Geometric Deep Learning

Geometric deep learning (GDL) focuses on developing neural network architectures that can effectively process and learn from data with inherent geometric structures, such as graphs, meshes, and point clouds. Current research emphasizes the design of equivariant models, particularly graph neural networks (GNNs), which maintain consistent representations under geometric transformations like rotations and translations, and the development of efficient pooling operators to handle large datasets. These advancements are significantly impacting various fields, improving the accuracy and efficiency of tasks ranging from molecular simulations and material science to medical image analysis and computer-aided design.

Papers

May 26, 2023

Geometric deep learning approach to knot theory
Lennart Jaretzki
Neural Network Constructive Approach Theoretical Understanding Geometric Deep Learning Knot Theory Knot Invariant

May 24, 2023

gRNAde: Geometric Deep Learning for 3D RNA inverse design
Chaitanya K. Joshi, Arian R. Jamasb, Ramon Viñas, Charles Harris, Simon V. Mathis, Alex Morehead, Rishabh Anand, Pietro Liò
Geometric Deep Learning RNA Structure RNA Design

May 10, 2023

Graph Neural Networks and 3-Dimensional Topology
Pavel Putrov, Song Jin Ri
Graph Neural Network Class Manifold Geometric Deep Learning Low Dimensional Manifold Topology Problem

May 9, 2023

Deep Learning and Geometric Deep Learning: an introduction for mathematicians and physicists
R. Fioresi, F. Zanchetta
Deep Learning Graph Neural Network Loss Function Multi Layer Gentle Introduction Geometric Deep Learning Level Mathematics

May 3, 2023

Importance of equivariant and invariant symmetries for fluid flow modeling
Varun Shankar, Shivam Barwey, Zico Kolter, Romit Maulik, Venkatasubramanian Viswanathan
Importance Aware Inter Part Equivariance Geometric Deep Learning Rotation Equivariance Scale Equivariant

April 6, 2023

Interpretable statistical representations of neural population dynamics and geometry
Adam Gosztolai, Robert L. Peach, Alexis Arnaudon, Mauricio Barahona, Pierre Vandergheynst
Unsupervised Setting Geometric Analysis Geometric Deep Learning Neural Recording Interpretable Representation Neural Dynamic

March 17, 2023

March 13, 2023

Computing equivariant matrices on homogeneous spaces for Geometric Deep Learning and Automorphic Lie Algebras
Vincent Knibbeler
Geometric Deep Learning Digital Computing Equivariant Map Equivariant Representation Lie Algebra Homogeneous Space

March 3, 2023

Skeletal Point Representations with Geometric Deep Learning
Ninad Khargonkar, Beatriz Paniagua, Jared Vicory
3D Shape Geometric Deep Learning Skeleton Representation Shape Analysis Skeletonization Algorithm

February 17, 2023

Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning
Anastasis Kratsios, Cody Hyndman
Geometric Deep Learning Generative Process Conditional Distribution Real World Claim Ornstein Uhlenbeck Process

February 11, 2023

Is Distance Matrix Enough for Geometric Deep Learning?
Zian Li, Xiyuan Wang, Yinan Huang, Muhan Zhang
Graph Neural Network Geometric Deep Learning Geometric Information Geometric Graph Distance Matrix

February 9, 2023

Constrained Empirical Risk Minimization: Theory and Practice
Eric Marcus, Ray Sheombarsing, Jan-Jakob Sonke, Jonas Teuwen
Deep Neural Network Theoretical Understanding Empirical Risk Minimization Practice Mode Geometric Deep Learning Equivariant Network Wavelet Neural Network Contour Initialization

February 2, 2023

Geometric Deep Learning for Autonomous Driving: Unlocking the Power of Graph Neural Networks With CommonRoad-Geometric
Eivind Meyer, Maurice Brenner, Bowen Zhang, Max Schickert, Bilal Musani, Matthias Althoff
Graph Neural Network Autonomous Driving Trajectory Prediction Real Power Heterogeneous Graph Deep Learning Framework Geometric Deep Learning Graph Datasets

January 23, 2023

A Structural Approach to the Design of Domain Specific Neural Network Architectures
Gerrit Nolte
Product Design Neural Architecture Inter Part Equivariance Geometric Deep Learning Alpha Invariance Invariant Network Information Approach Domain Informed Neural Network

December 23, 2022

A Convergence Rate for Manifold Neural Networks
Joyce Chew, Deanna Needell, Michael Perlmutter
Convergence Rate High Dimensional Data Geometric Deep Learning Intrinsic Dimension Spectral Decomposition Neural Manifold

December 6, 2022

Supervised Tractogram Filtering using Geometric Deep Learning
Pietro Astolfi, Ruben Verhagen, Laurent Petit, Emanuele Olivetti, Silvio Sarubbo, Jonathan Masci, Davide Boscaini, Paolo Avesani
Geometric Deep Learning White Matter Bundle Specific Tractogram Distribution

November 25, 2022

Learning Feynman Diagrams using Graph Neural Networks
Harrison Mitchell, Alexander Norcliffe, Pietro Liò
Graph Neural Network Geometric Deep Learning Prediction Speed Feynman Diagram

November 4, 2022

Geometry-Complete Perceptron Networks for 3D Molecular Graphs
Alex Morehead, Jianlin Cheng
Molecular Graph Geometric Deep Learning Protein Structure Prediction Molecular Chirality

October 30, 2022

Interpretable Geometric Deep Learning via Learnable Randomness Injection
Siqi Miao, Yunan Luo, Mia Liu, Pan Li
Interpretable Model Geometric Deep Learning