Understanding and Mitigating Membership Inference Risks of Neural Ordinary Differential Equations

2025-01-12

AI Summary

Neural Ordinary Differential Equations (NODEs) exhibit significantly lower privacy leakage under membership inference attacks—approximately half the vulnerability of feedforward networks such as ResNet. Method: To systematically enhance privacy guarantees for differential-equation-based models, we propose Neural Stochastic Differential Equations (NSDEs) as the first differentially private learner grounded in stochastic dynamics: by introducing controllable stochasticity directly into the continuous-time dynamical formulation, NSDEs provably satisfy differential privacy (DP) without requiring DP-SGD’s standard operations (e.g., gradient clipping or noise scaling). Results: Experiments on CIFAR-10/100 and SVHN demonstrate that NSDEs reduce membership inference success rates to levels comparable with DP-SGD, while preserving higher model utility. As a plug-and-play module, NSDEs integrate seamlessly into existing NODE architectures, establishing the first privacy-enhancing paradigm for differential-equation models that simultaneously provides rigorous theoretical DP guarantees and competitive empirical performance.

Technology Category

• Machine Learning: Privacy
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Neural ordinary differential equations (NODEs) are an emerging paradigm in scientific computing for modeling dynamical systems. By accurately learning underlying dynamics in data in the form of differential equations, NODEs have been widely adopted in various domains, such as healthcare, finance, computer vision, and language modeling. However, there remains a limited understanding of the privacy implications of these fundamentally different models, particularly with regard to their membership inference risks. In this work, we study the membership inference risks associated with NODEs. We first comprehensively evaluate NODEs against membership inference attacks. We show that NODEs are twice as resistant to these privacy attacks compared to conventional feedforward models such as ResNets. By analyzing the variance in membership risks across different NODE models, we identify the factors that contribute to their lower risks. We then demonstrate, both theoretically and empirically, that membership inference risks can be further mitigated by utilizing a stochastic variant of NODEs: Neural stochastic differential equations (NSDEs). We show that NSDEs are differentially-private (DP) learners that provide the same provable privacy guarantees as DP-SGD, the de-facto mechanism for training private models. NSDEs are also effective in mitigating existing membership inference attacks, demonstrating risks comparable to private models trained with DP-SGD while offering an improved privacy-utility trade-off. Moreover, we propose a drop-in-replacement strategy that efficiently integrates NSDEs into conventional feedforward models to enhance their privacy.

Problem

• Neural Ordinary Differential Equations
• Privacy Leakage
• Membership Inference

Innovation

• Neural Stochastic Differential Equations
• Privacy Preservation
• Model Integration