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Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…

Optimization and Control · Mathematics 2025-12-19 Enrique Zuazua

Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data. We study this phenomenon by analysing the dynamics and the performance of over-parameterised two-layer neural…

Machine Learning · Statistics 2022-03-28 Sebastian Goldt , Madhu S. Advani , Andrew M. Saxe , Florent Krzakala , Lenka Zdeborová

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question…

Computation and Language · Computer Science 2021-09-06 Paul Michel

The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that…

Machine Learning · Computer Science 2020-04-14 Andrzej Banburski , Qianli Liao , Brando Miranda , Lorenzo Rosasco , Fernanda De La Torre , Jack Hidary , Tomaso Poggio

Analysis of over-parameterized neural networks has drawn significant attention in recentyears. It was shown that such systems behave like convex systems under various restrictedsettings, such as for two-level neural networks, and when…

Machine Learning · Computer Science 2019-11-19 Cong Fang , Yihong Gu , Weizhong Zhang , Tong Zhang

What might sound like the beginning of a joke has become an attractive prospect for many cognitive scientists: the use of deep neural network models (DNNs) as models of human behavior in perceptual and cognitive tasks. Although DNNs have…

Artificial Intelligence · Computer Science 2020-05-06 Wei Ji Ma , Benjamin Peters

Deep learning models learn to fit training data while they are highly expected to generalize well to testing data. Most works aim at finding such models by creatively designing architectures and fine-tuning parameters. To adapt to…

Computer Vision and Pattern Recognition · Computer Science 2018-09-10 Tianyang Wang , Jun Huan , Bo Li

Neural networks can be powerful function approximators, which are able to model high-dimensional feature distributions from a subset of examples drawn from the target distribution. Naturally, they perform well at generalizing within the…

Machine Learning · Computer Science 2021-08-06 Aaron Eisermann , Jae Hee Lee , Cornelius Weber , Stefan Wermter

Deep neural networks with millions of parameters may suffer from poor generalization due to overfitting. To mitigate the issue, we propose a new regularization method that penalizes the predictive distribution between similar samples. In…

Machine Learning · Computer Science 2020-04-08 Sukmin Yun , Jongjin Park , Kimin Lee , Jinwoo Shin

For Internet applications like sponsored search, cautions need to be taken when using machine learning to optimize their mechanisms (e.g., auction) since self-interested agents in these applications may change their behaviors (and thus the…

Machine Learning · Computer Science 2014-10-14 Haifang Li , Fei Tian , Wei Chen , Tao Qin , Tie-Yan Liu

With a goal of understanding what drives generalization in deep networks, we consider several recently suggested explanations, including norm-based control, sharpness and robustness. We study how these measures can ensure generalization,…

Machine Learning · Computer Science 2017-07-07 Behnam Neyshabur , Srinadh Bhojanapalli , David McAllester , Nathan Srebro

The practice of deep learning has shown that neural networks generalize remarkably well even with an extreme number of learned parameters. This appears to contradict traditional statistical wisdom, in which a trade-off between model…

Machine Learning · Computer Science 2023-02-21 Yifei Wang , Yixuan Hua , Emmanuel Candés , Mert Pilanci

While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…

Machine Learning · Computer Science 2020-10-26 Yoonho Lee , Juho Lee , Sung Ju Hwang , Eunho Yang , Seungjin Choi

Continual Learning has inspired a plethora of approaches and evaluation settings; however, the majority of them overlooks the properties of a practical scenario, where the data stream cannot be shaped as a sequence of tasks and offline…

Machine Learning · Statistics 2020-10-23 Pietro Buzzega , Matteo Boschini , Angelo Porrello , Davide Abati , Simone Calderara

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

Machine Learning · Computer Science 2025-05-09 Haiyun He , Ziv Goldfeld

Neural networks (NNs) are known to exhibit simplicity bias where they tend to prefer learning 'simple' features over more 'complex' ones, even when the latter may be more informative. Simplicity bias can lead to the model making biased…

Machine Learning · Computer Science 2023-10-11 Bhavya Vasudeva , Kameron Shahabi , Vatsal Sharan

Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…

Machine Learning · Computer Science 2026-02-02 Christiaan P. Opperman , Anna S. Bosman , Katherine M. Malan

Along with the rapid development of deep learning in practice, the theoretical explanations for its success become urgent. Generalization and expressivity are two widely used measurements to quantify theoretical behaviors of deep learning.…

Machine Learning · Computer Science 2018-03-26 Shao-Bo Lin

Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on…

Machine Learning · Statistics 2018-06-18 Mikhail Belkin , Siyuan Ma , Soumik Mandal

Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we…

Machine Learning · Computer Science 2022-12-13 Qianyi Li , Haim Sompolinsky