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Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…

Numerical Analysis · Mathematics 2021-01-01 Ronald DeVore , Boris Hanin , Guergana Petrova

Most of convolutional neural networks share the same characteristic: each convolutional layer is followed by a nonlinear activation layer where Rectified Linear Unit (ReLU) is the most widely used. In this paper, we argue that the designed…

Computer Vision and Pattern Recognition · Computer Science 2018-09-03 Gangming Zhao , Zhaoxiang Zhang , He Guan , Peng Tang , Jingdong Wang

Deep Neural nets (NNs) with millions of parameters are at the heart of many state-of-the-art computer vision systems today. However, recent works have shown that much smaller models can achieve similar levels of performance. In this work,…

Computer Vision and Pattern Recognition · Computer Science 2015-07-23 Suraj Srinivas , R. Venkatesh Babu

Learning with neural networks relies on the complexity of the representable functions, but more importantly, the particular assignment of typical parameters to functions of different complexity. Taking the number of activation regions as a…

Machine Learning · Statistics 2021-12-17 Hanna Tseran , Guido Montúfar

Recurrent Neural Network (RNN) and its variations such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), have become standard building blocks for learning online data of sequential nature in many research areas, including…

Computation and Language · Computer Science 2020-05-12 Enmao Diao , Jie Ding , Vahid Tarokh

We propose ReDense as a simple and low complexity way to improve the performance of trained neural networks. We use a combination of random weights and rectified linear unit (ReLU) activation function to add a ReLU dense (ReDense) layer to…

Machine Learning · Computer Science 2020-10-27 Alireza M. Javid , Sandipan Das , Mikael Skoglund , Saikat Chatterjee

Linear Regression and neural networks are widely used to model data. Neural networks distinguish themselves from linear regression with their use of activation functions that enable modeling nonlinear functions. The standard argument for…

Machine Learning · Computer Science 2024-01-02 Anish Lakkapragada

Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut…

Disordered Systems and Neural Networks · Physics 2024-05-06 Carlo Baldassi , Enrico M. Malatesta , Riccardo Zecchina

Deep learning models like Transformers and Convolutional Neural Networks (CNNs) have revolutionized various domains, but their parameter-intensive nature hampers deployment in resource-constrained settings. In this paper, we introduce a…

Machine Learning · Computer Science 2024-01-31 Onur Can Koyun , Behçet Uğur Töreyin

Neural networks have recently become popular for a wide variety of uses, but have seen limited application in safety-critical domains such as robotics near and around humans. This is because it remains an open challenge to train a neural…

Machine Learning · Computer Science 2021-07-19 Long Kiu Chung , Adam Dai , Derek Knowles , Shreyas Kousik , Grace X. Gao

Neural networks are popular and useful in many fields, but they have the problem of giving high confidence responses for examples that are away from the training data. This makes the neural networks very confident in their prediction while…

Machine Learning · Computer Science 2024-10-15 Adrian Barbu , Hongyu Mou

Binary neural networks (BNNs), where both weights and activations are binarized into 1 bit, have been widely studied in recent years due to its great benefit of highly accelerated computation and substantially reduced memory footprint that…

Computer Vision and Pattern Recognition · Computer Science 2021-01-01 Zhuo Su , Linpu Fang , Deke Guo , Dewen Hu , Matti Pietikäinen , Li Liu

In neural network compression, most current methods reduce unnecessary parameters by measuring importance and redundancy. To augment already highly optimized existing solutions, we propose linearity-based compression as a novel way to…

Machine Learning · Computer Science 2025-06-27 Silas Dobler , Florian Lemmerich

In a function approximation with a neural network, an input dataset is mapped to an output index by optimizing the parameters of each hidden-layer unit. For a unary function, we present constraints on the parameters and its second…

Machine Learning · Statistics 2020-06-22 Masayo Inoue , Mana Futamura , Hirokazu Ninomiya

Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…

Machine Learning · Computer Science 2021-12-08 Lorenzo Chicchi , Lorenzo Giambagli , Lorenzo Buffoni , Timoteo Carletti , Marco Ciavarella , Duccio Fanelli

The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter…

Machine Learning · Computer Science 2023-06-13 J. Elisenda Grigsby , Kathryn Lindsey , David Rolnick

Rectified linear unit (ReLU) is a widely used activation function for deep convolutional neural networks. However, because of the zero-hard rectification, ReLU networks miss the benefits from negative values. In this paper, we propose a…

Computer Vision and Pattern Recognition · Computer Science 2018-01-30 Suo Qiu , Xiangmin Xu , Bolun Cai

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows…

Machine Learning · Computer Science 2021-05-27 Yatong Bai , Tanmay Gautam , Yu Gai , Somayeh Sojoudi

Training a neural network (NN) depends on multiple factors, including but not limited to the initial weights. In this paper, we focus on initializing deep NN parameters such that it performs better, comparing to random or zero…

Machine Learning · Computer Science 2020-11-10 Mohamad H. Danesh

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