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Deep learning models are yielding increasingly better performances thanks to multiple factors. To be successful, model may have large number of parameters or complex architectures and be trained on large dataset. This leads to large…

Machine Learning · Computer Science 2022-12-20 Jean-Roch Vlimant , Junqi Yin

Modern deep learning models employ considerably more parameters than required to fit the training data. Whereas conventional statistical wisdom suggests such models should drastically overfit, in practice these models generalize remarkably…

Machine Learning · Statistics 2020-08-18 Ben Adlam , Jeffrey Pennington

Promising resolutions of the generalization puzzle observe that the actual number of parameters in a deep network is much smaller than naive estimates suggest. The renormalization group is a compelling example of a problem which has very…

Machine Learning · Computer Science 2020-12-08 Anita de Mello Koch , Ellen de Mello Koch , Robert de Mello Koch

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks'…

In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero training loss, with their parameters hardly varying. In…

Optimization and Control · Mathematics 2020-01-08 Lenaic Chizat , Edouard Oyallon , Francis Bach

While deep learning has outperformed other methods for various tasks, theoretical frameworks that explain its reason have not been fully established. To address this issue, we investigate the excess risk of two-layer ReLU neural networks in…

Machine Learning · Statistics 2022-06-07 Shunta Akiyama , Taiji Suzuki

How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…

Neural and Evolutionary Computing · Computer Science 2019-10-02 Xin Dong , Shangyu Chen , Sinno Jialin Pan

Why heavily parameterized neural networks (NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency…

Machine Learning · Computer Science 2021-05-26 Yaoyu Zhang , Tao Luo , Zheng Ma , Zhi-Qin John Xu

Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

Classical Analysis and ODEs · Mathematics 2022-11-22 Matthew Thorpe , Yves van Gennip

Modern neural networks often have great expressive power and can be trained to overfit the training data, while still achieving a good test performance. This phenomenon is referred to as "benign overfitting". Recently, there emerges a line…

Machine Learning · Computer Science 2022-06-15 Yuan Cao , Zixiang Chen , Mikhail Belkin , Quanquan Gu

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been…

Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…

Machine Learning · Computer Science 2020-07-28 Surbhi Goel , Adam Klivans , Frederic Koehler

We explore some mathematical features of the loss landscape of overparameterized neural networks. A priori one might imagine that the loss function looks like a typical function from $\mathbb{R}^n$ to $\mathbb{R}$ - in particular,…

Machine Learning · Computer Science 2018-04-27 Y Cooper

Artificial neural networks have gone through a recent rise in popularity, achieving state-of-the-art results in various fields, including image classification, speech recognition, and automated control. Both the performance and…

Neural and Evolutionary Computing · Computer Science 2016-11-08 Sean C. Smithson , Guang Yang , Warren J. Gross , Brett H. Meyer

Large neural networks have proved remarkably effective in modern deep learning practice, even in the overparametrized regime where the number of active parameters is large relative to the sample size. This contradicts the classical…

Machine Learning · Computer Science 2023-08-01 Huiyuan Wang , Wei Lin

Overparameterized neural networks (NNs) are observed to generalize well even when trained to perfectly fit noisy data. This phenomenon motivated a large body of work on "benign overfitting", where interpolating predictors achieve…

Machine Learning · Computer Science 2024-03-22 Guy Kornowski , Gilad Yehudai , Ohad Shamir

We present a theoretically well-founded deep learning algorithm for nonparametric regression. It uses over-parametrized deep neural networks with logistic activation function, which are fitted to the given data via gradient descent. We…

Statistics Theory · Mathematics 2025-04-14 Michael Kohler , Adam Krzyzak

Human vision models are at the core of image processing. For instance, classical approaches to the problem of image quality are based on models that include knowledge about human vision. However, nowadays, deep learning approaches have…

Computer Vision and Pattern Recognition · Computer Science 2025-05-20 Jorge Vila-Tomás , Pablo Hernández-Cámara , Valero Laparra , Jesús Malo

A practical limitation of deep neural networks is their high degree of specialization to a single task and visual domain. Recently, inspired by the successes of transfer learning, several authors have proposed to learn instead universal,…

Computer Vision and Pattern Recognition · Computer Science 2018-03-28 Sylvestre-Alvise Rebuffi , Hakan Bilen , Andrea Vedaldi

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the…

Machine Learning · Computer Science 2017-02-28 Chiyuan Zhang , Samy Bengio , Moritz Hardt , Benjamin Recht , Oriol Vinyals