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It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal…

Machine Learning · Computer Science 2023-01-30 Jikai Jin , Zhiyuan Li , Kaifeng Lyu , Simon S. Du , Jason D. Lee

We identify an implicit under-parameterization phenomenon in value-based deep RL methods that use bootstrapping: when value functions, approximated using deep neural networks, are trained with gradient descent using iterated regression onto…

Machine Learning · Computer Science 2021-10-26 Aviral Kumar , Rishabh Agarwal , Dibya Ghosh , Sergey Levine

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Machine Learning · Computer Science 2020-06-16 Mao Li , Yingyi Ma , Xinhua Zhang

We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based…

Machine Learning · Statistics 2021-10-28 Fan Wu , Patrick Rebeschini

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…

Artificial Intelligence · Computer Science 2021-05-05 Paolo Milanesi , Hachem Kadri , Stéphane Ayache , Thierry Artières

We study the implicit regularization of gradient descent towards structured sparsity via a novel neural reparameterization, which we call a diagonally grouped linear neural network. We show the following intriguing property of our…

Machine Learning · Statistics 2023-01-31 Jiangyuan Li , Thanh V. Nguyen , Chinmay Hegde , Raymond K. W. Wong

The notion of implicit bias, or implicit regularization, has been suggested as a means to explain the surprising generalization ability of modern-days overparameterized learning algorithms. This notion refers to the tendency of the…

Machine Learning · Computer Science 2020-12-23 Assaf Dauber , Meir Feder , Tomer Koren , Roi Livni

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

Matrix factorization is a simple and natural test-bed to investigate the implicit regularization of gradient descent. Gunasekar et al. (2017) conjectured that Gradient Flow with infinitesimal initialization converges to the solution that…

Machine Learning · Computer Science 2021-04-13 Zhiyuan Li , Yuping Luo , Kaifeng Lyu

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Machine Learning · Computer Science 2025-10-29 Diego Doimo

In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep…

Machine Learning · Computer Science 2017-09-11 Behnam Neyshabur

While the Implicit Bias(or Implicit Regularization) of standard loss functions has been studied, the optimization geometry induced by discriminative metric-learning objectives remains largely unexplored.To the best of our knowledge, this…

Machine Learning · Computer Science 2026-04-13 Jiawen Li

Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work we provide sharp results for the implicit regularization…

Machine Learning · Computer Science 2023-07-17 Johan S. Wind , Vegard Antun , Anders C. Hansen

Gradient descent dynamics on the deep matrix factorization problem is extensively studied as a simplified theoretical model for deep neural networks. Although the convergence theory for two-layer matrix factorization is well-established, no…

Optimization and Control · Mathematics 2025-11-20 Minrui Luo , Weihang Xu , Xiang Gao , Maryam Fazel , Simon Shaolei Du

Implicit Neural Representations have gained prominence as a powerful framework for capturing complex data modalities, encompassing a wide range from 3D shapes to images and audio. Within the realm of 3D shape representation, Neural Signed…

Computer Vision and Pattern Recognition · Computer Science 2024-08-28 Amine Ouasfi , Adnane Boukhayma

We argue that the optimization plays a crucial role in generalization of deep learning models through implicit regularization. We do this by demonstrating that generalization ability is not controlled by network size but rather by some…

Machine Learning · Computer Science 2017-05-10 Behnam Neyshabur , Ryota Tomioka , Ruslan Salakhutdinov , Nathan Srebro

Referring back to the original text in the course of hierarchical learning is a common human trait that ensures the right direction of learning. The models developed based on the concept of Non-negative Matrix Factorization (NMF), in this…

Machine Learning · Computer Science 2024-05-24 Prasun Dutta , Rajat K. De

The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization;…

Machine Learning · Computer Science 2020-05-06 Mohammad Mahdi Bejani , Mehdi Ghatee

Despite overparameterization, deep networks trained via supervised learning are easy to optimize and exhibit excellent generalization. One hypothesis to explain this is that overparameterized deep networks enjoy the benefits of implicit…

Machine Learning · Computer Science 2021-12-10 Aviral Kumar , Rishabh Agarwal , Tengyu Ma , Aaron Courville , George Tucker , Sergey Levine

Recently there has been significant theoretical progress on understanding the convergence and generalization of gradient-based methods on nonconvex losses with overparameterized models. Nevertheless, many aspects of optimization and…

Machine Learning · Computer Science 2022-09-27 Dominik Stöger , Mahdi Soltanolkotabi