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Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data…

The phenomenon of double descent has challenged the traditional bias-variance trade-off in supervised learning but remains unexplored in unsupervised learning, with some studies arguing for its absence. In this study, we first demonstrate…

Machine Learning · Computer Science 2025-09-17 Kobi Rahimi , Yehonathan Refael , Tom Tirer , Ofir Lindenbaum

A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial…

Machine Learning · Computer Science 2021-12-07 Mohammad Pezeshki , Amartya Mitra , Yoshua Bengio , Guillaume Lajoie

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 2024-04-26 Yufei Gu , Xiaoqing Zheng , Tomaso Aste

Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…

Machine Learning · Statistics 2023-10-31 Alicia Curth , Alan Jeffares , Mihaela van der Schaar

The phenomenon of model-wise double descent, where the test error peaks and then reduces as the model size increases, is an interesting topic that has attracted the attention of researchers due to the striking observed gap between theory…

Machine Learning · Computer Science 2023-12-08 Chris Yuhao Liu , Jeffrey Flanigan

Finding the optimal size of deep learning models is very actual and of broad impact, especially in energy-saving schemes. Very recently, an unexpected phenomenon, the ``double descent'', has caught the attention of the deep learning…

Machine Learning · Computer Science 2023-12-27 Victor Quétu , Enzo Tartaglione

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

This paper explores the generalization loss of linear regression in variably parameterized families of models, both under-parameterized and over-parameterized. We show that the generalization curve can have an arbitrary number of peaks, and…

Machine Learning · Computer Science 2021-11-09 Lin Chen , Yifei Min , Mikhail Belkin , Amin Karbasi

In this paper, we studied two identically-trained neural networks (i.e. networks with the same architecture, trained on the same dataset using the same algorithm, but with different initialization) and found that their outputs discrepancy…

Machine Learning · Computer Science 2023-05-26 Yifan Luo , Bin Dong

Neoteric works have shown that modern deep learning models can exhibit a sparse double descent phenomenon. Indeed, as the sparsity of the model increases, the test performance first worsens since the model is overfitting the training data;…

Machine Learning · Computer Science 2024-02-09 Victor Quétu , Enzo Tartaglione

The relationship between the number of training data points, the number of parameters, and the generalization capabilities of models has been widely studied. Previous work has shown that double descent can occur in the over-parameterized…

Machine Learning · Statistics 2024-10-28 Xinyue Li , Rishi Sonthalia

Deep neural networks can achieve remarkable generalization performances while interpolating the training data perfectly. Rather than the U-curve emblematic of the bias-variance trade-off, their test error often follows a "double descent" -…

Machine Learning · Computer Science 2020-04-06 Stéphane d'Ascoli , Maria Refinetti , Giulio Biroli , Florent Krzakala

Classical learning theory describes a well-characterised U-shaped relationship between model complexity and prediction error, reflecting a transition from underfitting in underparameterised regimes to overfitting as complexity grows. Recent…

Machine Learning · Computer Science 2025-10-01 Guillermo Comesaña Cimadevila

Empirically it has been observed that the performance of deep neural networks steadily improves as we increase model size, contradicting the classical view on overfitting and generalization. Recently, the double descent phenomena has been…

Machine Learning · Computer Science 2021-07-28 Ilja Kuzborskij , Csaba Szepesvári , Omar Rivasplata , Amal Rannen-Triki , Razvan Pascanu

Combining empirical risk minimization with capacity control is a classical strategy in machine learning when trying to control the generalization gap and avoid overfitting, as the model class capacity gets larger. Yet, in modern deep…

Machine Learning · Computer Science 2024-03-18 Marc Lafon , Alexandre Thomas

This study demonstrates that double descent can be mitigated by adding a dropout layer adjacent to the fully connected linear layer. The unexpected double-descent phenomenon garnered substantial attention in recent years, resulting in…

Machine Learning · Computer Science 2025-08-08 Tian-Le Yang , Joe Suzuki

Recent studies observed a surprising concept on model test error called the double descent phenomenon, where the increasing model complexity decreases the test error first and then the error increases and decreases again. To observe this,…

Machine Learning · Statistics 2025-05-14 Chathurika S Abeykoon , Aleksandr Beknazaryan , Hailin Sang

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

The double descent curve is one of the most intriguing properties of deep neural networks. It contrasts the classical bias-variance curve with the behavior of modern neural networks, occurring where the number of samples nears the number of…

Machine Learning · Computer Science 2021-07-05 John Chen , Qihan Wang , Anastasios Kyrillidis
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