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We present a simplified computational rule for the back-propagation formulas for artificial neural networks. In this work, we provide a generic two-step rule for the back-propagation algorithm in matrix notation. Moreover, this rule…

Neural and Evolutionary Computing · Computer Science 2023-05-17 Ahmed Boughammoura

Efficient and biologically plausible alternatives to backpropagation in neural network training remain a challenge due to issues such as high computational complexity and additional assumptions about neural networks, which limit scalability…

Machine Learning · Computer Science 2024-03-20 Zeliang Zhang , Jinyang Jiang , Zhuo Liu , Susan Liang , Yijie Peng , Chenliang Xu

Learning an algorithm from examples is a fundamental problem that has been widely studied. Recently it has been addressed using neural networks, in particular by Neural Turing Machines (NTMs). These are fully differentiable computers that…

Machine Learning · Computer Science 2016-03-16 Łukasz Kaiser , Ilya Sutskever

The backpropagation of error algorithm (BP) is impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired proposals for understanding how the brain might learn across…

Machine Learning · Computer Science 2018-11-21 Sergey Bartunov , Adam Santoro , Blake A. Richards , Luke Marris , Geoffrey E. Hinton , Timothy Lillicrap

Many embedded real-time control systems suffer from resource constraints and dynamic workload variations. Although optimal feedback scheduling schemes are in principle capable of maximizing the overall control performance of multitasking…

Other Computer Science · Computer Science 2008-12-18 Feng Xia , Yu-Chu Tian , Youxian Sun , Jinxiang Dong

Training the deep convolutional neural network for computer vision problems is slow and inefficient, especially when it is large and distributed across multiple devices. The inefficiency is caused by the backpropagation algorithm's forward…

Machine Learning · Computer Science 2022-01-20 An Xu , Zhouyuan Huo , Heng Huang

New hardware can substantially increase the speed and efficiency of deep neural network training. To guide the development of future hardware architectures, it is pertinent to explore the hardware and machine learning properties of…

Machine Learning · Computer Science 2021-04-13 Atli Kosson , Vitaliy Chiley , Abhinav Venigalla , Joel Hestness , Urs Köster

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-02-01 Arya Prakash Padhi , Souvik Chakraborty , Anupam Chakrabarti , Rajib Chowdhury

A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a…

Machine Learning · Computer Science 2022-11-08 Luca Pinchetti , Tommaso Salvatori , Yordan Yordanov , Beren Millidge , Yuhang Song , Thomas Lukasiewicz

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…

Machine Learning · Computer Science 2024-12-16 Anselm Paulus , Georg Martius , Vít Musil

This paper introduces Selective-Backprop, a technique that accelerates the training of deep neural networks (DNNs) by prioritizing examples with high loss at each iteration. Selective-Backprop uses the output of a training example's forward…

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…

Optimization and Control · Mathematics 2025-08-26 Xiyan Hu , Titus Parker , Connor Phillips , Yifa Yu

Convolutional Neural Networks (CNNs) are pivotal in computer vision and Big Data analytics but demand significant computational resources when trained on large-scale datasets. Conventional training via back-propagation (BP) with losses like…

Machine Learning · Computer Science 2025-06-03 Aasish Kumar Sharma , Sanjeeb Prashad Pandey , Julian M. Kunkel

The backpropagation algorithm for neural networks is widely felt hard to understand, despite the existence of some well-written explanations and/or derivations. This paper provides a new derivation of this algorithm based on the concept of…

Machine Learning · Computer Science 2022-05-03 Yiping Cheng

The Graphics Processing Unit (GPU) is a powerful tool for parallel computing. In the past years the performance and capabilities of GPUs have increased, and the Compute Unified Device Architecture (CUDA) - a parallel computing architecture…

Computational Physics · Physics 2009-12-17 Ferenc Molnar , Tamas Szakaly , Robert Meszaros , Istvan Lagzi

Recent years have seen deep neural networks (DNNs) becoming wider and deeper to achieve better performance in many applications of AI. Such DNNs however require huge amounts of memory to store weights and intermediate results (e.g.,…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-04-27 Taro Sekiyama , Takashi Imamichi , Haruki Imai , Rudy Raymond

We introduce a Model Predictive Control (MPC) framework for training deep neural networks, systematically unifying the Back-Propagation (BP) and Forward-Forward (FF) algorithms. At the same time, it gives rise to a range of intermediate…

Machine Learning · Computer Science 2024-10-01 Lianhai Ren , Qianxiao Li

Neural network training entails heavy computation with obvious bottlenecks. The Compute Unified Device Architecture (CUDA) programming model allows us to accelerate computation by passing the processing workload from the CPU to the graphics…

Machine Learning · Computer Science 2019-08-22 Sterling Ramroach , Andrew Dhanoo , Brian Cockburn , Ajay Joshi

Deep neural networks are able to learn multi-layered representation via back propagation (BP). Although the gradient boosting decision tree (GBDT) is effective for modeling tabular data, it is non-differentiable with respect to its input,…

Machine Learning · Computer Science 2021-09-28 Zhendong Zhang

Modern representation learning methods often struggle to adapt quickly under non-stationarity because they suffer from catastrophic forgetting and decaying plasticity. Such problems prevent learners from fast adaptation since they may…

Machine Learning · Computer Science 2023-04-28 Mohamed Elsayed , A. Rupam Mahmood