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Backpropagation is the default learning rule for artificial neural networks and is often treated as the settled approach whenever differentiability is available. In this work, we revisit this convention through a theoretical lens of sample…

Machine Learning · Statistics 2026-05-28 Yibo Jacky Zhang , Zeyu Tang , Sanmi Koyejo

Back-propagation (BP) is widely used learning algorithm for neural network optimization. However, BP requires enormous computation cost and is too slow to train in central processing unit (CPU). Therefore current neural network optimizaiton…

Machine Learning · Computer Science 2023-08-22 Ryoungwoo Jang

We propose Path-CNN, a method for the segmentation of centerlines of tubular structures by embedding convolutional neural networks (CNNs) into the progressive minimal path method. Minimal path methods are widely used for topology-aware…

Computer Vision and Pattern Recognition · Computer Science 2022-04-06 Wei Liao

Channel Pruning, widely used for accelerating Convolutional Neural Networks, is an NP-hard problem due to the inter-layer dependency of channel redundancy. Existing methods generally ignored the above dependency for computation simplicity.…

Machine Learning · Computer Science 2019-03-28 Yuefu Zhou , Ya Zhang , Yanfeng Wang , Qi Tian

In this paper, we aim at providing an introduction to the gradient descent based optimization algorithms for learning deep neural network models. Deep learning models involving multiple nonlinear projection layers are very challenging to…

Machine Learning · Computer Science 2019-03-12 Jiawei Zhang

Building on our prior explorations of convolutional neural networks (CNNs) for financial data processing, this paper introduces two significant enhancements to refine our CNN model's predictive performance and robustness for financial…

Computational Finance · Quantitative Finance 2024-08-23 Sina Montazeri , Haseebullah Jumakhan , Sonia Abrasiabian , Amir Mirzaeinia

Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often…

Machine Learning · Computer Science 2021-10-26 Guhyun Kim , Doo Seok Jeong

After a more than decade-long period of relatively little research activity in the area of recurrent neural networks, several new developments will be reviewed here that have allowed substantial progress both in understanding and in…

Machine Learning · Computer Science 2012-12-17 Yoshua Bengio , Nicolas Boulanger-Lewandowski , Razvan Pascanu

Traditional knowledge distillation focuses on aligning the student's predicted probabilities with both ground-truth labels and the teacher's predicted probabilities. However, the transition to predicted probabilities from logits would…

Computer Vision and Pattern Recognition · Computer Science 2026-04-08 Penghui Yang , Chen-Chen Zong , Sheng-Jun Huang , Lei Feng , Bo An

This paper proposes a fractional order gradient method for the backward propagation of convolutional neural networks. To overcome the problem that fractional order gradient method cannot converge to real extreme point, a simplified…

Optimization and Control · Mathematics 2020-01-07 Dian Sheng , Yiheng Wei , Yuquan Chen , Yong Wang

The backpropagation algorithm remains the dominant and most successful method for training deep neural networks (DNNs). At the same time, training DNNs at scale comes at a significant computational cost and therefore a high carbon…

Machine Learning · Computer Science 2025-11-12 Sander Dalm , Joshua Offergeld , Nasir Ahmad , Marcel van Gerven

We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. The method requires only simple processing of existing stochastic…

Machine Learning · Computer Science 2020-08-26 Dong Lao , Peihao Zhu , Peter Wonka , Ganesh Sundaramoorthi

Saliency methods seek to explain the predictions of a model by producing an importance map across each input sample. A popular class of such methods is based on backpropagating a signal and analyzing the resulting gradient. Despite much…

Computer Vision and Pattern Recognition · Computer Science 2020-04-07 Sylvestre-Alvise Rebuffi , Ruth Fong , Xu Ji , Andrea Vedaldi

Convolutional neural networks (CNNs) have demonstrated their superiority in numerous computer vision tasks, yet their computational cost results prohibitive for many real-time applications such as pedestrian detection which is usually…

Computer Vision and Pattern Recognition · Computer Science 2018-01-03 Farzin Ghorban , Javier Marín , Yu Su , Alessandro Colombo , Anton Kummert

Adopting large-scale AI models in enterprise information systems is often hindered by high training costs and long development cycles, posing a significant managerial challenge. The standard end-to-end backpropagation (BP) algorithm is a…

Machine Learning · Computer Science 2026-02-04 Ming-Yao Ho , Cheng-Kai Wang , You-Teng Lin , Hung-Hsuan Chen

Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative. Treating the coupled variables independently while ignoring the interaction, however, leads to an insufficient optimization…

Machine Learning · Computer Science 2021-06-22 Runqi Wang , Baochang Zhang , Li'an Zhuo , Qixiang Ye , David Doermann

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

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…

Machine Learning · Computer Science 2019-04-09 Amirreza Shaban , Ching-An Cheng , Nathan Hatch , Byron Boots

Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…

Logic in Computer Science · Computer Science 2019-11-07 Alois Brunel , Damiano Mazza , Michele Pagani

Supervised learning in deep neural networks is commonly performed using error backpropagation. However, the sequential propagation of errors during the backward pass limits its scalability and applicability to low-powered neuromorphic…

Machine Learning · Computer Science 2023-08-22 Florian Bacho , Dominique Chu