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Over-parameterization and adaptive methods have played a crucial role in the success of deep learning in the last decade. The widespread use of over-parameterization has forced us to rethink generalization by bringing forth new phenomena,…

Machine Learning · Statistics 2020-12-01 Vatsal Shah , Soumya Basu , Anastasios Kyrillidis , Sujay Sanghavi

We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the…

Machine Learning · Computer Science 2024-05-02 Lorenzo Luzi , Yehuda Dar , Richard Baraniuk

Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably…

Machine Learning · Statistics 2020-08-18 Ben Adlam , Jeffrey Pennington

We provide (high probability) bounds on the condition number of random feature matrices. In particular, we show that if the complexity ratio $\frac{N}{m}$ where $N$ is the number of neurons and $m$ is the number of data samples scales like…

Machine Learning · Statistics 2021-11-08 Zhijun Chen , Hayden Schaeffer

Recent works demonstrated the existence of a double-descent phenomenon for the generalization error of neural networks, where highly overparameterized models escape overfitting and achieve good test performance, at odds with the standard…

Machine Learning · Computer Science 2024-04-02 Elizaveta Demyanenko , Christoph Feinauer , Enrico M. Malatesta , Luca Saglietti

We show that a variety of modern deep learning tasks exhibit a "double-descent" phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a…

Machine Learning · Computer Science 2019-12-06 Preetum Nakkiran , Gal Kaplun , Yamini Bansal , Tristan Yang , Boaz Barak , Ilya Sutskever

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with…

Machine Learning · Computer Science 2020-08-21 Yehuda Dar , Paul Mayer , Lorenzo Luzi , Richard G. Baraniuk

Deep neural networks are known to exhibit a `double descent' behavior as the number of parameters increases. Recently, it has also been shown that an `epochwise double descent' effect exists in which the generalization error initially…

Machine Learning · Computer Science 2021-08-30 Cory Stephenson , Tyler Lee

The double descent phenomenon, which deviates from the traditional bias-variance trade-off theory, attracts considerable research attention; however, the mechanism of its occurrence is not fully understood. On the other hand, in the study…

Computer Vision and Pattern Recognition · Computer Science 2025-03-05 Shun Iwase , Shuya Takahashi , Nakamasa Inoue , Rio Yokota , Ryo Nakamura , Hirokatsu Kataoka

We study the generalization behavior of transfer learning of deep neural networks (DNNs). We adopt the overparameterization perspective -- featuring interpolation of the training data (i.e., approximately zero train error) and the double…

Machine Learning · Computer Science 2023-06-13 Yehuda Dar , Lorenzo Luzi , Richard G. Baraniuk

Double descent refers to the phase transition that is exhibited by the generalization error of unregularized learning models when varying the ratio between the number of parameters and the number of training samples. The recent success of…

Machine Learning · Computer Science 2020-06-19 Michał Dereziński , Feynman Liang , Michael W. Mahoney

Classical regression has a simple geometric description in terms of a projection of the training labels onto the column space of the design matrix. However, for over-parameterized models -- where the number of fit parameters is large enough…

Machine Learning · Statistics 2021-04-28 Jason W. Rocks , Pankaj Mehta

People usually believe that network pruning not only reduces the computational cost of deep networks, but also prevents overfitting by decreasing model capacity. However, our work surprisingly discovers that network pruning sometimes even…

Machine Learning · Computer Science 2022-06-20 Zheng He , Zeke Xie , Quanzhi Zhu , Zengchang Qin

Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, with simpler models exhibiting high bias and more complex models exhibiting high…

Machine Learning · Statistics 2020-11-09 Ben Adlam , Jeffrey Pennington

In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n,d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$. Estimates of this type are important in many inverse…

Machine Learning · Computer Science 2020-04-29 Tomaso Poggio , Gil Kur , Andrzej Banburski

In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved…

Machine Learning · Statistics 2022-08-05 Jason W. Rocks , Pankaj Mehta

The volume of the distribution of weight sets associated with a loss value may be the source of implicit regularization from overparameterization due to the phenomenon of contracting volume with increasing dimensions for geometric figures…

Machine Learning · Computer Science 2022-09-27 Nicholas J. Teague

Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data…

Machine Learning · Statistics 2023-05-29 Ouns El Harzli , Bernardo Cuenca Grau , Guillermo Valle-Pérez , Ard A. Louis

We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon…

Machine Learning · Computer Science 2024-05-14 Yufei Gu