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This work finds the analytical expression of the global minima of a deep linear network with weight decay and stochastic neurons, a fundamental model for understanding the landscape of neural networks. Our result implies that the origin is…

Machine Learning · Statistics 2023-06-14 Liu Ziyin , Botao Li , Xiangming Meng

Graph neural networks (GNNs) have been demonstrated to achieve state-of-the-art for a number of graph-based learning tasks, which leads to a rise in their employment in various domains. However, it has been shown that GNNs may inherit and…

Machine Learning · Computer Science 2022-05-23 O. Deniz Kose , Yanning Shen

Weight decay (WD) is a traditional regularization technique in deep learning, but despite its ubiquity, its behavior is still an area of active research. Golatkar et al. have recently shown that WD only matters at the start of the training…

Machine Learning · Computer Science 2020-12-29 Johan Bjorck , Kilian Weinberger , Carla Gomes

Intriguing empirical evidence exists that deep learning can work well with exoticschedules for varying the learning rate. This paper suggests that the phenomenon may be due to Batch Normalization or BN, which is ubiquitous and provides…

Machine Learning · Computer Science 2019-11-22 Zhiyuan Li , Sanjeev Arora

The complexity of deep neural network algorithms for hardware implementation can be much lowered by optimizing the word-length of weights and signals. Direct quantization of floating-point weights, however, does not show good performance…

Machine Learning · Computer Science 2016-01-08 Wonyong Sung , Sungho Shin , Kyuyeon Hwang

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…

Machine Learning · Computer Science 2025-12-05 Hannah Laus , Suzanna Parkinson , Vasileios Charisopoulos , Felix Krahmer , Rebecca Willett

Why do neural networks trained with large learning rates for a longer time often lead to better generalization? In this paper, we delve into this question by examining the relation between training and testing loss in neural networks.…

Machine Learning · Computer Science 2024-01-23 Yinuo Ren , Chao Ma , Lexing Ying

Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of…

Machine Learning · Computer Science 2018-07-02 Amal Rannen Triki , Maxim Berman , Matthew B. Blaschko

There is a significant performance gap between Binary Neural Networks (BNNs) and floating point Deep Neural Networks (DNNs). We propose to improve the binary training method, by introducing a new regularization function that encourages…

Machine Learning · Computer Science 2020-04-22 Sajad Darabi , Mouloud Belbahri , Matthieu Courbariaux , Vahid Partovi Nia

The success of deep neural networks is in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice, as they improve generalization…

Machine Learning · Computer Science 2020-06-15 Yonatan Dukler , Quanquan Gu , Guido Montúfar

Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…

Machine Learning · Computer Science 2022-03-22 Jiaye Teng , Jianhao Ma , Yang Yuan

The weight initialization and the activation function of deep neural networks have a crucial impact on the performance of the training procedure. An inappropriate selection can lead to the loss of information of the input during forward…

Machine Learning · Statistics 2019-05-28 Soufiane Hayou , Arnaud Doucet , Judith Rousseau

Training of deep neural networks heavily depends on the data distribution. In particular, the networks easily suffer from class imbalance. The trained networks would recognize the frequent classes better than the infrequent classes. To…

Computer Vision and Pattern Recognition · Computer Science 2020-03-12 Byungju Kim , Junmo Kim

Batch Normalization (BatchNorm) is a widely adopted technique that enables faster and more stable training of deep neural networks (DNNs). Despite its pervasiveness, the exact reasons for BatchNorm's effectiveness are still poorly…

Machine Learning · Statistics 2019-04-16 Shibani Santurkar , Dimitris Tsipras , Andrew Ilyas , Aleksander Madry

Deep neural networks have been used in various machine learning applications and achieved tremendous empirical successes. However, training deep neural networks is a challenging task. Many alternatives have been proposed in place of…

Machine Learning · Computer Science 2020-09-09 Yeonjong Shin

Deep neural networks often work well when they are over-parameterized and trained with a massive amount of noise and regularization, such as weight decay and dropout. Although dropout is widely used as a regularization technique for fully…

Computer Vision and Pattern Recognition · Computer Science 2018-10-31 Golnaz Ghiasi , Tsung-Yi Lin , Quoc V. Le

Deep neural networks (DNNs) can be made hardware-efficient by reducing the numerical precision of the weights and activations of the network and by improving the network's resilience to noise. However, this gain in efficiency often comes at…

Regularization is essential when training large neural networks. As deep neural networks can be mathematically interpreted as universal function approximators, they are effective at memorizing sampling noise in the training data. This…

Machine Learning · Computer Science 2015-01-06 Jan Rudy , Weiguang Ding , Daniel Jiwoong Im , Graham W. Taylor

Unsupervised pretraining and dropout have been well studied, especially with respect to regularization and output consistency. However, our understanding about the explicit convergence rates of the parameter estimates, and their dependence…

Machine Learning · Computer Science 2017-02-23 Vamsi K. Ithapu , Sathya Ravi , Vikas Singh

Small neural networks with a constrained number of trainable parameters, can be suitable resource-efficient candidates for many simple tasks, where now excessively large models are used. However, such models face several problems during the…

Machine Learning · Computer Science 2021-09-21 Alexander Kovalenko , Pavel Kordík , Magda Friedjungová