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Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric…

Methodology · Statistics 2025-07-03 Rong Jiang , Keming Yu , Jiangfeng Wang

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show…

Computer Vision and Pattern Recognition · Computer Science 2024-02-20 Randall Balestriero , Yann LeCun

In this paper, we propose a geometric framework to analyze the convergence properties of gradient descent trajectories in the context of linear neural networks. We translate a well-known empirical observation of linear neural nets into a…

Machine Learning · Computer Science 2023-08-02 Yacine Chitour , Zhenyu Liao , Romain Couillet

This paper investigates how the compositional structure of neural networks shapes their optimization landscape and training dynamics. We analyze the gradient flow associated with overparameterized optimization problems, which can be…

Machine Learning · Computer Science 2025-11-14 Arthur Castello Branco de Oliveira , Dhruv Jatkar , Eduardo Sontag

Deep visual models are susceptible to adversarial perturbations to inputs. Although these signals are carefully crafted, they still appear noise-like patterns to humans. This observation has led to the argument that deep visual…

Computer Vision and Pattern Recognition · Computer Science 2021-06-22 Naveed Akhtar , Muhammad A. A. K. Jalwana , Mohammed Bennamoun , Ajmal Mian

The recent success of neural network models has shone light on a rather surprising statistical phenomenon: statistical models that perfectly fit noisy data can generalize well to unseen test data. Understanding this phenomenon of…

Machine Learning · Statistics 2022-09-13 Niladri S. Chatterji , Philip M. Long , Peter L. Bartlett

Several machine learning models, including neural networks, consistently misclassify adversarial examples---inputs formed by applying small but intentionally worst-case perturbations to examples from the dataset, such that the perturbed…

Machine Learning · Statistics 2015-03-24 Ian J. Goodfellow , Jonathon Shlens , Christian Szegedy

Supervisory signals have the potential to make low-dimensional data representations, like those learned by mixture and topic models, more interpretable and useful. We propose a framework for training latent variable models that explicitly…

The vulnerability of deep neural networks to adversarial attacks has been widely demonstrated (e.g., adversarial example attacks). Traditional attacks perform unstructured pixel-wise perturbation to fool the classifier. An alternative…

Machine Learning · Computer Science 2022-05-23 Shuo Wang , Surya Nepal , Carsten Rudolph , Marthie Grobler , Shangyu Chen , Tianle Chen

Overparametrized neural networks tend to perfectly fit noisy training data yet generalize well on test data. Inspired by this empirical observation, recent work has sought to understand this phenomenon of benign overfitting or harmless…

Machine Learning · Statistics 2022-02-23 Andrew D. McRae , Santhosh Karnik , Mark A. Davenport , Vidya Muthukumar

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the…

Machine Learning · Computer Science 2023-06-01 Takayuki Katsuki , Takayuki Osogami

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks'…

Neural networks have a number of shortcomings. Amongst the severest ones is the sensitivity to distribution shifts which allows models to be easily fooled into wrong predictions by small perturbations to inputs that are often imperceivable…

Computer Vision and Pattern Recognition · Computer Science 2023-03-23 Paul Gavrikov , Janis Keuper , Margret Keuper

The phenomenon of benign overfitting is one of the key mysteries uncovered by deep learning methodology: deep neural networks seem to predict well, even with a perfect fit to noisy training data. Motivated by this phenomenon, we consider…

Machine Learning · Statistics 2022-06-08 Peter L. Bartlett , Philip M. Long , Gábor Lugosi , Alexander Tsigler

Many machine learning classifiers are vulnerable to adversarial perturbations. An adversarial perturbation modifies an input to change a classifier's prediction without causing the input to seem substantially different to human perception.…

Machine Learning · Computer Science 2017-03-27 Dan Hendrycks , Kevin Gimpel

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…

Machine Learning · Statistics 2016-12-16 Theofanis Karaletsos

Robustness is a key requirement for widespread deployment of machine learning algorithms, and has received much attention in both statistics and computer science. We study a natural model of robustness for high-dimensional statistical…

Machine Learning · Computer Science 2020-06-03 Pranjal Awasthi , Xue Chen , Aravindan Vijayaraghavan

Over the past few years, several adversarial training methods have been proposed to improve the robustness of machine learning models against adversarial perturbations in the input. Despite remarkable progress in this regard, adversarial…

Machine Learning · Computer Science 2022-04-04 Adel Javanmard , Mohammad Mehrabi

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite…

Statistics Theory · Mathematics 2021-03-17 Peter L. Bartlett , Andrea Montanari , Alexander Rakhlin

Recent studies have noted an intriguing phenomenon termed Neural Collapse, that is, when the neural networks establish the right correlation between feature spaces and the training targets, their last-layer features, together with the…

Computer Vision and Pattern Recognition · Computer Science 2025-09-22 Yining Wang , Junjie Sun , Chenyue Wang , Mi Zhang , Min Yang