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In transfer learning, the learner leverages auxiliary data to improve generalization on a main task. However, the precise theoretical understanding of when and how auxiliary data help remains incomplete. We provide new insights on this…

Machine Learning · Computer Science 2026-03-31 Meitong Liu , Christopher Jung , Rui Li , Xue Feng , Han Zhao

We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…

Machine Learning · Computer Science 2022-07-12 Sharan Vaswani , Reza Babanezhad , Jose Gallego-Posada , Aaron Mishkin , Simon Lacoste-Julien , Nicolas Le Roux

We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We provide an effective theory for approximating the Bayes-optimal…

Machine Learning · Statistics 2025-04-02 Jean Barbier , Francesco Camilli , Minh-Toan Nguyen , Mauro Pastore , Rudy Skerk

We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a…

Machine Learning · Statistics 2025-09-30 Yunfei Yang

We theoretically demonstrate that the generalization error of interpolators for machine learning models under teacher-student settings becomes 0 once the number of training samples exceeds a certain threshold. Understanding the high…

Machine Learning · Computer Science 2025-12-09 Naoki Yoshida , Isao Ishikawa , Masaaki Imaizumi

Understanding generalization of overparametrized neural networks remains a fundamental challenge in machine learning. Most of the literature mostly studies generalization from an interpolation point of view, taking convergence of parameters…

Machine Learning · Computer Science 2025-06-13 Etienne Boursier , Nicolas Flammarion

Deep neural networks generalize well despite being exceedingly overparameterized and being trained without explicit regularization. This curious phenomenon has inspired extensive research activity in establishing its statistical principles:…

Machine Learning · Statistics 2021-09-16 Ke Wang , Christos Thrampoulidis

We propose a novel framework for exploring generalization errors of transfer learning through the lens of differential calculus on the space of probability measures. In particular, we consider two main transfer learning scenarios,…

Machine Learning · Statistics 2024-10-24 Gholamali Aminian , Łukasz Szpruch , Samuel N. Cohen

We provide an information-theoretic analysis of the generalization ability of Gibbs-based transfer learning algorithms by focusing on two popular transfer learning approaches, $\alpha$-weighted-ERM and two-stage-ERM. Our key result is an…

Machine Learning · Computer Science 2021-11-03 Yuheng Bu , Gholamali Aminian , Laura Toni , Miguel Rodrigues , Gregory Wornell

In some studies \citep[e.g.,][]{zhang2016understanding} of deep learning, it is observed that over-parametrized deep neural networks achieve a small testing error even when the training error is almost zero. Despite numerous works towards…

Machine Learning · Statistics 2022-02-25 Yue Xing , Qifan Song , Guang Cheng

When training neural networks as classifiers, it is common to observe an increase in average test loss while still maintaining or improving the overall classification accuracy on the same dataset. In spite of the ubiquity of this…

Machine Learning · Computer Science 2021-03-16 Arthur E. W. Venter , Marthinus W. Theunissen , Marelie H. Davel

Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…

Machine Learning · Statistics 2021-10-22 Eduard Oravkin , Patrick Rebeschini

Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum $\ell_2$…

Statistics Theory · Mathematics 2022-09-12 Trevor Hastie , Andrea Montanari , Saharon Rosset , Ryan J. Tibshirani

A popular assumption for out-of-distribution generalization is that the training data comprises sub-datasets, each drawn from a distinct distribution; the goal is then to "interpolate" these distributions and "extrapolate" beyond them --…

Machine Learning · Computer Science 2021-11-19 Elan Rosenfeld , Pradeep Ravikumar , Andrej Risteski

Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively…

Machine Learning · Computer Science 2022-09-20 Haiyun He , Hanshu Yan , Vincent Y. F. Tan

Modern machine learning methods have recently demonstrated remarkable capability to generalize under task shift, where latent knowledge is transferred to a different, often more difficult, task under a similar data distribution. We…

Machine Learning · Statistics 2025-02-20 Tyler LaBonte , Kuo-Wei Lai , Vidya Muthukumar

Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of…

Machine Learning · Computer Science 2020-06-19 Seyed Mohammadreza Mousavi Kalan , Zalan Fabian , A. Salman Avestimehr , Mahdi Soltanolkotabi

In this work we consider a model problem of deep neural learning, namely the learning of a given function when it is assumed that we have access to its point values on a finite set of points. The deep neural network interpolant is the the…

Machine Learning · Statistics 2023-06-27 Michail Loulakis , Charalambos G. Makridakis

The over-parameterized models attract much attention in the era of data science and deep learning. It is empirically observed that although these models, e.g. deep neural networks, over-fit the training data, they can still achieve small…

Machine Learning · Statistics 2019-09-27 Yue Xing , Qifan Song , Guang Cheng

Meta-learning automatically infers an inductive bias by observing data from a number of related tasks. The inductive bias is encoded by hyperparameters that determine aspects of the model class or training algorithm, such as initialization…

Machine Learning · Computer Science 2020-11-10 Sharu Theresa Jose , Osvaldo Simeone , Giuseppe Durisi