Symmetric Function

Symmetric functions, which remain unchanged under permutations of their input variables, are a central topic in mathematics and computer science, with research focusing on their efficient representation and approximation. Current efforts concentrate on developing neural network architectures, such as Deep Sets and Relational Networks, designed to handle the inherent symmetries, often employing techniques like invariant embeddings and dynamical systems to guarantee approximation capabilities. These advancements have significant implications for machine learning applications involving complex data structures like point sets and graphs, enabling the development of models that are robust to input ordering and efficient in handling large datasets.

Papers

October 24, 2024

Reinforcement Learning the Chromatic Symmetric Function
Gergely Bérczi, Jonas Klüver
Reinforcement Learning Automatic Counting Class Disjoint Data Symmetric Function

March 2, 2024

Uniform $\mathcal{C}^k$ Approximation of $G$-Invariant and Antisymmetric Functions, Embedding Dimensions, and Polynomial Representations
Soumya Ganguly, Khoa Tran, Rahul Sarkar
Box Dimension Symmetric Function Antisymmetric Function

November 20, 2023

A New Angle: On Evolving Rotation Symmetric Boolean Functions
Claude Carlet, Marko Ðurasevic, Bruno Gašperov, Domagoj Jakobovic, Luca Mariot, Stjepan Picek
Evolutionary Computation New Perspective Boolean Function Symmetric Function

September 4, 2023

On CNF formulas irredundant with respect to unit clause propagation
Petr Savický
Clause Elimination Symmetric 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

May 9, 2023

On the Information Capacity of Nearest Neighbor Representations
Kordag Mehmet Kilic, Jin Sima, Jehoshua Bruck
Computation Method Associative Memory Computational Power Associative Memory Model Neural Network Complexity Symmetric 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

June 2, 2022

Exponential Separations in Symmetric Neural Networks
Aaron Zweig, Joan Bruna
Neural Architecture Optimal Separation Symmetric Neural Network Representation Gap Symmetric Function