ChebLieNet, a spectral graph neural network turned equivariant by Riemannian geometry on Lie groups.

Overview

ChebLieNet: Invariant spectral graph NNs turned equivariant by Riemannian geometry on Lie groups

Hugo Aguettaz, Erik J. Bekkers, Michaël Defferrard

We introduce ChebLieNet, a group-equivariant method on (anisotropic) manifolds. Surfing on the success of graph- and group-based neural networks, we take advantage of the recent developments in the geometric deep learning field to derive a new approach to exploit any anisotropies in data. Via discrete approximations of Lie groups, we develop a graph neural network made of anisotropic convolutional layers (Chebyshev convolutions), spatial pooling and unpooling layers, and global pooling layers. Group equivariance is achieved via equivariant and invariant operators on graphs with anisotropic left-invariant Riemannian distance-based affinities encoded on the edges. Thanks to its simple form, the Riemannian metric can model any anisotropies, both in the spatial and orientation domains. This control on anisotropies of the Riemannian metrics allows to balance equivariance (anisotropic metric) against invariance (isotropic metric) of the graph convolution layers. Hence we open the doors to a better understanding of anisotropic properties. Furthermore, we empirically prove the existence of (data-dependent) sweet spots for anisotropic parameters on CIFAR10. This crucial result is evidence of the benefice we could get by exploiting anisotropic properties in data. We also evaluate the scalability of this approach on STL10 (image data) and ClimateNet (spherical data), showing its remarkable adaptability to diverse tasks.

Paper: OpenReview:WsfXFxqZXRO

Installation

Binder   Click the binder badge to run the code from your browser.

  1. Optionally, create and activate a virtual environment.

    python -m venv cheblienet
    source cheblienet/bin/activate
    python -m pip install --upgrade pip setuptools wheel
  2. Clone this repository.

    git clone https://github.com/haguettaz/ChebLieNet.git
  3. Install the ChebLieNet package and its dependencies.

    python -m pip install -e ChebLieNet

Notebooks

Reproducing our results

Train a WideResNet on MNIST with anisotropic kernels.

python -m train_mnist --path_to_graph ./saved_graphs --path_to_data ./data \
    --res_depth 2 --widen_factor 2 --anisotropic --coupled_sym --cuda

Train a WideResNet on CIFAR10 with spatial random pooling and anisotropic kernels.

python -m train_cifar10 --path_to_graph ./saved_graphs --path_to_data ./data \
    --res_depth 2 --widen_factor 4 --anisotropic --pool --reduction rand --cuda

Train a WideResNet on STL10 with spatial random pooling and anisotropic kernels.

python -m train_stl10 --path_to_graph ./saved_graphs --path_to_data ./data \
    --res_depth 3 --widen_factor 4 --anisotropic --reduction rand --cuda

Train a U-Net on ClimateNet with spatial max pooling, average unpooling, and anisotropic kernels.

python -m train_artc --path_to_graph ./saved_graphs --path_to_data ./data \
    --anisotropic --reduction max --expansion avg --cuda

License & citation

The content of this repository is released under the terms of the MIT license. Please cite our paper if you use it.

@inproceedings{cheblienet,
  title = {{ChebLieNet}: Invariant spectral graph {NN}s turned equivariant by Riemannian geometry on Lie groups},
  author = {Aguettaz, Hugo and Bekkers, Erik J and Defferrard, Michaël},
  year = {2021},
  url = {https://openreview.net/forum?id=WsfXFxqZXRO},
}
Owner
haguettaz
haguettaz
Weakly Supervised Scene Text Detection using Deep Reinforcement Learning

Weakly Supervised Scene Text Detection using Deep Reinforcement Learning This repository contains the setup for all experiments performed in our Paper

Emanuel Metzenthin 3 Dec 16, 2022
Streamlit app demonstrating an image browser for the Udacity self-driving-car dataset with realtime object detection using YOLO.

Streamlit Demo: The Udacity Self-driving Car Image Browser This project demonstrates the Udacity self-driving-car dataset and YOLO object detection in

Streamlit 992 Jan 04, 2023
Denoising Diffusion Probabilistic Models

Denoising Diffusion Probabilistic Models This repo contains code for DDPM training. Based on Denoising Diffusion Probabilistic Models, Improved Denois

Alexander Markov 7 Dec 15, 2022
A Robust Non-IoU Alternative to Non-Maxima Suppression in Object Detection

Confluence: A Robust Non-IoU Alternative to Non-Maxima Suppression in Object Detection 1. 介绍 用以替代 NMS,在所有 bbox 中挑选出最优的集合。 NMS 仅考虑了 bbox 的得分,然后根据 IOU 来

44 Sep 15, 2022
SAAVN - Sound Adversarial Audio-Visual Navigation,ICLR2022 (In PyTorch)

SAAVN SAAVN Code release for paper "Sound Adversarial Audio-Visual Navigation,IC

YinfengYu 10 Aug 30, 2022
Baseline and template code for node21 detection track

Nodule Detection Algorithm This codebase implements a baseline model, Faster R-CNN, for the nodule detection track in NODE21. It contains all necessar

node21challenge 11 Jan 15, 2022
TyXe: Pyro-based BNNs for Pytorch users

TyXe: Pyro-based BNNs for Pytorch users TyXe aims to simplify the process of turning Pytorch neural networks into Bayesian neural networks by leveragi

87 Jan 03, 2023
[ICRA 2022] An opensource framework for cooperative detection. Official implementation for OPV2V.

OpenCOOD OpenCOOD is an Open COOperative Detection framework for autonomous driving. It is also the official implementation of the ICRA 2022 paper OPV

Runsheng Xu 322 Dec 23, 2022
StyleGAN-Human: A Data-Centric Odyssey of Human Generation

StyleGAN-Human: A Data-Centric Odyssey of Human Generation Abstract: Unconditional human image generation is an important task in vision and graphics,

stylegan-human 762 Jan 08, 2023
MADT: Offline Pre-trained Multi-Agent Decision Transformer

MADT: Offline Pre-trained Multi-Agent Decision Transformer A link to our paper can be found on Arxiv. Overview Official codebase for Offline Pre-train

Linghui Meng 51 Dec 21, 2022
Extreme Lightwegith Portrait Segmentation

Extreme Lightwegith Portrait Segmentation Please go to this link to download code Requirements python 3 pytorch = 0.4.1 torchvision==0.2.1 opencv-pyt

HYOJINPARK 59 Dec 16, 2022
Official repository for Hierarchical Opacity Propagation for Image Matting

HOP-Matting Official repository for Hierarchical Opacity Propagation for Image Matting 🚧 🚧 🚧 Under Construction 🚧 🚧 🚧 🚧 🚧 🚧   Coming Soon   

Li Yaoyi 54 Dec 30, 2021
Pytorch domain adaptation package

DomainAdaptation This package is created to tackle the problem of domain shifts when dealing with two domains of different feature distributions. In d

Institute of Computational Perception 7 Oct 22, 2022
GPU implementation of $k$-Nearest Neighbors and Shared-Nearest Neighbors

GPU implementation of kNN and SNN GPU implementation of $k$-Nearest Neighbors and Shared-Nearest Neighbors Supported by numba cuda and faiss library E

Hyeon Jeon 7 Nov 23, 2022
A synthetic texture-invariant dataset for object detection of UAVs

A synthetic dataset for object detection of UAVs This repository contains a synthetic datasets accompanying the paper Sim2Air - Synthetic aerial datas

LARICS Lab 10 Aug 13, 2022
Code repo for "Cross-Scale Internal Graph Neural Network for Image Super-Resolution" (NeurIPS'20)

IGNN Code repo for "Cross-Scale Internal Graph Neural Network for Image Super-Resolution" [paper] [supp] Prepare datasets 1 Download training dataset

Shangchen Zhou 278 Jan 03, 2023
Shallow Convolutional Neural Networks for Human Activity Recognition using Wearable Sensors

-IEEE-TIM-2021-1-Shallow-CNN-for-HAR [IEEE TIM 2021-1] Shallow Convolutional Neural Networks for Human Activity Recognition using Wearable Sensors All

Wenbo Huang 1 May 17, 2022
School of Artificial Intelligence at the Nanjing University (NJU)School of Artificial Intelligence at the Nanjing University (NJU)

F-Principle This is an exercise problem of the digital signal processing (DSP) course at School of Artificial Intelligence at the Nanjing University (

Thyrix 5 Nov 23, 2022
This repository is based on Ultralytics/yolov5, with adjustments to enable rotate prediction boxes.

Rotate-Yolov5 This repository is based on Ultralytics/yolov5, with adjustments to enable rotate prediction boxes. Section I. Description The codes are

xinzelee 90 Dec 13, 2022
Video-Music Transformer

VMT Video-Music Transformer (VMT) is an attention-based multi-modal model, which generates piano music for a given video. Paper https://arxiv.org/abs/

Chin-Tung Lin 5 Jul 13, 2022