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While it has long been empirically observed that adversarial robustness may be at odds with standard accuracy and may have further disparate impacts on different classes, it remains an open question to what extent such observations hold and…

We revisit the problem of tolerant distribution testing. That is, given samples from an unknown distribution $p$ over $\{1, \dots, n\}$, is it $\varepsilon_1$-close to or $\varepsilon_2$-far from a reference distribution $q$ (in total…

The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…

In this paper, for the first time, we propose an evaluation method for deep learning models that assesses the performance of a model not only in an unseen test scenario, but also in extreme cases of noise, outliers and ambiguous input data.…

While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes…

Matching the performance of conditional Generative Adversarial Networks with little supervision is an important task, especially in venturing into new domains. We design a new training algorithm, which is robust to missing or ambiguous…

Adversarial training tends to result in models that are less accurate on natural (unperturbed) examples compared to standard models. This can be attributed to either an algorithmic shortcoming or a fundamental property of the training data…

We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…

It is well known that machine learning methods can be vulnerable to adversarially-chosen perturbations of their inputs. Despite significant progress in the area, foundational open problems remain. In this paper, we address several key…

Neural networks have revolutionized various domains, exhibiting remarkable accuracy in tasks like natural language processing and computer vision. However, their vulnerability to slight alterations in input samples poses challenges,…

Recently, it has been shown that deep neural networks (DNN) are subject to attacks through adversarial samples. Adversarial samples are often crafted through adversarial perturbation, i.e., manipulating the original sample with minor…

We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional…

Random sampling is a fundamental primitive in modern algorithms, statistics, and machine learning, used as a generic method to obtain a small yet "representative" subset of the data. In this work, we investigate the robustness of sampling…

We show how to turn any classifier that classifies well under Gaussian noise into a new classifier that is certifiably robust to adversarial perturbations under the $\ell_2$ norm. This "randomized smoothing" technique has been proposed…

With the perpetual increase of complexity of the state-of-the-art deep neural networks, it becomes a more and more challenging task to maintain their interpretability. Our work aims to evaluate the effects of adversarial training utilized…

Perceptual similarity metrics have progressively become more correlated with human judgments on perceptual similarity; however, despite recent advances, the addition of an imperceptible distortion can still compromise these metrics. In our…

We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when $d$ is large compared to $n$ but the covariance matrix $\Sigma$ of…

Benefiting from large-scale pre-training, we have witnessed significant performance boost on the popular Visual Question Answering (VQA) task. Despite rapid progress, it remains unclear whether these state-of-the-art (SOTA) models are…

Large language models adapt to new tasks through in-context learning (ICL) without parameter updates. Current theoretical explanations for this capability assume test tasks are drawn from a distribution similar to that seen during…

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…