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In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…

Machine Learning · Computer Science 2017-11-28 Pengtao Xie , Hongbao Zhang , Eric P. Xing

This paper introduces a distribution-dependent PAC-Chernoff bound that exhibits perfect tightness for interpolators, even within over-parameterized model classes. This bound, which relies on basic principles of Large Deviation Theory,…

Machine Learning · Computer Science 2025-02-11 Andrés R. Masegosa , Luis A. Ortega

Prior knowledge and symbolic rules in machine learning are often expressed in the form of label constraints, especially in structured prediction problems. In this work, we compare two common strategies for encoding label constraints in a…

Machine Learning · Computer Science 2023-07-11 Kaifu Wang , Hangfeng He , Tin D. Nguyen , Piyush Kumar , Dan Roth

Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement…

Statistics Theory · Mathematics 2013-11-13 Shachar Kaufman , Saharon Rosset

A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, it is commonly assumed…

Machine Learning · Computer Science 2023-04-18 Tomas McKelvey

We present an $\ell^2_2+\ell_1$-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator…

Numerical Analysis · Mathematics 2024-07-08 Congpei An , Jiashu Ran , Alvise Sommariva

Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…

Numerical Analysis · Mathematics 2014-11-25 Valeriya Naumova , Steffen Peter

Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…

Machine Learning · Statistics 2018-10-29 Mikhail Belkin , Daniel Hsu , Partha Mitra

This paper gives a general interpretation of Linear Prediction (LP) by interpolation framework different from the perspective of statistics. This interpretation is proved to be useful by several following results, such as: The mechanism of…

Signal Processing · Electrical Eng. & Systems 2019-05-21 Changcun Huang

This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…

Numerical Analysis · Mathematics 2016-08-03 Kristian Bredies , Barbara Kaltenbacher , Elena Resmerita

Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the sparsity level of learned neural networks. We first derive…

Machine Learning · Computer Science 2024-08-07 Lixin Shen , Rui Wang , Yuesheng Xu , Mingsong Yan

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to…

Machine Learning · Statistics 2022-06-08 Mikhail Belkin , Daniel Hsu , Siyuan Ma , Soumik Mandal

Aligning generative models with human preference via RLHF typically suffers from overoptimization, where an imperfectly learned reward model can misguide the generative model to output undesired responses. We investigate this problem in a…

Machine Learning · Computer Science 2024-12-05 Zhihan Liu , Miao Lu , Shenao Zhang , Boyi Liu , Hongyi Guo , Yingxiang Yang , Jose Blanchet , Zhaoran Wang

Calibrating a multiclass predictor, that outputs a distribution over labels, is particularly challenging due to the exponential number of possible prediction values. In this work, we propose a new definition of calibration error that…

Machine Learning · Computer Science 2025-09-30 Konstantina Bairaktari , Huy L. Nguyen

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…

Machine Learning · Computer Science 2025-08-20 Abhisek Ganguly , Alessandro Gabbana , Vybhav Rao , Sauro Succi , Santosh Ansumali

We demonstrate that the choice of optimizer, neural network architecture, and regularizer significantly affect the adversarial robustness of linear neural networks, providing guarantees without the need for adversarial training. To this…

Machine Learning · Computer Science 2021-06-08 Fartash Faghri , Sven Gowal , Cristina Vasconcelos , David J. Fleet , Fabian Pedregosa , Nicolas Le Roux

For overparameterized linear regression with isotropic Gaussian design and minimum-$\ell_p$ interpolator $p\in(1,2]$, we give a unified, high-probability characterization for the scaling of the family of parameter norms $ \\{ \lVert…

Machine Learning · Computer Science 2026-03-20 Shuofeng Zhang , Ard Louis

Despite breakthrough performance, modern learning models are known to be highly vulnerable to small adversarial perturbations in their inputs. While a wide variety of recent \emph{adversarial training} methods have been effective at…

Machine Learning · Computer Science 2020-02-26 Adel Javanmard , Mahdi Soltanolkotabi , Hamed Hassani

The "alignment tax" of post-training is typically framed as a drop in task accuracy. We show it also involves a severe loss of calibration, making models overconfident, less reliable, and model outputs less diverse. We show that this…

Computation and Language · Computer Science 2025-11-03 Tiancheng Hu , Benjamin Minixhofer , Nigel Collier

Data augmentation is used in machine learning to make the classifier invariant to label-preserving transformations. Usually this invariance is only encouraged implicitly by including a single augmented input during training. However,…

Machine Learning · Computer Science 2022-03-08 Aleksander Botev , Matthias Bauer , Soham De