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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

We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic…

Statistics Theory · Mathematics 2023-08-15 Zhichao Wang , Yizhe Zhu

We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…

Machine Learning · Computer Science 2023-03-15 Francis Bach

Kernel ridge regression, KRR, is a generalization of linear ridge regression that is non-linear in the data, but linear in the model parameters. Here, we introduce an equivalent formulation of the objective function of KRR, which opens up…

Machine Learning · Statistics 2025-03-10 Oskar Allerbo

The "double descent" risk curve was proposed to qualitatively describe the out-of-sample prediction accuracy of variably-parameterized machine learning models. This article provides a precise mathematical analysis for the shape of this…

Machine Learning · Computer Science 2020-12-22 Mikhail Belkin , Daniel Hsu , Ji Xu

Although overparameterized models have achieved remarkable practical success, their theoretical properties, particularly their generalization behavior, remain incompletely understood. The well known double descents phenomenon suggests that…

Machine Learning · Statistics 2026-01-06 Haoran Zhan , Yingcun Xia

A recent line of research has highlighted the existence of a "double descent" phenomenon in deep learning, whereby increasing the number of training examples $N$ causes the generalization error of neural networks to peak when $N$ is of the…

Machine Learning · Computer Science 2022-01-12 Stéphane d'Ascoli , Levent Sagun , Giulio Biroli

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

Machine Learning · Computer Science 2023-10-04 Tin Sum Cheng , Aurelien Lucchi , Ivan Dokmanić , Anastasis Kratsios , David Belius

Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…

Machine Learning · Computer Science 2023-08-30 Jian Li , Yong Liu , Yingying Zhang

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

The double descent (DD) paradox, where over-parameterized models see generalization improve past the interpolation point, remains largely unexplored in the non-stationary domain of Deep Reinforcement Learning (DRL). We present preliminary…

Machine Learning · Computer Science 2025-11-11 Viktor Veselý , Aleksandar Todorov , Matthia Sabatelli

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

Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment…

Machine Learning · Computer Science 2022-06-30 Arash A. Amini , Richard Baumgartner , Dai Feng

We demonstrate the ability of hybrid regularization methods to automatically avoid the double descent phenomenon arising in the training of random feature models (RFM). The hallmark feature of the double descent phenomenon is a spike in the…

Machine Learning · Computer Science 2020-12-15 Kelvin Kan , James G Nagy , Lars Ruthotto

We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF…

Machine Learning · Statistics 2022-10-18 Fanghui Liu , Johan A. K. Suykens , Volkan Cevher

Deep learning methods operate in regimes that defy the traditional statistical mindset. Neural network architectures often contain more parameters than training samples, and are so rich that they can interpolate the observed labels, even if…

Statistics Theory · Mathematics 2020-12-14 Song Mei , Andrea Montanari

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

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

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…

Machine Learning · Statistics 2024-07-01 Weihao Lu , Haobo Zhang , Yicheng Li , Manyun Xu , Qian Lin

Overfitting has long been considered a common issue to large neural network models in sequential recommendation. In our study, an interesting phenomenon is observed that overfitting is temporary. When the model scale is increased, the trend…

Information Retrieval · Computer Science 2022-10-25 Ruihong Qiu , Zi Huang , Hongzhi Yin