file is provided at env.yml
The repository contains implementation to the experiments from the paper: normal estimation for point clouds, the n-body experiment and graph separation tasks. To run on of the experiments go to the relevant folder, for example for the n-body experiment:
cd nbody
and follow the instrouctions in the folder's .md file.
@inproceedings{
puny2022frame,
title={Frame Averaging for Invariant and Equivariant Network Design},
author={Omri Puny and Matan Atzmon and Edward J. Smith and Ishan Misra and Aditya Grover and Heli Ben-Hamu and Yaron Lipman},
booktitle={International Conference on Learning Representations},
year={2022},
url={https://openreview.net/forum?id=zIUyj55nXR}
}