Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory

This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous convergence guarantees of FA-HMC on non-iid distributed data sets, under the strong convexity and Hessian smoothness assumptions. Our analysis investigates the effects of parameter space dimension, noise on gradients and momentum, and the frequency of communication (between the central node and local nodes) on the convergence and communication costs of FA-HMC. Beyond that, we establish the tightness of our analysis by showing that the convergence rate cannot be improved even for continuous FA-HMC process. Moreover, extensive empirical studies demonstrate that FA-HMC outperforms the existing Federated Averaging-Langevin Monte Carlo (FA-LD) algorithm.

Large Language Model Sentinel: Advancing Adversarial Robustness by LLM Agent

Over the past two years, the use of large language models (LLMs) has advanced rapidly. While these LLMs offer considerable convenience, they also raise security concerns, as LLMs are vulnerable to adversarial attacks by some well-designed textual perturbations. In this paper, we introduce a novel defense technique named Large LAnguage MOdel Sentinel (LLAMOS), which is designed to enhance the adversarial robustness of LLMs by purifying the adversarial textual examples before feeding them into the target LLM. Our method comprises two main components: a) Agent instruction, which can simulate a new agent for adversarial defense, altering minimal characters to maintain the original meaning of the sentence while defending against attacks; b) Defense guidance, which provides strategies for modifying clean or adversarial examples to ensure effective defense and accurate outputs from the target LLMs. Remarkably, the defense agent demonstrates robust defensive capabilities even without learning from adversarial examples. Additionally, we conduct an intriguing adversarial experiment where we develop two agents, one for defense and one for defense, and engage them in mutual confrontation. During the adversarial interactions, neither agent completely beat the other. Extensive experiments on both open-source and closed-source LLMs demonstrate that our method effectively defends against adversarial attacks, thereby enhancing adversarial robustness.

Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a \emph{quadratic} behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency.

Robust Diffusion Models for Adversarial Purification

Diffusion models (DMs) based adversarial purification (AP) has shown to be the most powerful alternative to adversarial training (AT). However, these methods neglect the fact that pre-trained diffusion models themselves are not robust to adversarial attacks as well. Additionally, the diffusion process can easily destroy semantic information and generate a high quality image but totally different from the original input image after the reverse process, leading to degraded standard accuracy. To overcome these issues, a natural idea is to harness adversarial training strategy to retrain or fine-tune the pre-trained diffusion model, which is computationally prohibitive. We propose a novel robust reverse process with adversarial guidance, which is independent of given pre-trained DMs and avoids retraining or fine-tuning the DMs. This robust guidance can not only ensure to generate purified examples retaining more semantic content but also mitigate the accuracy-robustness trade-off of DMs for the first time, which also provides DM-based AP an efficient adaptive ability to new attacks. Extensive experiments are conducted to demonstrate that our method achieves the state-of-the-art results and exhibits generalization against different attacks.

Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks

In this paper, we adopt conformal prediction, a distribution-free uncertainty quantification (UQ) framework, to obtain confidence prediction intervals with coverage guarantees for Deep Operator Network (DeepONet) regression. Initially, we enhance the uncertainty quantification frameworks (B-DeepONet and Prob-DeepONet) previously proposed by the authors by using split conformal prediction. By combining conformal prediction with our Prob- and B-DeepONets, we effectively quantify uncertainty by generating rigorous confidence intervals for DeepONet prediction. Additionally, we design a novel Quantile-DeepONet that allows for a more natural use of split conformal prediction. We refer to this distribution-free effective uncertainty quantification framework as split conformal Quantile-DeepONet regression. Finally, we demonstrate the effectiveness of the proposed methods using various ordinary, partial differential equation numerical examples, and multi-fidelity learning.

Adversarial Training on Purification (AToP): Advancing Both Robustness and Generalization

The deep neural networks are known to be vulnerable to well-designed adversarial attacks. The most successful defense technique based on adversarial training (AT) can achieve optimal robustness against particular attacks but cannot generalize well to unseen attacks. Another effective defense technique based on adversarial purification (AP) can enhance generalization but cannot achieve optimal robustness. Meanwhile, both methods share one common limitation on the degraded standard accuracy. To mitigate these issues, we propose a novel framework called Adversarial Training on Purification (AToP), which comprises two components: perturbation destruction by random transforms (RT) and purifier model fine-tuned (FT) by adversarial loss. RT is essential to avoid overlearning to known attacks resulting in the robustness generalization to unseen attacks and FT is essential for the improvement of robustness. To evaluate our method in an efficient and scalable way, we conduct extensive experiments on CIFAR-10, CIFAR-100, and ImageNette to demonstrate that our method achieves state-of-the-art results and exhibits generalization ability against unseen attacks.

Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo

Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when demanding high accuracy. To address this, we propose an approximate Thompson sampling strategy, utilizing underdamped Langevin Monte Carlo, where the latter is the go-to workhorse for simulations of high-dimensional posteriors. Based on the standard smoothness and log-concavity conditions, we study the accelerated posterior concentration and sampling using a specific potential function. This design improves the sample complexity for realizing logarithmic regrets from $\mathcal{\tilde O}(d)$ to $\mathcal{\tilde O}(\sqrt{d})$. The scalability and robustness of our algorithm are also empirically validated through synthetic experiments in high-dimensional bandit problems.

Unbiasing Enhanced Sampling on a High-dimensional Free Energy Surface with Deep Generative Model

Biased enhanced sampling methods utilizing collective variables (CVs) are powerful tools for sampling conformational ensembles. Due to high intrinsic dimensions, efficiently generating conformational ensembles for complex systems requires enhanced sampling on high-dimensional free energy surfaces. While methods like temperature-accelerated molecular dynamics (TAMD) can adopt many CVs in a simulation, unbiasing the simulation requires accurate modeling of a high-dimensional CV probability distribution, which is challenging for traditional density estimation techniques. Here we propose an unbiasing method based on the score-based diffusion model, a deep generative learning method that excels in density estimation across complex data landscapes. We test the score-based diffusion unbiasing method on TAMD simulations. The results demonstrate that this unbiasing approach significantly outperforms traditional unbiasing methods, and can generate accurate unbiased conformational ensembles for simulations with a number of CVs higher than usual ranges.

B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functions

Deep Operator Network (DeepONet) is a neural network framework for learning nonlinear operators such as those from ordinary differential equations (ODEs) describing complex systems. Multiple-input deep neural operators (MIONet) extended DeepONet to allow multiple input functions in different Banach spaces. MIONet offers flexibility in training dataset grid spacing, without constraints on output location. However, it requires offline inputs and cannot handle varying sequence lengths in testing datasets, limiting its real-time application in dynamic complex systems. This work redesigns MIONet, integrating Long Short Term Memory (LSTM) to learn neural operators from time-dependent data. This approach overcomes data discretization constraints and harnesses LSTM's capability with variable-length, real-time data. Factors affecting learning performance, like algorithm extrapolation ability are presented. The framework is enhanced with uncertainty quantification through a novel Bayesian method, sampling from MIONet parameter distributions. Consequently, we develop the B-LSTM-MIONet, incorporating LSTM's temporal strengths with Bayesian robustness, resulting in a more precise and reliable model for noisy datasets.

Fair Supervised Learning with A Simple Random Sampler of Sensitive Attributes

As the data-driven decision process becomes dominating for industrial applications, fairness-aware machine learning arouses great attention in various areas. This work proposes fairness penalties learned by neural networks with a simple random sampler of sensitive attributes for non-discriminatory supervised learning. In contrast to many existing works that critically rely on the discreteness of sensitive attributes and response variables, the proposed penalty is able to handle versatile formats of the sensitive attributes, so it is more extensively applicable in practice than many existing algorithms. This penalty enables us to build a computationally efficient group-level in-processing fairness-aware training framework. Empirical evidence shows that our framework enjoys better utility and fairness measures on popular benchmark data sets than competing methods. We also theoretically characterize estimation errors and loss of utility of the proposed neural-penalized risk minimization problem.