Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks

Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent studies have demonstrated that neural Ordinary Differential Equations (ODEs) are intrinsically more robust against adversarial attacks compared to vanilla DNNs. In this work, we propose a stable neural ODE with Lyapunov-stable equilibrium points for defending against adversarial attacks (SODEF). By ensuring that the equilibrium points of the ODE solution used as part of SODEF is Lyapunov-stable, the ODE solution for an input with a small perturbation converges to the same solution as the unperturbed input. We provide theoretical results that give insights into the stability of SODEF as well as the choice of regularizers to ensure its stability. Our analysis suggests that our proposed regularizers force the extracted feature points to be within a neighborhood of the Lyapunov-stable equilibrium points of the ODE. SODEF is compatible with many defense methods and can be applied to any neural network's final regressor layer to enhance its stability against adversarial attacks.

A Hybrid Bandit Framework for Diversified Recommendation

The interactive recommender systems involve users in the recommendation procedure by receiving timely user feedback to update the recommendation policy. Therefore, they are widely used in real application scenarios. Previous interactive recommendation methods primarily focus on learning users' personalized preferences on the relevance properties of an item set. However, the investigation of users' personalized preferences on the diversity properties of an item set is usually ignored. To overcome this problem, we propose the Linear Modular Dispersion Bandit (LMDB) framework, which is an online learning setting for optimizing a combination of modular functions and dispersion functions. Specifically, LMDB employs modular functions to model the relevance properties of each item, and dispersion functions to describe the diversity properties of an item set. Moreover, we also develop a learning algorithm, called Linear Modular Dispersion Hybrid (LMDH) to solve the LMDB problem and derive a gap-free bound on its n-step regret. Extensive experiments on real datasets are performed to demonstrate the effectiveness of the proposed LMDB framework in balancing the recommendation accuracy and diversity.