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Related papers: Benign Overfitting in Single-Head Attention

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This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining…

Machine Learning · Computer Science 2023-06-01 Zhenyu Zhu , Fanghui Liu , Grigorios G Chrysos , Francesco Locatello , Volkan Cevher

Overfitting is defined as the fact that the current model fits a specific data set perfectly, resulting in weakened generalization, and ultimately may affect the accuracy in predicting future data. In this research we used an EHR dataset…

Machine Learning · Computer Science 2022-08-04 Chuhan Xu , Pablo Coen-Pirani , Xia Jiang

Although numerous methods to reduce the overfitting of convolutional neural networks (CNNs) exist, it is still not clear how to confidently measure the degree of overfitting. A metric reflecting the overfitting level might be, however,…

Machine Learning · Computer Science 2022-09-28 Svetlana Pavlitskaya , Joël Oswald , J. Marius Zöllner

In this work, we investigate the behavior of ridge regression in an overparameterized binary classification task. We assume examples are drawn from (anisotropic) class-conditional cluster distributions with opposing means and we allow for…

Machine Learning · Statistics 2025-03-12 Alexander Tsigler , Luiz F. O. Chamon , Spencer Frei , Peter L. Bartlett

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

In deep learning, often the training process finds an interpolator (a solution with 0 training loss), but the test loss is still low. This phenomenon, known as benign overfitting, is a major mystery that received a lot of recent attention.…

Machine Learning · Computer Science 2023-05-29 Mo Zhou , Rong Ge

Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit…

Machine Learning · Statistics 2024-02-15 Eliot Wong-Toi , Alex Boyd , Vincent Fortuin , Stephan Mandt

Assisted by the availability of data and high performance computing, deep learning techniques have achieved breakthroughs and surpassed human performance empirically in difficult tasks, including object recognition, speech recognition, and…

Machine Learning · Computer Science 2019-01-23 Shaeke Salman , Xiuwen Liu

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns:…

Machine Learning · Computer Science 2025-05-29 Jianliang He , Xintian Pan , Siyu Chen , Zhuoran Yang

Neural networks trained by gradient descent (GD) have exhibited a number of surprising generalization behaviors. First, they can achieve a perfect fit to noisy training data and still generalize near-optimally, showing that overfitting can…

Machine Learning · Computer Science 2023-10-05 Zhiwei Xu , Yutong Wang , Spencer Frei , Gal Vardi , Wei Hu

We present a theoretical analysis of the performance of transformer with softmax attention in in-context learning with linear regression tasks. While the existing literature predominantly focuses on the convergence of transformers with…

Machine Learning · Computer Science 2024-02-01 Yingqian Cui , Jie Ren , Pengfei He , Jiliang Tang , Yue Xing

Multi-head attention enables transformer models to represent multiple attention patterns simultaneously. Empirically, head specialization emerges in distinct stages during training, while many heads remain redundant and learn similar…

Machine Learning · Computer Science 2026-03-05 M. Sagitova , O. Duranthon , L. Zdeborová

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

Large language models rely on attention mechanisms with a softmax activation. Yet the dominance of softmax over alternatives (e.g., component-wise or linear) remains poorly understood, and many theoretical works have focused on the…

Machine Learning · Computer Science 2026-02-27 O. Duranthon , P. Marion , C. Boyer , B. Loureiro , L. Zdeborová

Over-parameterized neural network models often lead to significant performance discrepancies between training and test sets, a phenomenon known as overfitting. To address this, researchers have proposed numerous regularization techniques…

Machine Learning · Computer Science 2025-01-27 RuiZhe Jiang , Haotian Lei

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

We develop a theoretical framework for generalization in the interpolating regime of statistical learning. The central question is why highly overparameterized estimators can attain zero empirical risk while still achieving nontrivial…

Machine Learning · Statistics 2026-04-13 Gustav Olaf Yunus Laitinen-Lundström Fredriksson-Imanov

We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE), with linear regression models. As the development of machine learning for causal inference, a wide range of large-scale models for…

Econometrics · Economics 2022-02-17 Masahiro Kato , Masaaki Imaizumi

Despite the empirical advances of deep learning across a variety of learning tasks, our theoretical understanding of its success is still very restricted. One of the key challenges is the overparametrized nature of modern models, enabling…

Machine Learning · Computer Science 2023-02-24 Sotiris Anagnostidis , Gregor Bachmann , Lorenzo Noci , Thomas Hofmann

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the…

Machine Learning · Computer Science 2020-03-05 Leslie Rice , Eric Wong , J. Zico Kolter