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Given a neural network, training data, and a threshold, it was known that it is NP-hard to find weights for the neural network such that the total error is below the threshold. We determine the algorithmic complexity of this fundamental…

Computational Complexity · Computer Science 2021-11-22 Mikkel Abrahamsen , Linda Kleist , Tillmann Miltzow

The backpropagation algorithm, which had been originally introduced in the 1970s, is the workhorse of learning in neural networks. This backpropagation algorithm makes use of the famous machine learning algorithm known as Gradient Descent,…

Machine Learning · Computer Science 2018-02-02 Varun Ranganathan , S. Natarajan

Backpropagation is the core learning mechanism underlying deep learning. However, whether and how this algorithm is implemented in the brain remains highly debated. In particular, while forward activations of pretrained models reliably map…

We introduce the chi-square test neural network: a single hidden layer backpropagation neural network using chi-square test theorem to redefine the cost function and the error function. The weights and thresholds are modified using standard…

Machine Learning · Computer Science 2018-09-05 Yuan Wu , Lingling Li , Lian Li

How can we build agents that keep learning from experience, quickly and efficiently, after their initial training? Here we take inspiration from the main mechanism of learning in biological brains: synaptic plasticity, carefully tuned by…

Neural and Evolutionary Computing · Computer Science 2018-08-01 Thomas Miconi , Jeff Clune , Kenneth O. Stanley

The brain cortex, which processes visual, auditory and sensory data in the brain, is known to have many recurrent connections within its layers and from higher to lower layers. But, in the case of machine learning with neural networks, it…

Machine Learning · Computer Science 2020-10-22 Sebastian Sanokowski

Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity…

Dynamical Systems · Mathematics 2025-08-29 Eugene Tan , Débora Corrêa , Thomas Stemler , Michael Small

Training neural networks for neuromorphic deployment is non-trivial. There have been a variety of approaches proposed to adapt back-propagation or back-propagation-like algorithms appropriate for training. Considering that these networks…

The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward…

Neural and Evolutionary Computing · Computer Science 2025-04-01 Niccolò Tosato , Lorenzo Basile , Emanuele Ballarin , Giuseppe de Alteriis , Alberto Cazzaniga , Alessio Ansuini

Realization of deep learning with coherent optical field has attracted remarkably attentions presently, which benefits on the fact that optical matrix manipulation can be executed at speed of light with inherent parallel computation as well…

Signal Processing · Electrical Eng. & Systems 2020-03-19 Yong-Liang Xiao , Rongguang Liang , Jianxin Zhong , Xianyu Su , Zhisheng You

Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing and controlling the network Jacobian. We first provide a…

Machine Learning · Computer Science 2026-02-12 Alex Massucco , Davide Murari , Carola-Bibiane Schönlieb

Deep neural networks are powerful parametric models that can be trained efficiently using the backpropagation algorithm. Stochastic neural networks combine the power of large parametric functions with that of graphical models, which makes…

Machine Learning · Computer Science 2016-02-26 Shixiang Gu , Sergey Levine , Ilya Sutskever , Andriy Mnih

Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded…

Machine Learning · Computer Science 2022-07-20 Jacob Renn , Ian Sotnek , Benjamin Harvey , Brian Caffo

In this paper we investigate the supervised backpropagation training of multilayer neural networks from a dynamical systems point of view. We discuss some links with the qualitative theory of differential equations and introduce the overfly…

Machine Learning · Computer Science 2019-01-15 Alexei Tsygvintsev

Finding biologically plausible alternatives to back-propagation of errors is a fundamentally important challenge in artificial neural network research. In this paper, we propose a learning algorithm called error-driven Local Representation…

Neural and Evolutionary Computing · Computer Science 2018-11-19 Alexander G. Ororbia , Ankur Mali

Classical neural networks achieve only limited convergence in hard problems such as XOR or parity when the number of hidden neurons is small. With the motivation to improve the success rate of neural networks in these problems, we propose a…

Neural and Evolutionary Computing · Computer Science 2024-02-27 Kristína Malinovská , Slavomír Holenda , Ľudovít Malinovský

Empowered by the backpropagation (BP) algorithm, deep neural networks have dominated the race in solving various cognitive tasks. The restricted training pattern in the standard BP requires end-to-end error propagation, causing large memory…

Machine Learning · Computer Science 2022-05-17 Wenzhe Guo , Mohammed E Fouda , Ahmed M. Eltawil , Khaled N. Salama

The ever-growing demand for further advances in artificial intelligence motivated research on unconventional computation based on analog physical devices. While such computation devices mimic brain-inspired analog information processing,…

Neural and Evolutionary Computing · Computer Science 2022-05-02 Mitsumasa Nakajima , Katsuma Inoue , Kenji Tanaka , Yasuo Kuniyoshi , Toshikazu Hashimoto , Kohei Nakajima

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations…

Machine Learning · Computer Science 2024-10-24 Chia-Hsiang Kao , Bharath Hariharan

Despite the widespread adoption of Backpropagation algorithm-based Deep Neural Networks, the biological infeasibility of the BP algorithm could potentially limit the evolution of new DNN models. To find a biologically plausible algorithm to…

Neural and Evolutionary Computing · Computer Science 2024-02-29 Jian-Hui Chen , Cheng-Lin Liu , Zuoren Wang