Transformer-based architectures have recently exhibited remarkable successes across different domains beyond just powering large language models. However, existing approaches typically focus on predictive accuracy and computational cost, largely ignoring certain other practical issues such as robustness to contaminated samples. In this paper, by re-interpreting the self-attention mechanism as a non-parametric kernel density estimator, we adapt classical robust kernel density estimation methods to develop novel classes of transformers that are resistant to adversarial attacks and data contamination. We first propose methods that down-weight outliers in RKHS when computing the self-attention operations. We empirically show that these methods produce improved performance over existing state-of-the-art methods, particularly on image data under adversarial attacks. Then we leverage the median-of-means principle to obtain another efficient approach that results in noticeably enhanced performance and robustness on language modeling and time series classification tasks. Our methods can be combined with existing transformers to augment their robust properties, thus promising to impact a wide variety of applications.

Proposition 1. Assume the robust loss function is non-decreasing in [0, 1 ], (0) = 0 and The proof of Proposition 1 is mainly adapted from the proof in Kim & Scott ( 2012). For any given function: R! We first introduce a few notations that are useful for stating this result. B> (2 +) |O| where is the failure probability. By adapting Lemma 1 in Nguyen et al. ( 2022c) to uniform concentration bound, ImageNet We use the full ImageNet dataset that contains 1 .

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While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What ``robustness'' means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper. To construct a robust KDE we scale the traditional KDE and project it to its nearest weighted KDE in the $L^2$ norm. Because the squared $L^2$ norm penalizes point-wise errors superlinearly this causes the weighted KDE to allocate more weight to high density regions. We demonstrate the robustness of the SPKDE with numerical experiments and a consistency result which shows that asymptotically the SPKDE recovers the uncontaminated density under sufficient conditions on the contamination.

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What "robustness" means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper.

Transformer-based architectures have recently exhibited remarkable successes across different domains beyond just powering large language models. However, existing approaches typically focus on predictive accuracy and computational cost, largely ignoring certain other practical issues such as robustness to contaminated samples. In this paper, by re-interpreting the self-attention mechanism as a non-parametric kernel density estimator, we adapt classical robust kernel density estimation methods to develop novel classes of transformers that are resistant to adversarial attacks and data contamination. We first propose methods that down-weight outliers in RKHS when computing the self-attention operations. We empirically show that these methods produce improved performance over existing state-of-the-art methods, particularly on image data under adversarial attacks.

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What robustness'' means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper. To construct a robust KDE we scale the traditional KDE and project it to its nearest weighted KDE in the L 2 norm.

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What "robustness" means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper.

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What robustness'' means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper. To construct a robust KDE we scale the traditional KDE and project it to its nearest weighted KDE in the $L 2$ norm.

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What ``robustness'' means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper. To construct a robust KDE we scale the traditional KDE and project it to its nearest weighted KDE in the $L^2$ norm. Because the squared $L^2$ norm penalizes point-wise errors superlinearly this causes the weighted KDE to allocate more weight to high density regions. We demonstrate the robustness of the SPKDE with numerical experiments and a consistency result which shows that asymptotically the SPKDE recovers the uncontaminated density under sufficient conditions on the contamination.