Ridge Function

Ridge functions, simple functions that depend on a linear combination of input variables, are fundamental building blocks for understanding and improving complex machine learning models. Current research focuses on leveraging ridge functions to analyze and enhance the explainability and performance of neural networks, including convolutional and quantum architectures, by representing them as combinations of these simpler functions. This approach offers insights into the approximation capabilities of these models, leading to improved design and optimization strategies for various applications, such as image processing and inverse problems in medical imaging. The resulting advancements contribute to both theoretical understanding of neural network behavior and practical improvements in model accuracy and interpretability.

Papers

November 6, 2024

A Fundamental Accuracy--Robustness Trade-off in Regression and Classification
Sohail Bahmani
Classification Code Adversarial Robustness Novel Regression Adversarial Risk Accuracy Robustness Ridge Function

July 21, 2023

Mercer Large-Scale Kernel Machines from Ridge Function Perspective
Karol Dziedziul, Sergey Kryzhevich
Small Kernel Approximation Theory Large Scale Kernel Ridge Function

January 12, 2023

On the explainability of quantum neural networks based on variational quantum circuits
Ammar Daskin
Neural Network High Explainability Quantum Physic Variational Quantum Circuit Ridge Function

November 22, 2022

A Neural-Network-Based Convex Regularizer for Inverse Problems
Alexis Goujon, Sebastian Neumayer, Pakshal Bohra, Stanislas Ducotterd, Michael Unser
Inverse Problem Denoising Process Deep Learning Based Convex Regularization Ridge Function

February 24, 2022

Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functions
Zhiying Fang, Guang Cheng
Convolutional Neural Network Deep Convolutional Neural Network Dimensional Input Optimal Convergence Rate Convolutional Structure Ridge Function

Ridge Function

Papers

A Fundamental Accuracy--Robustness Trade-off in Regression and Classification

Mercer Large-Scale Kernel Machines from Ridge Function Perspective

On the explainability of quantum neural networks based on variational quantum circuits

A Neural-Network-Based Convex Regularizer for Inverse Problems

Optimal Convergence Rates of Deep Convolutional Neural Networks: Additive Ridge Functions