Invariant Function

Invariant functions, which produce the same output regardless of certain transformations applied to their input (e.g., permutations of data points or rotations of images), are a central focus in machine learning research. Current efforts concentrate on developing efficient neural network architectures, including DeepSets and equivariant ensembles, to learn these functions, often focusing on proving universal approximation capabilities and minimizing computational complexity. This research is crucial for handling structured data like graphs and point clouds, improving the efficiency and robustness of algorithms in various applications, such as molecule property prediction and path planning. The development of theoretically grounded methods for constructing and approximating invariant functions is driving progress in numerous scientific fields.

Papers

September 21, 2024

On Lexical Invariance on Multisets and Graphs
Muhan Zhang
Graph Drawing Word Representation Language Space Lexical Matching Invariant Function

August 26, 2024

Symmetry & Critical Points
Yossi Arjevani
Cyclic Symmetry Symmetry Breaking Nonconvex Function Invariant Function Critical Point

May 13, 2024

Learning functions on symmetric matrices and point clouds via lightweight invariant features
Ben Blum-Smith, Ningyuan Huang, Marco Cuturi, Soledad Villar
Machine Learning Point Cloud Molecular Property Invariant Feature Learned Function Symmetric Positive Definite Matrix Invariant Function

March 19, 2024

Equivariant Ensembles and Regularization for Reinforcement Learning in Map-based Path Planning
Mirco Theile, Hongpeng Cao, Marco Caccamo, Alberto L. Sangiovanni-Vincentelli
Reinforcement Learning Path Planning Equivariant Machine Learning Invariant Function Passive Symmetry Equivariant Policy

March 4, 2024

Permutation invariant functions: statistical tests, density estimation, and computationally efficient embedding
Wee Chaimanowong, Ying Zhu
Density Estimation Reproducing Kernel Hilbert Space Machine Permutation Permutation Invariance Statistical Test Invariant Function Invariant Distribution

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

September 11, 2023

Neural Discovery of Permutation Subgroups
Pavan Karjol, Rohan Kashyap, Prathosh A P
Automatic Discovery Subgroup Description Invariant Function

August 1, 2023

Neural approximation of Wasserstein distance via a universal architecture for symmetric and factorwise group invariant functions
Samantha Chen, Yusu Wang
Wasserstein Distance Distance Function Neural Network Approximation Invariant Function Group Wise Symmetric Function

July 17, 2023

Results on Counterfactual Invariance
Jake Fawkes, Robin J. Evans
Key Result Conditional Independence Invariant Function Graphical Representation Counterfactual Simulatability

October 27, 2022

On the Approximation and Complexity of Deep Neural Networks to Invariant Functions
Gao Zhang, Jin-Hui Wu, Shao-Qun Zhang
Convolutional Neural Network Deep Neural Network Complexity Matter Average Approximation Neural Network Model Complex Valued Neural Network Invariant Function

August 18, 2022

Deep Neural Network Approximation of Invariant Functions through Dynamical Systems
Qianxiao Li, Ting Lin, Zuowei Shen
Dynamical System Universal Approximation Deep Neural Network Approximation Roto Translation Invariant Function Symmetric Function

Invariant Function

Papers

On Lexical Invariance on Multisets and Graphs

Symmetry & Critical Points

Learning functions on symmetric matrices and point clouds via lightweight invariant features

Equivariant Ensembles and Regularization for Reinforcement Learning in Map-based Path Planning

Permutation invariant functions: statistical tests, density estimation, and computationally efficient embedding

Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups

Neural Discovery of Permutation Subgroups

Neural approximation of Wasserstein distance via a universal architecture for symmetric and factorwise group invariant functions

Results on Counterfactual Invariance

On the Approximation and Complexity of Deep Neural Networks to Invariant Functions

Deep Neural Network Approximation of Invariant Functions through Dynamical Systems