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Convolutional neural networks (CNNs) perform well on problems such as handwriting recognition and image classification. However, the performance of the networks is often limited by budget and time constraints, particularly when trying to…

Computer Vision and Pattern Recognition · Computer Science 2014-09-23 Benjamin Graham

The $\ell_{1\text{-}2}$ regularization method has a strong sparsity promoting capability in approaching sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. This…

Optimization and Control · Mathematics 2026-03-04 Yaohua Hu , Hao Wang , Xiaoqi Yang

We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed…

Computer Vision and Pattern Recognition · Computer Science 2020-05-26 Yoojin Choi , Mostafa El-Khamy , Jungwon Lee

A low precision deep neural network training technique for producing sparse, ternary neural networks is presented. The technique incorporates hard- ware implementation costs during training to achieve significant model compression for…

Computer Vision and Pattern Recognition · Computer Science 2017-10-11 Julian Faraone , Nicholas Fraser , Giulio Gambardella , Michaela Blott , Philip H. W. Leong

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

Statistics Theory · Mathematics 2021-08-10 Ilsang Ohn , Yongdai Kim

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…

Machine Learning · Computer Science 2023-09-06 Jiaxi Ying , José Vinícius de M. Cardoso , Daniel P. Palomar

Regularization plays a major role in modern deep learning. From classic techniques such as L1,L2 penalties to other noise-based methods such as Dropout, regularization often yields better generalization properties by avoiding overfitting.…

Machine Learning · Statistics 2021-06-08 Soufiane Hayou , Fadhel Ayed

Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic…

Machine Learning · Computer Science 2025-02-10 Chris Kolb , Tobias Weber , Bernd Bischl , David Rügamer

Regularization techniques such as $\mathcal{L}_1$ and $\mathcal{L}_2$ regularizers are effective in sparsifying neural networks (NNs). However, to remove a certain neuron or channel in NNs, all weight elements related to that neuron or…

Machine Learning · Computer Science 2023-05-31 Ali Haisam Muhammad Rafid , Adrian Sandu

Convolutional neural networks (CNNs) are reported to be overparametrized. The search for optimal (minimal) and sufficient architecture is an NP-hard problem as the hyperparameter space for possible network configurations is vast. Here, we…

Computer Vision and Pattern Recognition · Computer Science 2024-04-09 Tin Barisin , Illia Horenko

We propose a sparse reconstruction framework for solving inverse problems. Opposed to existing sparse regularization techniques that are based on frame representations, we train an encoder-decoder network by including an $\ell^1$-penalty.…

Numerical Analysis · Mathematics 2019-08-07 Daniel Obmann , Johannes Schwab , Markus Haltmeier

Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either…

Image and Video Processing · Electrical Eng. & Systems 2022-06-10 Andreas Kofler , Christian Wald , Tobias Schaeffter , Markus Haltmeier , Christoph Kolbitsch

This paper presents an algorithm for efficient training of sparse linear models with elastic net regularization. Extending previous work on delayed updates, the new algorithm applies stochastic gradient updates to non-zero features only,…

Machine Learning · Computer Science 2015-07-06 Zachary C. Lipton , Charles Elkan

Dynamic Sparse Training (DST) methods train neural networks by maintaining sparsity while dynamically adapting the network topology. Despite the promise of reduced computation, DST methods converge significantly slower than dense training,…

Machine Learning · Computer Science 2026-05-28 Mohammed Adnan , Rohan Jain , Tom Jacobs , Ekansh Sharma , Rahul G. Krishnan , Rebekka Burkholz , Yani Ioannou

This paper proposes an algorithm (RMDA) for training neural networks (NNs) with a regularization term for promoting desired structures. RMDA does not incur computation additional to proximal SGD with momentum, and achieves variance…

Machine Learning · Computer Science 2022-05-02 Zih-Syuan Huang , Ching-pei Lee

This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…

Optimization and Control · Mathematics 2025-06-16 Long Li , Liang Ding

Sparse optimization is a fundamental challenge in various practical applications. A popular approach to sparse optimization is $\ell_p$ regularization. However, it may encounter optimization instability due to the unbounded gradients when…

Machine Learning · Computer Science 2026-05-29 Huangyu Xu , Jingqin Yang , Qianqian Xu , Jiaye Teng

The most widely used form of convolutional sparse coding uses an $\ell_1$ regularization term. While this approach has been successful in a variety of applications, a limitation of the $\ell_1$ penalty is that it is homogeneous across the…

Computer Vision and Pattern Recognition · Computer Science 2017-11-09 Brendt Wohlberg

Convolutional neural networks have been achieving the best possible accuracies in many visual pattern classification problems. However, due to the model capacity required to capture such representations, they are often oversensitive to…

Computer Vision and Pattern Recognition · Computer Science 2020-01-27 Yahia Assiri

Despite its nonconvex nature, $\ell_0$ sparse approximation is desirable in many theoretical and application cases. We study the $\ell_0$ sparse approximation problem with the tool of deep learning, by proposing Deep $\ell_0$ Encoders. Two…

Machine Learning · Computer Science 2015-11-24 Zhangyang Wang , Qing Ling , Thomas S. Huang