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Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

Machine Learning · Statistics 2020-12-08 Javier Antorán , James Urquhart Allingham , José Miguel Hernández-Lobato

Deep Learning's outstanding track record across several domains has stemmed from the use of error backpropagation (BP). Several studies, however, have shown that it is impossible to execute BP in a real brain. Also, BP still serves as an…

Machine Learning · Computer Science 2021-06-11 Swaroop Mishra , Anjana Arunkumar

Deep learning is also known as hierarchical learning, where the learner _learns_ to represent a complicated target function by decomposing it into a sequence of simpler functions to reduce sample and time complexity. This paper formally…

Machine Learning · Computer Science 2023-07-10 Zeyuan Allen-Zhu , Yuanzhi Li

Current reinforcement learning algorithms train an agent using forward-generated trajectories, which provide little guidance so that the agent can explore as much as possible. While realizing the value of reinforcement learning results from…

Artificial Intelligence · Computer Science 2023-09-06 KyungMin Ko

Recurrent neural network architectures can have useful computational properties, with complex temporal dynamics and input-sensitive attractor states. However, evaluation of recurrent dynamic architectures requires solution of systems of…

Neural and Evolutionary Computing · Computer Science 2019-11-18 Dylan Richard Muir

The success of deep neural networks has inspired many to wonder whether other learners could benefit from deep, layered architectures. We present a general framework called forward thinking for deep learning that generalizes the…

Machine Learning · Statistics 2017-05-23 Kevin Miller , Chris Hettinger , Jeffrey Humpherys , Tyler Jarvis , David Kartchner

Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase…

Machine Learning · Computer Science 2023-06-14 Ali Momeni , Babak Rahmani , Matthieu Mallejac , Philipp Del Hougne , Romain Fleury

We present a new training methodology for transformers using a multilevel, layer-parallel approach. Through a neural ODE formulation of transformers, our application of a multilevel parallel-in-time algorithm for the forward and…

Machine Learning · Computer Science 2026-01-27 Shuai Jiang , Marc Salvadó-Benasco , Eric C. Cyr , Alena Kopaničáková , Rolf Krause , Jacob B. Schroder

Forward gradient learning computes a noisy directional gradient and is a biologically plausible alternative to backprop for learning deep neural networks. However, the standard forward gradient algorithm, when applied naively, suffers from…

Machine Learning · Computer Science 2023-03-03 Mengye Ren , Simon Kornblith , Renjie Liao , Geoffrey Hinton

Iterative approximation methods using backpropagation enable the optimization of neural networks, but they remain computationally expensive, especially when used at scale. This paper presents an efficient alternative for optimizing neural…

Machine Learning · Computer Science 2023-11-14 Jake Ryland Williams , Haoran Zhao

Neural networks are a convenient way to automatically fit functions that are too complex to be described by hand. The downside of this approach is that it leads to build a black-box without understanding what happened inside. Finding the…

Machine Learning · Computer Science 2022-08-29 Théo Nancy , Vassili Maillet , Johann Barbier

Deep neural networks trained with backpropagation have achieved outstanding performance in vision tasks but remain biologically implausible, computationally demanding, and difficult to interpret. The Forward-Forward (FF) algorithm offers a…

Computer Vision and Pattern Recognition · Computer Science 2026-05-26 Jie-En Yao , Hong-En Chen , C. -C. Jay Kuo

Backpropagation has been the cornerstone of neural network training for decades, yet its inefficiencies in time and energy consumption limit its suitability for resource-constrained edge devices. While low-precision neural network…

Machine Learning · Computer Science 2025-07-01 Jingxiao Ma , Priyadarshini Panda , Sherief Reda

Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive…

Neural and Evolutionary Computing · Computer Science 2011-08-10 Daohang Sha , Vladimir B. Bajic

Recent years have witnessed the great advance of deep learning in a variety of vision tasks. Many state-of-the-art deep neural networks suffer from large size and high complexity, which makes it difficult to deploy in resource-limited…

Computer Vision and Pattern Recognition · Computer Science 2019-05-29 Zhengguang Zhou , Wengang Zhou , Xutao Lv , Xuan Huang , Xiaoyu Wang , Houqiang Li

The back-propagation (BP) algorithm has been considered the de-facto method for training deep neural networks. It back-propagates errors from the output layer to the hidden layers in an exact manner using the transpose of the feedforward…

Neural and Evolutionary Computing · Computer Science 2018-05-01 Hongyin Luo , Jie Fu , James Glass

This work is focused on improving the character recognition capability of feed-forward back-propagation neural network by using one, two and three hidden layers and the modified additional momentum term. 182 English letters were collected…

Neural and Evolutionary Computing · Computer Science 2011-03-01 Amit Choudhary , Rahul Rishi

A recent paper by Boughammoura (2023) describes the back-propagation algorithm in terms of an alternative formulation called the F-adjoint method. In particular, by the F-adjoint algorithm the computation of the loss gradient, with respect…

Machine Learning · Computer Science 2024-07-17 Ahmed Boughammoura

Deep neural networks employing error back-propagation for learning can suffer from exploding and vanishing gradient problems. Numerous solutions have been proposed such as normalisation techniques or limiting activation functions to linear…

Machine Learning · Computer Science 2023-09-08 Sama Daryanavard , Bernd Porr

This study investigates the layerwise importance of feed-forward networks (FFNs) in Transformer-based language models during pretraining. We introduce an experimental approach that, while maintaining the total parameter count, increases the…

Computation and Language · Computer Science 2025-08-26 Wataru Ikeda , Kazuki Yano , Ryosuke Takahashi , Jaesung Lee , Keigo Shibata , Jun Suzuki