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We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported…

机器学习 · 计算机科学 2023-11-08 Elan Rosenfeld , Andrej Risteski

A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient…

机器学习 · 计算机科学 2018-07-02 Tomaso Poggio , Qianli Liao , Brando Miranda , Andrzej Banburski , Xavier Boix , Jack Hidary

Neural network grokking -- the abrupt memorization-to-generalization transition -- challenges our understanding of learning dynamics. Through finite-size scaling of gradient avalanche dynamics across eight model scales, we find that…

机器学习 · 计算机科学 2026-04-07 Ping Wang

Various methods using machine and deep learning have been proposed to tackle different tasks in predictive process monitoring, forecasting for an ongoing case e.g. the most likely next event or suffix, its remaining time, or an…

机器学习 · 计算机科学 2022-12-14 Jari Peeperkorn , Seppe vanden Broucke , Jochen De Weerdt

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…

机器学习 · 计算机科学 2025-12-05 Hannah Laus , Suzanna Parkinson , Vasileios Charisopoulos , Felix Krahmer , Rebecca Willett

This work investigates the generalization behavior of deep neural networks (DNNs), focusing on the phenomenon of "fooling examples," where DNNs confidently classify inputs that appear random or unstructured to humans. To explore this…

机器学习 · 计算机科学 2025-08-22 Yen-Lung Lai , Zhe Jin

Delayed generalization, termed grokking, in a machine learning calculation occurs when the increase in test accuracy is delayed relative to the training accuracy. This paper examines grokking in the context of a dense neural network trained…

无序系统与神经网络 · 物理学 2026-02-06 Karolina Hutchison , David Yevick

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

机器学习 · 计算机科学 2024-02-21 Elena Agliari , Francesco Alemanno , Miriam Aquaro , Alberto Fachechi

Generalized linear models (GLMs) arise in high-dimensional machine learning, statistics, communications and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing,…

信息论 · 计算机科学 2019-04-01 Jean Barbier , Florent Krzakala , Nicolas Macris , Léo Miolane , Lenka Zdeborová

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or…

机器学习 · 计算机科学 2024-03-06 Darshil Doshi , Aritra Das , Tianyu He , Andrey Gromov

In order to develop complex relationships between their inputs and outputs, deep neural networks train and adjust large number of parameters. To make these networks work at high accuracy, vast amounts of data are needed. Sometimes, however,…

机器学习 · 计算机科学 2022-01-19 Joshua Shunk

It is fundamental to measure model complexity of deep neural networks. The existing literature on model complexity mainly focuses on neural networks with piecewise linear activation functions. Model complexity of neural networks with…

机器学习 · 计算机科学 2020-06-17 Xia Hu , Weiqing Liu , Jiang Bian , Jian Pei

Neural architecture search has attracted wide attentions in both academia and industry. To accelerate it, researchers proposed weight-sharing methods which first train a super-network to reuse computation among different operators, from…

机器学习 · 计算机科学 2020-12-16 Xin Chen , Lingxi Xie , Jun Wu , Longhui Wei , Yuhui Xu , Qi Tian

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking…

机器学习 · 计算机科学 2023-09-06 Vikrant Varma , Rohin Shah , Zachary Kenton , János Kramár , Ramana Kumar

Adversarial training is a widely used method to improve the robustness of deep neural networks (DNNs) over adversarial perturbations. However, it is empirically observed that adversarial training on over-parameterized networks often suffers…

机器学习 · 统计学 2024-01-25 Zhongjie Shi , Fanghui Liu , Yuan Cao , Johan A. K. Suykens

Grokking is a phenomenon where a model trained on an algorithmic task first overfits but, then, after a large amount of additional training, undergoes a phase transition to generalize perfectly. We empirically study the internal structure…

机器学习 · 计算机科学 2023-03-22 William Merrill , Nikolaos Tsilivis , Aman Shukla

Overfitting is one of the most common problems when training deep neural networks on comparatively small datasets. Here, we demonstrate that neural network activation sparsity is a reliable indicator for overfitting which we utilize to…

机器学习 · 计算机科学 2020-02-24 Karim Huesmann , Soeren Klemm , Lars Linsen , Benjamin Risse

Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the…

机器学习 · 计算机科学 2020-02-18 Yu Bai , Jason D. Lee

Overfitting in deep learning has been the focus of a number of recent works, yet its exact impact on the behavior of neural networks is not well understood. This study analyzes overfitting by examining how the distribution of logits alters…

机器学习 · 计算机科学 2019-10-02 Zeju Li , Konstantinos Kamnitsas , Ben Glocker

Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and…

机器学习 · 计算机科学 2019-03-07 Masayoshi Kubo , Ryotaro Banno , Hidetaka Manabe , Masataka Minoji