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Discrete decision tasks in machine learning exhibit a fundamental misalignment between training and inference: models are optimized with continuous-valued outputs but evaluated using discrete predictions. This misalignment arises from the…

Computer Vision and Pattern Recognition · Computer Science 2025-12-24 Hao Shu

The study on the implicit regularization induced by gradient-based optimization is a longstanding pursuit. In the present paper, we characterize the implicit regularization of momentum gradient descent (MGD) with early stopping by comparing…

Machine Learning · Computer Science 2022-01-17 Li Wang , Yingcong Zhou , Zhiguo Fu

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

We study the implicit regularization imposed by gradient descent for learning multi-layer homogeneous functions including feed-forward fully connected and convolutional deep neural networks with linear, ReLU or Leaky ReLU activation. We…

Machine Learning · Computer Science 2018-11-01 Simon S. Du , Wei Hu , Jason D. Lee

Private machine learning involves addition of noise while training, resulting in lower accuracy. Intuitively, greater stability can imply greater privacy and improve this privacy-utility tradeoff. We study this role of stability in private…

Machine Learning · Computer Science 2020-06-26 Lauren Watson , Benedek Rozemberczki , Rik Sarkar

Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…

Optimization and Control · Mathematics 2025-05-19 Xiaotian Jiang , Ioannis Tsaknakis , Prashant Khanduri , Mingyi Hong

Learning algorithms that learn linear models often have high representation bias on real-world problems. In this paper, we show that this representation bias can be greatly reduced by discretization. Discretization is a common procedure in…

Machine Learning · Computer Science 2017-01-26 Nayyar A. Zaidi , Yang Du , Geoffrey I. Webb

A number of competing hypotheses have been proposed to explain why small-batch Stochastic Gradient Descent (SGD)leads to improved generalization over the full-batch regime, with recent work crediting the implicit regularization of various…

Machine Learning · Computer Science 2022-11-30 Zachary Novack , Simran Kaur , Tanya Marwah , Saurabh Garg , Zachary C. Lipton

While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…

Machine Learning · Computer Science 2020-08-14 Tong Yang , Long Sha , Pengyu Hong

Due to its speed and simplicity, subgradient descent is one of the most used optimization algorithms in convex machine learning algorithms. However, tuning its learning rate is probably its most severe bottleneck to achieve consistent good…

Machine Learning · Computer Science 2023-07-25 Keyi Chen , Francesco Orabona

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so…

Machine Learning · Computer Science 2024-11-01 Timm Hess , Tinne Tuytelaars , Gido M. van de Ven

Methods from convex optimization such as accelerated gradient descent are widely used as building blocks for deep learning algorithms. However, the reasons for their empirical success are unclear, since neural networks are not convex and…

Machine Learning · Computer Science 2016-04-11 David Balduzzi

Recent work across many machine learning disciplines has highlighted that standard descent methods, even without explicit regularization, do not merely minimize the training error, but also exhibit an implicit bias. This bias is typically…

Machine Learning · Computer Science 2020-06-22 Ziwei Ji , Miroslav Dudík , Robert E. Schapire , Matus Telgarsky

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in…

Computer Science and Game Theory · Computer Science 2015-12-14 Vasilis Syrgkanis , Alekh Agarwal , Haipeng Luo , Robert E. Schapire

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Optimization and Control · Mathematics 2025-11-11 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…

Machine Learning · Computer Science 2022-10-21 Alberto Lanconelli , Christopher S. A. Lauria

We study the implicit regularization effects of deep learning in tensor factorization. While implicit regularization in deep matrix and 'shallow' tensor factorization via linear and certain type of non-linear neural networks promotes…

Machine Learning · Computer Science 2022-07-27 Kais Hariz , Hachem Kadri , Stéphane Ayache , Maher Moakher , Thierry Artières

Deep neural networks are the most commonly used function approximators in offline reinforcement learning. Prior works have shown that neural nets trained with TD-learning and gradient descent can exhibit implicit regularization that can be…

Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly…

Machine Learning · Computer Science 2026-05-01 Francesco D'Amico , Dario Bocchi , Matteo Negri

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

Machine Learning · Statistics 2025-10-29 Hannes Matt , Dominik Stöger