Canonical Lipschitz Mechanism

The canonical Lipschitz mechanism is a method for ensuring differential privacy in data analysis, particularly for tasks like top-k selection, by adding noise calibrated to the Lipschitz continuity of a loss function. Current research focuses on improving the efficiency and utility of this mechanism, often employing neural network architectures like mixtures of experts to manage complexity in high-dimensional spaces. This work is significant because it offers a principled approach to balancing privacy preservation with the accuracy of data-driven insights, impacting fields ranging from machine learning to data security. The Lipschitz property itself is also being investigated in broader contexts, such as its relationship to the generalization performance of neural networks and the robustness of dynamical system models.

Papers

July 1, 2024

Metric-Entropy Limits on Nonlinear Dynamical System Learning
Yang Pan, Clemens Hutter, Helmut Bölcskei
Recurrent Neural Network Dynamical System Continuum Limit Canonical Lipschitz Mechanism Metric Entropy

April 13, 2024

Mixture of Experts Soften the Curse of Dimensionality in Operator Learning
Anastasis Kratsios, Takashi Furuya, Jose Antonio Lara Benitez, Matti Lassas, Maarten de Hoop
Mixture Component Neural Operator Operator Learning Data Dimensionality Universal Approximation Reversal Curse Non Linear Operator Canonical Lipschitz Mechanism

September 24, 2023

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense
Julia Ackermann, Arnulf Jentzen, Thomas Kruse, Benno Kuckuck, Joshua Lee Padgett
Deep Neural Network High Dimensional Partial Differential Equation \Ell_p$ Norm Leaky ReLU Kolmogorov Flow Canonical Lipschitz Mechanism

August 17, 2023

General Lipschitz: Certified Robustness Against Resolvable Semantic Transformations via Transformation-Dependent Randomized Smoothing
Dmitrii Korzh, Mikhail Pautov, Olga Tsymboi, Ivan Oseledets
Native Robustness Randomized Smoothing Left Corner Transformation Preserving Transformation Robustness Certificate Canonical Lipschitz Mechanism Lipschitz Continuity

March 29, 2023

Lipschitzness Effect of a Loss Function on Generalization Performance of Deep Neural Networks Trained by Adam and AdamW Optimizers
Mohammad Lashkari, Amin Gheibi
Deep Neural Network Strong Generalization Loss Function Generalization Performance Generalization Error Lipschitz Constant Canonical Lipschitz Mechanism

February 21, 2023

Some Fundamental Aspects about Lipschitz Continuity of Neural Networks
Grigory Khromov, Sidak Pal Singh
Neural Network Native Robustness Adversarial Vulnerability Basic Concept Tighter Bound Canonical Lipschitz Mechanism Lipschitz Continuity

September 26, 2022

Convergence rate of the (1+1)-evolution strategy on locally strongly convex functions with lipschitz continuous gradient and their monotonic transformations
Daiki Morinaga, Kazuto Fukuchi, Jun Sakuma, Youhei Akimoto
Convergence Rate Convex Function Evolution Strategy Derivative Free Optimization Continuous Gradient Numerical Black Box Optimization Canonical Lipschitz Mechanism

February 16, 2022

Single Trajectory Nonparametric Learning of Nonlinear Dynamics
Ingvar Ziemann, Henrik Sandberg, Nikolai Matni
Dynamical System Nonlinear Dynamic Trajectory Regularization Canonical Lipschitz Mechanism Metric Entropy

January 31, 2022

Differentially Private Top-k Selection via Canonical Lipschitz Mechanism
Michael Shekelyan, Grigorios Loukides
Differential Privacy Exponential Mechanism Canonical Lipschitz Mechanism Private Selection

December 15, 2021

LTB curves with Lipschitz turn are par-regular
Etienne Le Quentrec, Loïc Mazo, Étienne Baudrier, Mohamed Tajine
Aggregated Curve Planar Curve Canonical Lipschitz Mechanism Geometric Regularity