Certified adversarial robustness of large-scale deep networks has progressed substantially after the introduction of randomized smoothing. Deep net classifiers are now provably robust in their predictions against a large class of threat models, including $\ell_1$, $\ell_2$, and $\ell_\infty$ norm-bounded attacks. Certified robustness analysis by randomized smoothing has not been performed for deep regression networks where the output variable is continuous and unbounded. In this paper, we extend the existing results for randomized smoothing into regression models using powerful tools from robust statistics, in particular, $\alpha$-trimming filter as the smoothing function. Adjusting the hyperparameter $\alpha$ achieves a smooth trade-off between desired certified robustness and utility. For the first time, we propose a benchmark for certified robust regression in visual positioning systems using the Cambridge Landmarks dataset where robustness analysis is essential for autonomous navigation of AI agents and self-driving cars.

This work studies the evaluation of explaining graph neural networks (GNNs), which is crucial to the credibility of post-hoc explainability in practical usage. Conventional evaluation metrics, and even explanation methods -- which mainly follow the paradigm of feeding the explanatory subgraph and measuring output difference -- always suffer from the notorious out-of-distribution (OOD) issue.

Joint visual and language modeling on large-scale datasets has recently shown good progress in multi-modal tasks when compared to single modal learning. However, robustness of these approaches against real-world perturbations has not been studied. In this work, we perform the first extensive robustness study of video-language models against various real-world perturbations. We focus on text-to-video retrieval and propose two large-scale benchmark datasets, MSRVTT-P and YouCook2-P, which utilize 90 different visual and 35 different text perturbations. The study reveals some interesting initial findings from the studied models: 1) models are more robust when text is perturbed versus when video is perturbed, 2) models that are pre-trained are more robust than those trained from scratch, 3) models attend more to scene and objects rather than motion and action. We hope this study will serve as a benchmark and guide future research in robust video-language learning. The benchmark introduced in this study along with the code and datasets is available at https://bit.ly/3CNOly4.

This work proposes a novel analysis of stochastic gradient descent (SGD) for non-convex and smooth optimization.

Multi-criteria decision-making methods provide decision-makers with appropriate tools to make better decisions in uncertain, complex, and conflicting situations. Fuzzy set theory primarily deals with the uncertainty inherent in human thoughts and perceptions and attempts to quantify this uncertainty. Fuzzy logic and fuzzy set theory are utilized with multi-criteria decision-making methods because they effectively handle uncertainty and fuzziness in decision-makers' judgments, allowing for verbal judgments of the problem. This study utilizes the Fermatean fuzzy environment, a generalization of fuzzy sets. An optimization model based on the deviation maximization method is proposed to determine partially known feature weights. This method is combined with interval-valued Fermatean fuzzy sets. The proposed method was applied to the problem of selecting renewable energy sources. The reason for choosing renewable energy sources is that meeting energy needs from renewable sources, balancing carbon emissions, and mitigating the effects of global climate change are among the most critical issues of the recent period. Even though selecting renewable energy sources is a technical issue, the managerial and political implications of this issue are also important, and are discussed in this study.

Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In this work, we investigate learning-based models that imitate a model-based time-optimal trajectory planner to accelerate trajectory generation. Given a dataset of collision-free geometric paths, we show that modeling architectures can effectively learn the patterns underlying time-optimal trajectories. We introduce a quantitative framework to analyze local analytic properties of the learned models, and link them to the Backward Reachable Tube of the geometric tracking controller. To enhance robustness, we propose a data augmentation scheme that applies random perturbations to the input paths. Compared to classical planners, our method achieves substantial speedups, and we validate its real-time feasibility on a hardware quadrotor platform. Experiments demonstrate that the learned models generalize to previously unseen path lengths. The code for our approach can be found here: https://github.com/maokat12/lbTOPPQuad

The use of robotic technology has drastically increased in manufacturing in the 21st century. But by utilizing their sensory cues, humans still outperform machines, especially in micro scale manufacturing, which requires high-precision robot manipulators. These sensory cues naturally compensate for high levels of uncertainties that exist in the manufacturing environment. Uncertainties in performing manufacturing tasks may come from measurement noise, model inaccuracy, joint compliance (e.g., elasticity), etc. Although advanced metrology sensors and high precision microprocessors, which are utilized in modern robots, have compensated for many structural and dynamic errors in robot positioning, a well-designed control algorithm still works as a comparable and cheaper alternative to reduce uncertainties in automated manufacturing. Our work illustrates that a multi-robot control system that simulates the positioning process for fastening and unfastening applications can reduce various uncertainties, which may occur in this process, to a great extent. In addition, most research papers in visual servoing mainly focus on developing control and observation architectures in various scenarios, but few have discussed the importance of the camera's location in the configuration. In a manufacturing environment, the quality of camera estimations may vary significantly from one observation location to another, as the combined effects of environmental conditions result in different noise levels of a single image shot at different locations. Therefore, in this paper, we also propose a novel algorithm for the camera's moving policy so that it explores the camera workspace and searches for the optimal location where the image noise level is minimized.

Certified adversarial robustness of large-scale deep networks has progressed substantially after the introduction of randomized smoothing. Deep net classifiers are now provably robust in their predictions against a large class of threat models, including \ell_1, \ell_2, and \ell_\infty norm-bounded attacks. Certified robustness analysis by randomized smoothing has not been performed for deep regression networks where the output variable is continuous and unbounded. In this paper, we extend the existing results for randomized smoothing into regression models using powerful tools from robust statistics, in particular, \alpha -trimming filter as the smoothing function. Adjusting the hyperparameter \alpha achieves a smooth trade-off between desired certified robustness and utility.

Weaknesses: While the "biased expectation" appears to be a powerful tool, the overall results are restricted to the gradients of the algorithm at _some_ time t in the last T iterates. While this is a common outcome of the standard analysis of SGD, it would be nice if (with some additional assumptions on f) the results could be transposed to f(x_t) or x_t within some basin of attraction. The special case of s 0 needs much more detailed treatment. While the authors point out in the supplement that \phi is continuous at s 0, much of the document switches between looking at s- 0 or s 0 without explanation. Assumption 1: I see that the authors need to contol X_t 2 in Thm 1. (Eq.