Euclidean Neural Network

Euclidean neural networks (ENNs) are a class of machine learning models traditionally designed for data residing in Euclidean space, but recent research increasingly addresses their limitations when dealing with data exhibiting non-Euclidean geometries, such as those found in graphs, manifolds, or hyperbolic spaces. Current research focuses on adapting ENNs to these non-Euclidean settings through techniques like Riemannian geometry, hyperbolic geometry, and the development of specialized architectures (e.g., Riemannian ResNets, hyperbolic collaborative filtering) that incorporate geometric properties into the network's structure and operations. This work is significant because it expands the applicability of neural networks to a wider range of complex data types, improving performance in various fields including computer vision, drug discovery, and recommendation systems.

Papers

September 20, 2024

Neural Configuration Distance Function for Continuum Robot Control
Kehan Long, Hardik Parwana, Georgios Fainekos, Bardh Hoxha, Hideki Okamoto, Nikolay Atanasov
Dynamic Obstacle Continuum Robot Distance Function Euclidean Neural Network

September 11, 2024

Current Symmetry Group Equivariant Convolution Frameworks for Representation Learning
Ramzan Basheer, Deepak Mishra
Representation Learning Representation Space Geometric Deep Learning Group Convolution Euclidean Neural Network Equivariant Deep Probabilistic Equivariant Continuous Convolution

September 4, 2024

A Fashion Item Recommendation Model in Hyperbolic Space
Ryotaro Shimizu, Yu Wang, Masanari Kimura, Yuki Hirakawa, Takashi Wada, Yuki Saito, Julian McAuley
Multi Task Learning Hyperbolic Space Multi Task Learning Framework Item Representation Euclidean Neural Network

July 31, 2024

Deep Fr\'echet Regression
Su I Iao, Yidong Zhou, Hans-Georg Müller
High Dimensional Non Euclidean Euclidean Neural Network Fr\'echet Regression

July 15, 2024

Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry
Ziheng Chen, Yue Song, Xiao-Jun Wu, Gaowen Liu, Nicu Sebe
Camera Lens Covariance Matrix Riemannian Geometry Euclidean Neural Network Riemannian Classifier Global Covariance Pooling

December 6, 2023

Data is Overrated: Perceptual Metrics Can Lead Learning in the Absence of Training Data
Tashi Namgyal, Alexander Hepburn, Raul Santos-Rodriguez, Valero Laparra, Jesus Malo
LeArning Abstract Training Data Raw Data Autoencoder Based Perceptual Loss Euclidean Neural Network Perceptual Metric

October 16, 2023

Riemannian Residual Neural Networks
Isay Katsman, Eric Ming Chen, Sidhanth Holalkere, Anna Asch, Aaron Lou, Ser-Nam Lim, Christopher De Sa
Geometric Deep Learning Residual Neural Network Euclidean Neural Network Neural Manifold Riemannian Graph

May 18, 2023

Riemannian Multinomial Logistics Regression for SPD Neural Networks
Ziheng Chen, Yue Song, Gaowen Liu, Ramana Rao Kompella, Xiaojun Wu, Nicu Sebe
Hyperbolic Neural Network Euclidean Neural Network Symmetric Positive Definite Riemannian Classifier

May 8, 2023

Building Neural Networks on Matrix Manifolds: A Gyrovector Space Approach
Xuan Son Nguyen, Shuo Yang
Class Manifold Euclidean Neural Network Grassmann Manifold

April 24, 2023

An Approximation Theory for Metric Space-Valued Functions With A View Towards Deep Learning
Anastasis Kratsios, Chong Liu, Matti Lassas, Maarten V. de Hoop, Ivan Dokmanić
Deep Learning Best View North Star Metric Vector Valued Euclidean Neural Network Polish Space

February 15, 2023

SupSiam: Non-contrastive Auxiliary Loss for Learning from Molecular Conformers
Michael Maser, Ji Won Park, Joshua Yao-Yu Lin, Jae Hyeon Lee, Nathan C. Frey, Andrew Watkins
LeArning Abstract Siamese Network Molecular Conformation Euclidean Neural Network Bioactivity Prediction

October 10, 2022

Hierarchical Learning in Euclidean Neural Networks
Joshua A. Rackers, Pranav Rao
Semantic Feature Hierarchical Learning Equivariant Model Euclidean Neural Network Equivariant Machine Learning

August 2, 2022

Curved Geometric Networks for Visual Anomaly Recognition
Jie Hong, Pengfei Fang, Weihao Li, Junlin Han, Lars Petersson, Mehrtash Harandi
Anomaly Detection 2 Dimensional Visual Anomaly Detection Multi Class Anomaly Detection Euclidean Neural Network

July 19, 2022

HICF: Hyperbolic Informative Collaborative Filtering
Menglin Yang, Zhihao Li, Min Zhou, Jiahong Liu, Irwin King
Movie Recommendation Margin Maximization Euclidean Neural Network Hyperbolic Model Hyperbolic Informative Collaborative Filtering

July 18, 2022

e3nn: Euclidean Neural Networks
Mario Geiger, Tess Smidt
Equivariant Network Euclidean Neural Network Equivariant Generative

July 11, 2022

Deep Squared Euclidean Approximation to the Levenshtein Distance for DNA Storage
Alan J. X. Guo, Cong Liang, Qing-Hu Hou
Jina Embeddings Biological Sequence Euclidean Neural Network DNA Related Bioinformatics Domain Euclidean Distance Levenshtein Distance DNA Storage

June 9, 2022

A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks
Mehrdad Khatir, Nurendra Choudhary, Sutanay Choudhury, Khushbu Agarwal, Chandan K. Reddy
Hyperbolic Representation Multi Relational Hyperbolic Neural Network Euclidean Neural Network Hyperbolic Graph

June 7, 2022

Towards Scalable Hyperbolic Neural Networks using Taylor Series Approximations
Nurendra Choudhary, Chandan K. Reddy
Hyperbolic Space Hyperbolic Neural Network Euclidean Neural Network Taylor Expansion Hyperbolic Model Hyperbolic Network

March 14, 2022

FisheyeHDK: Hyperbolic Deformable Kernel Learning for Ultra-Wide Field-of-View Image Recognition
Ola Ahmad, Freddy Lecue
Convolution Kernel Euclidean Neural Network Kernel Regime Hyperbolic Classifier

February 14, 2022

Random Laplacian Features for Learning with Hyperbolic Space
Tao Yu, Christopher De Sa
Random Feature Hyperbolic Space Hyperbolic Embeddings Geometric Prior Euclidean Neural Network Hyperbolic Network