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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

Convolutional neural networks (CNNs) have achieved state-of-the-art performance on various tasks in computer vision. However, recent studies demonstrate that these models are vulnerable to carefully crafted adversarial samples and suffer…

Machine Learning · Computer Science 2020-12-15 Xin Li , Xiangrui Li , Deng Pan , Dongxiao Zhu

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically…

Machine Learning · Computer Science 2026-01-14 Katharina Flügel , Daniel Coquelin , Marie Weiel , Charlotte Debus , Achim Streit , Markus Götz

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later…

Machine Learning · Computer Science 2025-04-01 Erwan Fagnou , Paul Caillon , Blaise Delattre , Alexandre Allauzen

Backpropagation (BP) is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, BP is considered as a de-facto choice in a variety of machine learning…

Machine Learning · Computer Science 2024-01-11 Ziang Li , Yiwen Guo , Haodi Liu , Changshui Zhang

The de facto algorithm for training the back pass of a feedforward neural network is backpropagation (BP). The use of almost-everywhere differentiable activation functions made it efficient and effective to propagate the gradient backwards…

Neural and Evolutionary Computing · Computer Science 2022-06-14 John Waldo

With increasing scale in model and dataset size, the training of deep neural networks becomes a massive computational burden. One approach to speed up the training process is Selective Backprop. For this approach, we perform a forward pass…

Machine Learning · Computer Science 2023-12-11 Lukas Balles , Cedric Archambeau , Giovanni Zappella

Back-propagation is a popular machine learning algorithm that uses gradient descent in training neural networks for supervised learning, but can be very slow. A number of algorithms have been developed to speed up convergence and improve…

Neural and Evolutionary Computing · Computer Science 2020-09-29 Ho Ling Li

This paper proposes a new method, that we call VisualBackProp, for visualizing which sets of pixels of the input image contribute most to the predictions made by the convolutional neural network (CNN). The method heavily hinges on exploring…

Computer Vision and Pattern Recognition · Computer Science 2017-05-23 Mariusz Bojarski , Anna Choromanska , Krzysztof Choromanski , Bernhard Firner , Larry Jackel , Urs Muller , Karol Zieba

Current artificial neural networks are trained with parameters encoded as floating point numbers that occupy lots of memory space at inference time. Due to the increase in the size of deep learning models, it is becoming very difficult to…

Machine Learning · Computer Science 2024-08-09 Ben Crulis , Barthelemy Serres , Cyril de Runz , Gilles Venturini

Deep neural network training involves both forward propagation (from features through logits to loss) and backward propagation (from loss through gradients to parameter updates). While perturbations along the forward chain, including…

Machine Learning · Computer Science 2026-05-29 Hua Li

This paper proposes a new method to improve the training efficiency of deep convolutional neural networks. During training, the method evaluates scores to measure how much each layer's parameters change and whether the layer will continue…

Computer Vision and Pattern Recognition · Computer Science 2026-04-28 Giorgio Cruciata , Luca Cruciata , Liliana Lo Presti , Jan Van Gemert , Marco La Cascia

Probabilistic modeling enables combining domain knowledge with learning from data, thereby supporting learning from fewer training instances than purely data-driven methods. However, learning probabilistic models is difficult and has not…

Machine Learning · Computer Science 2017-05-17 Avi Pfeffer

While backpropagation--reverse-mode automatic differentiation--has been extraordinarily successful in deep learning, it requires two passes (forward and backward) through the neural network and the storage of intermediate activations.…

Machine Learning · Computer Science 2025-11-06 Daniel Wang , Evan Markou , Dylan Campbell

Artificial Intelligence algorithms have been steadily increasing in popularity and usage. Deep Learning, allows neural networks to be trained using huge datasets and also removes the need for human extracted features, as it automates the…

Neural and Evolutionary Computing · Computer Science 2020-05-11 Vasco Lopes , Paulo Fazendeiro

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient…

Machine Learning · Computer Science 2023-06-13 Louis Fournier , Stéphane Rivaud , Eugene Belilovsky , Michael Eickenberg , Edouard Oyallon

This paper studies interpretability of convolutional networks by means of saliency maps. Most approaches based on Class Activation Maps (CAM) combine information from fully connected layers and gradient through variants of backpropagation.…

Computer Vision and Pattern Recognition · Computer Science 2024-04-24 Felipe Torres Figueroa , Hanwei Zhang , Ronan Sicre , Yannis Avrithis , Stephane Ayache

We propose Sideways, an approximate backpropagation scheme for training video models. In standard backpropagation, the gradients and activations at every computation step through the model are temporally synchronized. The forward…

Machine Learning · Computer Science 2020-04-01 Mateusz Malinowski , Grzegorz Swirszcz , Joao Carreira , Viorica Patraucean

The classification decisions of neural networks can be misled by small imperceptible perturbations. This work aims to explain the misled classifications using saliency methods. The idea behind saliency methods is to explain the…

Computer Vision and Pattern Recognition · Computer Science 2019-10-22 Jindong Gu , Volker Tresp

The explanation for deep neural networks has drawn extensive attention in the deep learning community over the past few years. In this work, we study the visual saliency, a.k.a. visual explanation, to interpret convolutional neural…

Computer Vision and Pattern Recognition · Computer Science 2022-04-06 Lin Cheng , Pengfei Fang , Yanjie Liang , Liao Zhang , Chunhua Shen , Hanzi Wang
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