Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, training deep learning models robust to adversarial attacks is still an open problem. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparameterized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in this limit BNN posteriors are robust to gradient-based adversarial attacks. Crucially, we prove that the expected gradient of the loss with respect to the BNN posterior distribution is vanishing, even when each neural network sampled from the posterior is vulnerable to gradient-based attacks. Experimental results on the MNIST, Fashion MNIST, and half moons datasets, representing the finite data regime, with BNNs trained with Hamiltonian Monte Carlo and Variational Inference, support this line of arguments, showing that BNNs can display both high accuracy on clean data and robustness to both gradient-based and gradient-free based adversarial attacks.

Inverse UQ is the process to inversely quantify the model input uncertainties based on experimental data. This work focuses on developing an inverse UQ process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the inverse UQ of TRACE physical model parameters using the FEBA transient experimental data. The measurement data is time-dependent peak cladding temperature (PCT). Since the quantity-of-interest (QoI) is time-dependent that corresponds to infinite-dimensional responses, PCA is used to reduce the QoI dimension while preserving the transient profile of the PCT, in order to make the inverse UQ process more efficient. However, conventional PCA applied directly to the PCT time series profiles can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information of the transient PCT profiles before dimensionality reduction. DNNs are then trained using PC scores from functional PCA to build surrogate models of TRACE in order to reduce the computational cost in Markov Chain Monte Carlo sampling. Bayesian neural networks are used to estimate the uncertainties of DNN surrogate model predictions. In this study, we compared four different inverse UQ processes with different dimensionality reduction methods and surrogate models. The proposed approach shows an improvement in reducing the dimension of the TRACE transient simulations, and the forward propagation of inverse UQ results has a better agreement with the experimental data.

The linearized-Laplace approximation (LLA) has been shown to be effective and efficient in constructing Bayesian neural networks. It is theoretically compelling since it can be seen as a Gaussian process posterior with the mean function given by the neural network's maximum-a-posteriori predictive function and the covariance function induced by the empirical neural tangent kernel. However, while its efficacy has been studied in large-scale tasks like image classification, it has not been studied in sequential decision-making problems like Bayesian optimization where Gaussian processes -- with simple mean functions and kernels such as the radial basis function -- are the de-facto surrogate models. In this work, we study the usefulness of the LLA in Bayesian optimization and highlight its strong performance and flexibility. However, we also present some pitfalls that might arise and a potential problem with the LLA when the search space is unbounded.

Deep Boltzmann machines (DBMs), one of the first ``deep'' learning methods ever studied, are multi-layered probabilistic models governed by a pairwise energy function that describes the likelihood of all variables/nodes in the network. In practice, DBMs are often constrained, i.e., via the \emph{restricted} Boltzmann machine (RBM) architecture (which does not permit intra-layer connections), in order to allow for more efficient inference. In this work, we revisit the generic DBM approach, and ask the question: are there other possible restrictions to their design that would enable efficient (approximate) inference? In particular, we develop a new class of restricted model, the monotone DBM, which allows for arbitrary self-connection in each layer, but restricts the \emph{weights} in a manner that guarantees the existence and global uniqueness of a mean-field fixed point. To do this, we leverage tools from the recently-proposed monotone Deep Equilibrium model and show that a particular choice of activation results in a fixed-point iteration that gives a variational mean-field solution. While this approach is still largely conceptual, it is the first architecture that allows for efficient approximate inference in fully-general weight structures for DBMs. We apply this approach to simple deep convolutional Boltzmann architectures and demonstrate that it allows for tasks such as the joint completion and classification of images, within a single deep probabilistic setting, while avoiding the pitfalls of mean-field inference in traditional RBMs.

In reinforcement learning, the objective is almost always defined as a \emph{cumulative} function over the rewards along the process. However, there are many optimal control and reinforcement learning problems in various application fields, especially in communications and networking, where the objectives are not naturally expressed as summations of the rewards. In this paper, we recognize the prevalence of non-cumulative objectives in various problems, and propose a modification to existing algorithms for optimizing such objectives. Specifically, we dive into the fundamental building block for many optimal control and reinforcement learning algorithms: the Bellman optimality equation. To optimize a non-cumulative objective, we replace the original summation operation in the Bellman update rule with a generalized operation corresponding to the objective. Furthermore, we provide sufficient conditions on the form of the generalized operation as well as assumptions on the Markov decision process under which the globally optimal convergence of the generalized Bellman updates can be guaranteed. We demonstrate the idea experimentally with the bottleneck objective, i.e., the objectives determined by the minimum reward along the process, on classical optimal control and reinforcement learning tasks, as well as on two network routing problems on maximizing the flow rates.

In today's vast literature landscape, a manual review is very time-consuming. To address this challenge, this paper proposes a semi-automated tool for solution method review and selection. It caters to researchers, practitioners, and decision-makers while serving as a benchmark for future work. The tool comprises three modules: (1) paper selection and scoring, using a keyword selection scheme to query Scopus API and compute relevancy; (2) solution method extraction in papers utilizing OpenAI API; (3) sensitivity analysis and post-analyzes. It reveals trends, relevant papers, and methods. AI in the oncology case study and several use cases are presented with promising results, comparing the tool to manual ground truth.

Probabilistic hyperproperties specify quantitative relations between the probabilities of reaching different target sets of states from different initial sets of states. This class of behavioral properties is suitable for capturing important security, privacy, and system-level requirements. We propose a new approach to solve the controller synthesis problem for Markov decision processes (MDPs) and probabilistic hyperproperties. Our specification language builds on top of the logic HyperPCTL and enhances it with structural constraints over the synthesized controllers. Our approach starts from a family of controllers represented symbolically and defined over the same copy of an MDP. We then introduce an abstraction refinement strategy that can relate multiple computation trees and that we employ to prune the search space deductively. The experimental evaluation demonstrates that the proposed approach considerably outperforms HyperProb, a state-of-the-art SMT-based model checking tool for HyperPCTL. Moreover, our approach is the first one that is able to effectively combine probabilistic hyperproperties with additional intra-controller constraints (e.g.

Variational Bayes is a popular method for approximate inference but its derivation can be cumbersome. To simplify the process, we give a 3-step recipe to identify the posterior form by explicitly looking for linearity with respect to expectations of well-known distributions. We can then directly write the update by simply ``reading-off'' the terms in front of those expectations. The recipe makes the derivation easier, faster, shorter, and more general.

We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i.e. Ising models that may only be observed at their leaf nodes. On the learning side, we obtain efficient algorithms for learning a tree-structured Ising model whose leaf node distribution is close in Total Variation Distance, improving on the results of prior work. On the testing side, we provide an efficient algorithm with fewer samples for testing whether two latent-tree Ising models have leaf-node distributions that are close or far in Total Variation distance. We obtain our algorithms by showing novel localization results for the total variation distance between the leaf-node distributions of tree-structured Ising models, in terms of their marginals on pairs of leaves.

Robotic peg-in-hole assembly represents a critical area of investigation in robotic automation. The fusion of reinforcement learning (RL) and deep neural networks (DNNs) has yielded remarkable breakthroughs in this field. However, existing RL-based methods grapple with delivering optimal performance under the unique environmental and mission constraints of fusion applications. As a result, we propose an inventively designed RL-based approach. In contrast to alternative methods, our focus centers on enhancing the DNN architecture rather than the RL model. Our strategy receives and integrates data from the RGB camera and force/torque (F/T) sensor, training the agent to execute the peg-in-hole assembly task in a manner akin to human hand-eye coordination. All training and experimentation unfold within a realistic environment, and empirical outcomes demonstrate that this multi-sensor fusion approach excels in rigid peg-in-hole assembly tasks, surpassing the repeatable accuracy of the robotic arm utilized--0.1 mm--in uncertain and unstable conditions.