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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

Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we theoretically explore how data geometry controls this…

Machine Learning · Statistics 2026-05-08 Tongtong Liang , Alexander Cloninger , Rahul Parhi , Yu-Xiang Wang

We propose that learning in deep neural networks proceeds in two phases: a rapid curve fitting phase followed by a slower compression or coarse graining phase. This view is supported by the shared temporal structure of three phenomena:…

High Energy Physics - Theory · Physics 2025-07-28 Robert de Mello Koch , Animik Ghosh

While metric and similarity learning has been extensively studied from several theoretical perspectives, a rigorous understanding of its generalization performance is still lacking. In this paper, we investigate the generalization behavior…

Machine Learning · Statistics 2026-05-19 Junyu Zhou , Puyu Wang , Ding-Xuan Zhou

We examine the role of memorization in deep learning, drawing connections to capacity, generalization, and adversarial robustness. While deep networks are capable of memorizing noise data, our results suggest that they tend to prioritize…

Contrary to most machine learning models, modern deep artificial neural networks typically include multiple components that contribute to regularization. Despite the fact that some (explicit) regularization techniques, such as weight decay…

Computer Vision and Pattern Recognition · Computer Science 2020-11-13 Alex Hernández-García , Peter König

A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional…

Machine Learning · Computer Science 2024-09-24 Devon Jarvis , Richard Klein , Benjamin Rosman , Andrew M. Saxe

Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…

Machine Learning · Computer Science 2019-10-21 Dae Hoon Park , Chiu Man Ho , Yi Chang , Huaqing Zhang

Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of $L_2$…

Machine Learning · Computer Science 2018-10-30 Guodong Zhang , Chaoqi Wang , Bowen Xu , Roger Grosse

Why does training deep neural networks using stochastic gradient descent (SGD) result in a generalization error that does not worsen with the number of parameters in the network? To answer this question, we advocate a notion of effective…

Machine Learning · Computer Science 2019-01-15 Vaishnavh Nagarajan , J. Zico Kolter

Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…

Computation and Language · Computer Science 2018-11-05 Deren Lei , Zichen Sun , Yijun Xiao , William Yang Wang

We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural…

Machine Learning · Computer Science 2024-10-15 Wenlin Chen , Hong Ge

Regularizers help deep neural networks prevent feature co-adaptations. Dropout, as a commonly used regularization technique, stochastically disables neuron activations during network optimization. However, such complete feature disposal can…

Machine Learning · Computer Science 2022-01-25 Tiange Xiang , Chaoyi Zhang , Yang Song , Siqi Liu , Hongliang Yuan , Weidong Cai

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions…

Machine Learning · Computer Science 2026-05-05 Elon Litman , Gabe Guo

We take a geometrical viewpoint and present a unifying view on supervised deep learning with the Bregman divergence loss function - this entails frequent classification and prediction tasks. Motivated by simulations we suggest that there is…

Machine Learning · Computer Science 2021-07-07 Petr Taborsky , Lars Kai Hansen

We study the dynamics of gradient flow with small weight decay on general training losses $F: \mathbb{R}^d \to \mathbb{R}$. Under mild regularity assumptions and assuming convergence of the unregularised gradient flow, we show that the…

Machine Learning · Computer Science 2025-11-06 Etienne Boursier , Scott Pesme , Radu-Alexandru Dragomir

Graph Neural Networks (GNNs) are currently dominating in modeling graph-structure data, while their high reliance on graph structure for inference significantly impedes them from widespread applications. By contrast, Graph-regularized MLPs…

Despite the remarkable capabilities of modern large language models (LLMs), the mechanisms behind their problem-solving abilities remain elusive. In this work, we aim to better understand how the learning dynamics of LLM finetuning shapes…

Machine Learning · Computer Science 2024-11-19 Katie Kang , Amrith Setlur , Dibya Ghosh , Jacob Steinhardt , Claire Tomlin , Sergey Levine , Aviral Kumar

The deep learning recipe of casting real-world problems as mathematical optimisation and tackling the optimisation by training deep neural networks using gradient-based optimisation has undoubtedly proven to be a fruitful one. The…

Machine Learning · Statistics 2023-10-24 Mihaela Claudia Rosca

Standard deep-learning pipelines usually choose the network architecture before training and keep it fixed throughout optimization. In contrast, a model can also be adapted by editing its structure during training, for example by pruning…

Machine Learning · Computer Science 2026-05-18 Lute Lillo , Nick Cheney