We study the sensitivity of a MAP configuration of a discrete probabilistic graphical model with respect to perturbations of its parameters. These perturbations are global, in the sense that simultaneous perturbations of all the parameters (or any chosen subset of them) are allowed. Our main contribution is an exact algorithm that can check whether the MAP configuration is robust with respect to given perturbations. Its complexity is essentially the same as that of obtaining the MAP configuration itself, so it can be promptly used with minimal effort. We use our algorithm to identify the largest global perturbation that does not induce a change in the MAP configuration, and we successfully apply this robustness measure in two practical scenarios: the prediction of facial action units with posed images and the classification of multiple real public data sets. A strong correlation between the proposed robustness measure and accuracy is verified in both scenarios.

Bayesian optimization based on Gaussian process upper confidence bound (GP-UCB) has a theoretical guarantee for optimizing black-box functions. Black-box functions often have input uncertainty, but even in this case, GP-UCB can be extended to optimize evaluation measures called robustness measures. However, GP-UCB-based methods for robustness measures include a trade-off parameter $\beta$, which must be excessively large to achieve theoretical validity, just like the original GP-UCB. In this study, we propose a new method called randomized robustness measure GP-UCB (RRGP-UCB), which samples the trade-off parameter $\beta$ from a probability distribution based on a chi-squared distribution and avoids explicitly specifying $\beta$. The expected value of $\beta$ is not excessively large. Furthermore, we show that RRGP-UCB provides tight bounds on the expected value of regret based on the optimal solution and estimated solutions. Finally, we demonstrate the usefulness of the proposed method through numerical experiments.

Determining the robustness of deep learning models is an established and ongoing challenge within automated decision-making systems. With the advent and success of techniques that enable advanced deep learning (DL), these models are being used in widespread applications, including high-stake ones like healthcare, education, border-control. Therefore, it is critical to understand the limitations of these models and predict their regions of failures, in order to create the necessary guardrails for their successful and safe deployment. In this work, we revisit robustness, specifically investigating the sufficiency of robust accuracy (RA), within the context of deepfake detection. We present robust ratio (RR) as a complementary metric, that can quantify the changes to the normalized or probability outcomes under input perturbation. We present a comparison of RA and RR and demonstrate that despite similar RA between models, the models show varying RR under different tolerance (perturbation) levels.

Abstract-- This letter aims to generate a continuous-time trajectory consisting of piecewise Bézier curves that satisfy signal temporal logic (STL) specifications with piecewise time-varying robustness. Our time-varying robustness is less conservative than the real-valued robustness, which enables more effective tracking in practical applications. Specifically, our continuoustime trajectories account for dynamic feasibility, leading to smaller tracking errors and ensuring that the STL specifications can be met by the tracking trajectory. Comparative experiments demonstrate the efficiency and effectiveness of the proposed approach. Figure 1: A simple reach-avoid task: (a) presents a reference I. INTRODUCTION To meet (c) illustrates that the Bézier curves (blue solid line) violate these expectations, signal temporal logic (STL) offers a the specifications due to incorrectly chosen control points.

Linear Temporal Logic (LTL) offers a precise means for constraining the behavior of reinforcement learning agents. However, in many tasks, LTL is insufficient for task specification; LTL-constrained policy optimization, where the goal is to optimize a scalar reward under LTL constraints, is needed. Prior methods for this constrained problem are restricted to finite state spaces. In this work, we present Cycle Experience Replay (CyclER), a reward-shaping approach to this problem that allows continuous state and action spaces and the use of function approximations. CyclER guides a policy towards satisfaction by encouraging partial behaviors compliant with the LTL constraint, using the structure of the constraint. In doing so, it addresses the optimization challenges stemming from the sparse nature of LTL satisfaction. We evaluate CyclER in three continuous control domains. On these tasks, CyclER outperforms existing reward-shaping methods at finding performant and LTL-satisfying policies.

A robotic behavior model that can reliably generate behaviors from natural language inputs in real time would substantially expedite the adoption of industrial robots due to enhanced system flexibility. To facilitate these efforts, we construct a framework in which learned behaviors, created by a natural language abstractor, are verifiable by construction. Leveraging recent advancements in motion primitives and probabilistic verification, we construct a natural-language behavior abstractor that generates behaviors by synthesizing a directed graph over the provided motion primitives. If these component motion primitives are constructed according to the criteria we specify, the resulting behaviors are probabilistically verifiable. We demonstrate this verifiable behavior generation capacity in both simulation on an exploration task and on hardware with a robot scooping granular media.

Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning hedging against distributional uncertainty, e.g., the uncertainty of an empirical distribution compared to the true underlying distribution. This paper investigates the connections among the three frameworks and, in particular, explores why these frameworks tend to have smaller generalization errors. Specifically, first, we suggest a quantitative definition for "distributional robustness", propose the concept of "robustness measure", and formalize several philosophical concepts in distributionally robust optimization. Second, we show that Bayesian methods are distributionally robust in the probably approximately correct (PAC) sense; In addition, by constructing a Dirichlet-process-like prior in Bayesian nonparametrics, it can be proven that any regularized empirical risk minimization method is equivalent to a Bayesian method. Third, we show that generalization errors of machine learning models can be characterized using the distributional uncertainty of the nominal distribution and the robustness measures of these machine learning models, which is a new perspective to bound generalization errors, and therefore, explain the reason why distributionally robust machine learning models, Bayesian models, and regularization models tend to have smaller generalization errors.

Learning multimodal representations involves integrating information from multiple heterogeneous sources of data. It is a challenging yet crucial area with numerous real-world applications in multimedia, affective computing, robotics, finance, human-computer interaction, and healthcare. Unfortunately, multimodal research has seen limited resources to study (1) generalization across domains and modalities, (2) complexity during training and inference, and (3) robustness to noisy and missing modalities. In order to accelerate progress towards understudied modalities and tasks while ensuring real-world robustness, we release MultiBench, a systematic and unified large-scale benchmark spanning 15 datasets, 10 modalities, 20 prediction tasks, and 6 research areas. MultiBench provides an automated end-to-end machine learning pipeline that simplifies and standardizes data loading, experimental setup, and model evaluation. To enable holistic evaluation, MultiBench offers a comprehensive methodology to assess (1) generalization, (2) time and space complexity, and (3) modality robustness. MultiBench introduces impactful challenges for future research, including scalability to large-scale multimodal datasets and robustness to realistic imperfections. To accompany this benchmark, we also provide a standardized implementation of 20 core approaches in multimodal learning. Simply applying methods proposed in different research areas can improve the state-of-the-art performance on 9/15 datasets. Therefore, MultiBench presents a milestone in unifying disjoint efforts in multimodal research and paves the way towards a better understanding of the capabilities and limitations of multimodal models, all the while ensuring ease of use, accessibility, and reproducibility. MultiBench, our standardized code, and leaderboards are publicly available, will be regularly updated, and welcomes inputs from the community.

Deep learning models have been shown to be vulnerable to adversarial attacks. This perception led to analyzing deep learning models not only from the perspective of their performance measures but also their robustness to certain types of adversarial attacks. We take another step forward in relating the architectural structure of neural networks from a graph theoretic perspective to their robustness. We aim to investigate any existing correlations between graph theoretic properties and the robustness of Sparse Neural Networks. Our hypothesis is, that graph theoretic properties as a prior of neural network structures are related to their robustness. To answer to this hypothesis, we designed an empirical study with neural network models obtained through random graphs used as sparse structural priors for the networks. We additionally investigated the evaluation of a randomly pruned fully connected network as a point of reference. We found that robustness measures are independent of initialization methods but show weak correlations with graph properties: higher graph densities correlate with lower robustness, but higher average path lengths and average node eccentricities show negative correlations with robustness measures. We hope to motivate further empirical and analytical research to tightening an answer to our hypothesis.

Recent works have demonstrated that deep learning on graphs is vulnerable to adversarial attacks, in that imperceptible perturbations on input data can lead to dramatic performance deterioration. In this paper, we focus on the underlying problem of learning robust representations on graphs via mutual information. In contrast to previous works measure the task-specific robustness based on the label space, we here take advantage of the representation space to study a task-free robustness measure given the joint input space w.r.t graph topology and node attributes. We formulate this problem as a constrained saddle point optimization problem and solve it efficiently in a reduced search space. Furthermore, we provably establish theoretical connections between our task-free robustness measure and the robustness of downstream classifiers. Extensive experiments demonstrate that our proposed method is able to enhance robustness against adversarial attacks on graphs, yet even increases natural accuracy.