Local Lipschitz

Local Lipschitz continuity, a measure of a function's smoothness around a specific point, is increasingly important in analyzing the robustness and reliability of machine learning models, particularly deep neural networks (DNNs). Current research focuses on efficiently computing local Lipschitz constants for various architectures, including ReLU-based feedforward networks and convolutional networks like UNETs, often leveraging techniques from semidefinite programming and model reduction. This research is driven by the strong correlation found between local Lipschitz constants and model performance metrics like mean absolute error and adversarial robustness, impacting areas such as medical image reconstruction and improving the trustworthiness of AI systems. The ability to quantify and control local Lipschitzness offers a powerful tool for enhancing model reliability and generalization.

Papers

October 17, 2023

Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification
Yoshio Ebihara, Xin Dai, Victor Magron, Dimitri Peaucelle, Sophie Tarbouriech
Neural Network Semidefinite Programming Upper Bound Lipschitz Constant Local Lipschitz

May 12, 2023

Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitz
Danyal F. Bhutto, Bo Zhu, Jeremiah Z. Liu, Neha Koonjoo, Hongwei B. Li, Bruce R. Rosen, Matthew S. Rosen
Distribution Detection Uncertainty Estimation Magnetic Resonance Imaging Image Reconstruction Magnetic Resonance Imaging Denoising Learning Based Image Reconstruction Local Lipschitz

June 2, 2022

Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient
Zhaosong Lu, Sanyou Mei
Convex Optimization Non Convex First Order Method Continuous Gradient Constrained Convex Optimization Local Lipschitz

June 1, 2022

The robust way to stack and bag: the local Lipschitz way
Thulasi Tholeti, Sheetal Kalyani
Adversarial Robustness Ensemble Learning Bag Prototype Lipschitz Constant Robust Method Ensemble Architecture Local Lipschitz

February 26, 2022

Adversarial robustness of sparse local Lipschitz predictors
Ramchandran Muthukumar, Jeremias Sulam
Native Robustness Adversarial Robustness Robust Generalization Local Lipschitz

Local Lipschitz

Papers

Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification

Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitz

Accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient

The robust way to stack and bag: the local Lipschitz way

Adversarial robustness of sparse local Lipschitz predictors