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This paper investigates the double descent phenomenon in two-layer neural networks, focusing on the role of L1 regularization and representation dimensions. It explores an alternative double descent phenomenon, named sparse double descent.…

Machine Learning · Computer Science 2024-01-22 Ya Shi Zhang

The Lottery Ticket Hypothesis continues to have a profound practical impact on the quest for small scale deep neural networks that solve modern deep learning tasks at competitive performance. These lottery tickets are identified by pruning…

Machine Learning · Computer Science 2022-05-06 Rebekka Burkholz

Grokking, the unusual phenomenon for algorithmic datasets where generalization happens long after overfitting the training data, has remained elusive. We aim to understand grokking by analyzing the loss landscapes of neural networks,…

Machine Learning · Computer Science 2023-03-24 Ziming Liu , Eric J. Michaud , Max Tegmark

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…

Machine Learning · Computer Science 2021-05-04 Michael M. Bronstein , Joan Bruna , Taco Cohen , Petar Veličković

Deep learning is currently the most widespread and successful technology in artificial intelligence. It promises to push the frontier of scientific discovery beyond current limits. However, skeptics have worried that deep neural networks…

Machine Learning · Computer Science 2020-03-27 Cameron Buckner

The great success of deep learning shows that its technology contains profound truth, and understanding its internal mechanism not only has important implications for the development of its technology and effective application in various…

Machine Learning · Computer Science 2018-05-23 Dian Lei , Xiaoxiao Chen , Jianfei Zhao

The training dynamics of deep neural networks often defy expectations, even as these models form the foundation of modern machine learning. Two prominent examples are grokking, where test performance improves abruptly long after the…

Machine Learning · Computer Science 2026-01-28 Keitaro Sakamoto , Issei Sato

Grokking, the phenomenon of delayed generalization, is often attributed to the depth and compositional structure of deep neural networks. We study grokking in one of the simplest possible settings: the learning of a linear model with…

Machine Learning · Computer Science 2026-02-10 Nataraj Das , Atreya Vedantam , Chandrashekar Lakshminarayanan

Recent research on the grokking phenomenon has illuminated the intricacies of neural networks' training dynamics and their generalization behaviors. Grokking refers to a sharp rise of the network's generalization accuracy on the test set,…

Machine Learning · Computer Science 2024-05-31 Simin Fan , Razvan Pascanu , Martin Jaggi

A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial…

Machine Learning · Computer Science 2021-12-07 Mohammad Pezeshki , Amartya Mitra , Yoshua Bengio , Guillaume Lajoie

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized.…

Machine Learning · Computer Science 2021-03-12 Fengxiang He , Dacheng Tao

The lottery ticket hypothesis states that sparse subnetworks exist in randomly initialized dense networks that can be trained to the same accuracy as the dense network they reside in. However, the subsequent work has failed to replicate…

Machine Learning · Computer Science 2021-06-15 Jaron Maene , Mingxiao Li , Marie-Francine Moens

Recent advancements in machine learning research, i.e., deep learning, introduced methods that excel conventional algorithms as well as humans in several complex tasks, ranging from detection of objects in images and speech recognition to…

The theory of bias-variance used to serve as a guide for model selection when applying Machine Learning algorithms. However, modern practice has shown success with over-parameterized models that were expected to overfit but did not. This…

Machine Learning · Computer Science 2022-11-21 Luis Sa-Couto , Jose Miguel Ramos , Miguel Almeida , Andreas Wichert

A variety of techniques have been proposed to train machine learning classifiers that are independent of a given feature. While this can be an essential technique for enabling background estimation, it may also be useful for reducing…

High Energy Physics - Phenomenology · Physics 2022-02-09 Aishik Ghosh , Benjamin Nachman

Deep learning research aims at discovering learning algorithms that discover multiple levels of distributed representations, with higher levels representing more abstract concepts. Although the study of deep learning has already led to…

Machine Learning · Computer Science 2013-06-10 Yoshua Bengio

Grokking, a phenomenon where machine learning models generalize long after overfitting, has been primarily observed and studied in algorithmic tasks. This paper explores grokking in real-world datasets using deep neural networks for…

Machine Learning · Computer Science 2024-06-21 Satvik Golechha

Auctions are important mechanisms extensively implemented in various markets, e.g., search engines' keyword auctions, antique auctions, etc. Finding an optimal auction mechanism is extremely difficult due to the constraints of imperfect…

Machine Learning · Computer Science 2025-07-28 Jiayin Liu , Chenglong Zhang

We investigate the phenomenon of grokking -- delayed generalization accompanied by non-monotonic test loss behavior -- in a simple binary logistic classification task, for which "memorizing" and "generalizing" solutions can be strictly…

Machine Learning · Statistics 2025-07-22 Alon Beck , Noam Levi , Yohai Bar-Sinai

Recognition tasks, such as object recognition and keypoint estimation, have seen widespread adoption in recent years. Most state-of-the-art methods for these tasks use deep networks that are computationally expensive and have huge memory…

Computer Vision and Pattern Recognition · Computer Science 2021-04-20 Sharath Girish , Shishira R. Maiya , Kamal Gupta , Hao Chen , Larry Davis , Abhinav Shrivastava