Equivariant Function

Equivariant functions are mathematical functions that maintain their output structure under specific transformations of their input, reflecting inherent symmetries in the data. Current research focuses on developing and analyzing neural network architectures that learn these functions, including equivariant multilayer perceptrons and fully convolutional networks, often leveraging group theory and Lie algebra for efficient parameterization and improved performance. This work is significant because it allows for the development of more sample-efficient and robust machine learning models, particularly in domains with inherent symmetries like physics, graph analysis, and 3D point cloud processing. The resulting models offer improved accuracy and speed compared to traditional methods for tasks such as sparse vector recovery and polynomial optimization.

Papers

June 3, 2024

Learning equivariant tensor functions with applications to sparse vector recovery
Wilson G. Gregory, Josué Tonelli-Cueto, Nicholas F. Marshall, Andrew S. Lee, Soledad Villar
LeArning Abstract Financial Application Equivariant Machine Learning Permutation Equivariance Equivariant Function Tensor Rank Input Tensor Vector Retrieval

December 14, 2023

Symmetry Breaking and Equivariant Neural Networks
Sékou-Oumar Kaba, Siamak Ravanbakhsh
Inter Part Equivariance Equivariant Neural Network Cyclic Symmetry Symmetry Breaking Equivariant Function Soft Equivariance

December 4, 2023

September 24, 2023

Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups
Kathlén Kohn, Anna-Laura Sattelberger, Vahid Shahverdi
Geometric Analysis Inter Part Equivariance Equivariant Network Alpha Invariance Linear Neural Network Invariant Network Algebraic Variety Equivariant Function Invariant Function

July 15, 2023

Graph Automorphism Group Equivariant Neural Networks
Edward Pearce-Crump, William J. Knottenbelt
Approximate Symmetry Equivariant Neural Network Equivariant Graph Neural Network Equivariant Function

June 5, 2023

Learning Probabilistic Symmetrization for Architecture Agnostic Equivariance
Jinwoo Kim, Tien Dat Nguyen, Ayhan Suleymanzade, Hyeokjun An, Seunghoon Hong
Inter Part Equivariance Equivariant Network Equivariant Architecture Equivariant Function Learning Probabilistic Symmetrization Agnostic Equivariance

November 25, 2022

On the Universal Approximation Property of Deep Fully Convolutional Neural Networks
Ting Lin, Zuowei Shen, Qianxiao Li
Convolutional Neural Network Universal Approximation Free Counterpart Equivariant Function

October 17, 2022

A tradeoff between universality of equivariant models and learnability of symmetries
Vasco Portilheiro
Approximate Symmetry Equivariant Network K$ Universality Equivariant Model Group Convolution Equivariant Function Group Convolutional Neural Network

September 29, 2022

Machine learning and invariant theory
Ben Blum-Smith, Soledad Villar
Machine Learning Invariant Representation Dynamical Invariant Equivariant Map Equivariant Machine Learning Equivariant Function

March 2, 2022

A Simple and Universal Rotation Equivariant Point-cloud Network
Ben Finkelshtein, Chaim Baskin, Haggai Maron, Nadav Dym
Inter Part Equivariance Alpha Invariance Equivariant Neural Network Equivariant Function 3D Learning Equivariant Point

December 7, 2021

Permutation Equivariant Generative Adversarial Networks for Graphs
Yoann Boget, Magda Gregorova, Alexandros Kalousis
Graph Drawing GAN Model Generative Modeling Equivariant Generative Equivariant Function Permutation Equivariant Neural

November 23, 2021

Multiset-Equivariant Set Prediction with Approximate Implicit Differentiation
Yan Zhang, David W. Zhang, Simon Lacoste-Julien, Gertjan J. Burghouts, Cees G. M. Snoek
Implicit Differentiation Equivariant Generative Equivariant Function Set Prediction Network Equivariant Operation Agnostic Equivariance