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Data scarcity drives the need for more sample-efficient large language models. In this work, we use the double descent phenomenon to holistically compare the sample efficiency of discrete diffusion and autoregressive models. We show that…

Machine Learning · Computer Science 2025-09-30 Ahmad Fraij , Sam Dauncey

We study the performance of machine learning binary classification techniques in terms of error probabilities. The statistical test is based on the Data-Driven Decision Function (D3F), learned in the training phase, i.e., what is…

Machine Learning · Computer Science 2023-01-19 Paolo Braca , Leonardo M. Millefiori , Augusto Aubry , Antonio De Maio , Peter Willett

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

Classical statistical learning theory predicts a U-shaped relationship between test loss and model capacity, driven by the bias-variance trade-off. Recent advances in modern machine learning have revealed a more complex pattern,…

Machine Learning · Statistics 2026-04-23 Yin Liu , Jianwen Cai , Didong Li

We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…

Machine Learning · Computer Science 2024-05-09 Dwight Nwaigwe , Marek Rychlik

Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…

Statistics Theory · Mathematics 2007-06-13 Wei Zhang

We study the problem of transfer learning and fine-tuning in linear models for both regression and binary classification. In particular, we consider the use of stochastic gradient descent (SGD) on a linear model initialized with pretrained…

Machine Learning · Computer Science 2025-02-25 Reza Ghane , Danil Akhtiamov , Babak Hassibi

Catastrophic overfitting is a phenomenon observed during Adversarial Training (AT) with the Fast Gradient Sign Method (FGSM) where the test robustness steeply declines over just one epoch in the training stage. Prior work has attributed…

Machine Learning · Computer Science 2021-11-23 Varun Sivashankar , Nikil Selvam

The generalization performance of a machine learning algorithm such as a neural network depends in a non-trivial way on the structure of the data distribution. To analyze the influence of data structure on test loss dynamics, we study an…

Machine Learning · Statistics 2022-03-16 Blake Bordelon , Cengiz Pehlevan

We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…

Machine Learning · Computer Science 2021-02-09 Yahya Sattar , Samet Oymak

We propose double/debiased machine learning approaches to infer (at the parametric rate) the parametric component of a logistic partially linear model with the binary response following a conditional logistic model of a low dimensional…

Methodology · Statistics 2020-10-01 Molei Liu , Yi Zhang , Doudou Zhou

We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…

Machine Learning · Computer Science 2024-04-12 Roi Livni

In this paper, we study the dynamics of gradient descent in learning neural networks for classification problems. Unlike in existing works, we consider the linearly non-separable case where the training data of different classes lie in…

Machine Learning · Computer Science 2020-12-11 Ziang Long , Penghang Yin , Jack Xin

We study the convergence of gradient descent (GD) and stochastic gradient descent (SGD) for training $L$-hidden-layer linear residual networks (ResNets). We prove that for training deep residual networks with certain linear transformations…

Machine Learning · Computer Science 2020-03-03 Difan Zou , Philip M. Long , Quanquan Gu

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…

Machine Learning · Statistics 2017-06-28 Ilya Trofimov , Alexander Genkin

There has been a recent surge of interest in understanding the convergence of gradient descent (GD) and stochastic gradient descent (SGD) in overparameterized neural networks. Most previous works assume that the training data is provided a…

Machine Learning · Statistics 2021-05-04 Jiaming Xu , Hanjing Zhu

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training…

Optimization and Control · Mathematics 2020-06-23 Lenaic Chizat , Francis Bach

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

Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this…

Machine Learning · Computer Science 2022-01-04 Yuan Cao , Quanquan Gu , Mikhail Belkin

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