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Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…

Machine Learning · Statistics 2022-11-10 Bat-Sheva Einbinder , Yaniv Romano , Matteo Sesia , Yanfei Zhou

Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime where classical learning theory would instead predict that they would severely overfit. While many…

Machine Learning · Statistics 2019-04-23 Guillermo Valle-Pérez , Chico Q. Camargo , Ard A. Louis

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

Machine Learning · Computer Science 2019-12-06 Gauthier Gidel , Francis Bach , Simon Lacoste-Julien

Overfitting is a major problem in training machine learning models, specifically deep neural networks. This problem may be caused by imbalanced datasets and initialization of the model parameters, which conforms the model too closely to the…

Neural and Evolutionary Computing · Computer Science 2019-02-26 Hojjat Salehinejad , Shahrokh Valaee

Statistical wisdom suggests that very complex models, interpolating training data, will be poor at predicting unseen examples.Yet, this aphorism has been recently challenged by the identification of benign overfitting regimes, specially…

Statistics Theory · Mathematics 2023-02-10 Ludovic Arnould , Claire Boyer , Erwan Scornet

Linearly transforming stimulus representations of deep neural networks yields high-performing models of behavioral and neural responses to complex stimuli. But does the test accuracy of such predictions identify genuine representational…

Neurons and Cognition · Quantitative Biology 2026-01-05 Itamar Avitan , Tal Golan

Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…

Machine Learning · Computer Science 2024-03-27 Cédric Gerbelot , Avetik Karagulyan , Stefani Karp , Kavya Ravichandran , Menachem Stern , Nathan Srebro

Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…

Statistics Theory · Mathematics 2021-06-14 Qixian Zhong , Jane-Ling Wang

Machine learning and statistics typically focus on building models that capture the vast majority of the data, possibly ignoring a small subset of data as "noise" or "outliers." By contrast, here we consider the problem of jointly…

Machine Learning · Computer Science 2016-08-19 Brendan Juba

Miscalibration in deep learning refers to there is a discrepancy between the predicted confidence and performance. This problem usually arises due to the overfitting problem, which is characterized by learning everything presented in the…

Machine Learning · Computer Science 2024-07-16 Zongbo Han , Yifeng Yang , Changqing Zhang , Linjun Zhang , Joey Tianyi Zhou , Qinghua Hu

One explanation for the strong generalization ability of neural networks is implicit bias. Yet, the definition and mechanism of implicit bias in non-linear contexts remains little understood. In this work, we propose to characterize…

Machine Learning · Computer Science 2025-08-14 Jingwei Li , Jing Xu , Zifan Wang , Huishuai Zhang , Jingzhao Zhang

Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…

Machine Learning · Computer Science 2018-01-31 Maruan Al-Shedivat , Avinava Dubey , Eric P. Xing

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…

Machine Learning · Computer Science 2012-06-15 Matus Telgarsky

In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…

Machine Learning · Computer Science 2024-02-22 Daniel LeJeune , Sina Alemohammad

In human-in-the-loop machine learning, the user provides information beyond that in the training data. Many algorithms and user interfaces have been designed to optimize and facilitate this human--machine interaction; however, fewer studies…

Human-Computer Interaction · Computer Science 2018-03-12 Pedram Daee , Tomi Peltola , Aki Vehtari , Samuel Kaski

Early stopping is a simple and widely used method to prevent over-training neural networks. We develop theoretical results to reveal the relationship between the optimal early stopping time and model dimension as well as sample size of the…

Machine Learning · Computer Science 2022-02-25 Ruoqi Shen , Liyao Gao , Yi-An Ma

It has been observed \citep{zhang2016understanding} that deep neural networks can memorize: they achieve 100\% accuracy on training data. Recent theoretical results explained such behavior in highly overparametrized regimes, where the…

Machine Learning · Computer Science 2019-09-27 Rong Ge , Runzhe Wang , Haoyu Zhao

Despite the remarkable success of Vision Transformers (ViTs) across a wide range of vision tasks, recent studies have revealed that they remain vulnerable to adversarial examples, much like Convolutional Neural Networks (CNNs). A common…

Machine Learning · Computer Science 2026-04-22 Jiaming Zhang , Meng Ding , Shaopeng Fu , Jingfeng Zhang , Di Wang

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…

Machine Learning · Statistics 2017-10-11 Madhu S. Advani , Andrew M. Saxe

In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies…

Machine Learning · Statistics 2020-09-18 Ryumei Nakada , Masaaki Imaizumi