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The goal of this document is to provide a pedagogical introduction to the main concepts underpinning the training of deep neural networks using gradient descent; a process known as backpropagation. Although we focus on a very influential…

Machine Learning · Computer Science 2018-11-30 Laurent Boué

Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…

Machine Learning · Computer Science 2025-09-09 Viet Hoang Pham , Hyo-Sung Ahn

Deep learning has revolutionized industries like computer vision, natural language processing, and speech recognition. However, back propagation, the main method for training deep neural networks, faces challenges like computational…

Machine Learning · Computer Science 2023-08-15 Gokulprasath R

The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage…

Machine Learning · Computer Science 2021-12-20 Dongpin Oh , Bonggun Shin

In this study, we investigate how the updating of weights during forward operation and the computation of gradients during backpropagation impact the optimization process, training procedure, and overall performance of the neural network,…

Machine Learning · Computer Science 2024-07-10 Amir Noorizadegan , D. L. Young , Y. C. Hon , C. S. Chen

Deep Neural Networks (DNNs) are typically trained by backpropagation in a batch learning setting, which requires the entire training data to be made available prior to the learning task. This is not scalable for many real-world scenarios…

Machine Learning · Computer Science 2017-11-13 Doyen Sahoo , Quang Pham , Jing Lu , Steven C. H. Hoi

Integrating model-based machine learning methods into deep neural architectures allows one to leverage both the expressive power of deep neural nets and the ability of model-based methods to incorporate domain-specific knowledge. In…

Machine Learning · Computer Science 2020-12-10 Chonghyuk Song , Eunseok Kim , Inwook Shim

In this paper, we present MLEANN (Meta-Learning Evolutionary Artificial Neural Network), an automatic computational framework for the adaptive optimization of artificial neural networks wherein the neural network architecture, activation…

Artificial Intelligence · Computer Science 2007-05-23 Ajith Abraham

Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…

Machine Learning · Computer Science 2020-06-26 Mauricio E. Tano , Gavin D. Portwood , Jean C. Ragusa

Binary Neural Networks (BNNs) significantly reduce computational complexity and memory usage in machine and deep learning by representing weights and activations with just one bit. However, most existing training algorithms for BNNs rely on…

Machine Learning · Computer Science 2025-12-08 Luca Colombo , Fabrizio Pittorino , Manuel Roveri

Compared to Multilayer Neural Networks with real weights, Binary Multilayer Neural Networks (BMNNs) can be implemented more efficiently on dedicated hardware. BMNNs have been demonstrated to be effective on binary classification tasks with…

Neural and Evolutionary Computing · Computer Science 2015-03-24 Zhiyong Cheng , Daniel Soudry , Zexi Mao , Zhenzhong Lan

Deep learning, as a highly efficient method for metasurface inverse design, commonly use simulation data to train deep neural networks (DNNs) that can map desired functionalities to proper metasurface designs. However, the assumptions and…

Signal Processing · Electrical Eng. & Systems 2023-08-07 Jingxin Zhang , Jiawei Xi , Peixing Li , Ray C. C. Cheung , Alex M. H. Wong , Jensen Li

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…

Machine Learning · Statistics 2019-05-09 Arild Nøkland , Lars Hiller Eidnes

The effectiveness of deep neural networks (DNN) in vision, speech, and language processing has prompted a tremendous demand for energy-efficient high-performance DNN inference systems. Due to the increasing memory intensity of most DNN…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-15 Skanda Koppula , Lois Orosa , Abdullah Giray Yağlıkçı , Roknoddin Azizi , Taha Shahroodi , Konstantinos Kanellopoulos , Onur Mutlu

Natural Language Processing (NLP) is widely used in fields like machine translation and sentiment analysis. However, traditional NLP models struggle with accuracy and efficiency. This paper introduces Deep Convolutional Neural Networks…

Computation and Language · Computer Science 2024-12-23 Chang Weng , Scott Rood , Mehdi Ali Ramezani , Amir Aslani , Reza Zarrab , Wang Zwuo , Sanjeev Salimans , Tim Satheesh

Developing strong AI signifies the arrival of technological singularity, contributing greatly to advancing human civilization and resolving social issues. Neural networks (NNs) and deep learning, which utilize NNs, are expected to lead to…

Machine Learning · Computer Science 2024-09-09 Kei Itoh

Well-trained deep neural networks (DNNs) treat all test samples equally during prediction. Adaptive DNN inference with early exiting leverages the observation that some test examples can be easier to predict than others. This paper presents…

Neural network training is inherently sequential where the layers finish the forward propagation in succession, followed by the calculation and back-propagation of gradients (based on a loss function) starting from the last layer. The…

Machine Learning · Computer Science 2023-12-01 Vahid Janfaza , Shantanu Mandal , Farabi Mahmud , Abdullah Muzahid

Error backpropagation is a highly effective mechanism for learning high-quality hierarchical features in deep networks. Updating the features or weights in one layer, however, requires waiting for the propagation of error signals from…

Neural and Evolutionary Computing · Computer Science 2017-11-21 Hesham Mostafa , Vishwajith Ramesh , Gert Cauwenberghs

Autoregressive (AR) models remain widely used in time series analysis due to their interpretability, but convencional parameter estimation methods can be computationally expensive and prone to convergence issues. This paper proposes a…

Machine Learning · Statistics 2026-03-20 Anaísa Lucena , Ana Martins , Armando J. Pinho , Sónia Gouveia