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Recent work has shown that 3D Gaussian-based SLAM enables high-quality reconstruction, accurate pose estimation, and real-time rendering of scenes. However, these approaches are built on a tremendous number of redundant 3D Gaussian…
We prove the first robust dimension free isoperimetric result for the standard Gaussian measure $\gamma_n$ and the corresponding boundary measure $\gamma_n^+$ in $\mathbb {R}^n$. The main result in the theory of Gaussian isoperimetry…
The fragility of modern machine learning models has drawn a considerable amount of attention from both academia and the public. While immense interests were in either crafting adversarial attacks as a way to measure the robustness of neural…
This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…
Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…
Recent studies have revealed the vulnerability of large language models to adversarial attacks, where adversaries craft specific input sequences to induce harmful, violent, private, or incorrect outputs. In this work, we study their…
Deep learning-based malware detection systems are vulnerable to adversarial EXEmples - carefully-crafted malicious programs that evade detection with minimal perturbation. As such, the community is dedicating effort to develop mechanisms to…
Random subspaces $X$ of $\mathbb{R}^n$ of dimension proportional to $n$ are, with high probability, well-spread with respect to the $\ell_2$-norm. Namely, every nonzero $x \in X$ is "robustly non-sparse" in the following sense: $x$ is…
Let $A$ be a compact $d$-dimensional $C^2$ Riemannian manifold with boundary, embedded in ${\bf R}^m$ where $m \geq d \geq 2$, and let $B$ be a nice subset of $A$ (possibly $B=A$). Let $X_1,X_2, \ldots $ be independent random uniform points…
To improve the off-sample generalization of classical procedures minimizing the empirical risk under potentially heavy-tailed data, new robust learning algorithms have been proposed in recent years, with generalized median-of-means…
Recent studies indicate that current adversarial attack methods are flawed and easy to fail when encountering some deliberately designed defense. Sometimes even a slight modification in the model details will invalidate the attack. We find…
It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on…
We consider the problem of droplet impact and droplet spreading on a smooth surface in the case of a viscous Newtonian fluid. We revisit the concept of the rim-lamella model, in which the droplet spreading is described by a system of…
The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of…
In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees…
This paper presents preliminary work on a novel connection between certified robustness in machine learning and the modeling of 3D objects. We highlight an intriguing link between the Maximal Certified Radius (MCR) of a classifier…
Accurate and robust trajectory prediction is essential for safe and efficient autonomous driving, yet recent work has shown that even state-of-the-art prediction models are highly vulnerable to inputs being mildly perturbed by adversarial…
Existing techniques for certifying the robustness of models for discrete data either work only for a small class of models or are general at the expense of efficiency or tightness. Moreover, they do not account for sparsity in the input…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for $d$-dimensional Gaussian distributions with known covariance $\Sigma$, we can test whether the distribution…