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In this paper, we introduce a new type of generalized neural network where neurons and synapses maintain multiple states. We show that classical gradient-based backpropagation in neural networks can be seen as a special case of a two-state…

Machine Learning · Computer Science 2021-06-15 Mark Sandler , Max Vladymyrov , Andrey Zhmoginov , Nolan Miller , Andrew Jackson , Tom Madams , Blaise Aguera y Arcas

In current deep network architectures, deeper layers in networks tend to contain hundreds of independent neurons which makes it hard for humans to understand how they interact with each other. By organizing the neurons by correlation,…

Computer Vision and Pattern Recognition · Computer Science 2020-07-14 Randy Tan , Naimul Khan , Ling Guan

Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification…

Machine Learning · Computer Science 2016-07-21 Julius , Gopinath Mahale , Sumana T. , C. S. Adityakrishna

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance…

Machine Learning · Computer Science 2025-11-17 Thomas Pethick , Kimon Antonakopoulos , Antonio Silveti-Falls , Leena Chennuru Vankadara , Volkan Cevher

Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…

Machine Learning · Computer Science 2018-11-21 Kar-Ann Toh

The success of deep learning in the computer vision and natural language processing communities can be attributed to training of very deep neural networks with millions or billions of parameters which can then be trained with massive…

Machine Learning · Computer Science 2021-02-17 Kei Ota , Devesh K. Jha , Asako Kanezaki

Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural…

Machine Learning · Statistics 2025-10-30 Andrea Montanari , Pierfrancesco Urbani

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…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…

Machine Learning · Computer Science 2018-10-11 Marco Mondelli , Andrea Montanari

Neural networks have achieved remarkable performance in various application domains. Nevertheless, a large number of weights in pre-trained deep neural networks prohibit them from being deployed on smartphones and embedded systems. It is…

Machine Learning · Computer Science 2023-07-19 Shibo Yao , Dantong Yu , Ioannis Koutis

Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…

Machine Learning · Statistics 2021-03-18 Zhenyu Liao , Romain Couillet

Single layer feedforward networks with random weights are known for their non-iterative and fast training algorithms and are successful in a variety of classification and regression problems. A major drawback of these networks is that they…

Machine Learning · Computer Science 2020-09-25 Ajay M. Patrikar

Low bit-width weights and activations are an effective way of combating the increasing need for both memory and compute power of Deep Neural Networks. In this work, we present a probabilistic training method for Neural Network with both…

Machine Learning · Computer Science 2018-09-11 Jorn W. T. Peters , Max Welling

A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the…

Machine Learning · Computer Science 2019-06-12 Difan Zou , Quanquan Gu

This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal…

Machine Learning · Computer Science 2019-12-20 Eric C. Cyr , Stefanie Günther , Jacob B. Schroder

In the training of large deep neural networks, there is a need for vast amounts of training data. To meet this need, data is collected from multiple domains, such as Wikipedia and GitHub. These domains are heterogeneous in both data quality…

Machine Learning · Computer Science 2025-11-11 Mahdi Salmani , Pratik Worah , Meisam Razaviyayn , Vahab Mirrokni

In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed strategy shares an (almost) identical network structure and…

Numerical Analysis · Mathematics 2020-09-25 Eric Chung , Wing Tat Leung , Sai-Mang Pun , Zecheng Zhang

Sophisticated multilayer neural networks have achieved state of the art results on multiple supervised tasks. However, successful applications of such multilayer networks to control have so far been limited largely to the perception portion…

Machine Learning · Computer Science 2013-11-08 Sergey Levine

Neural network based methods have obtained great progress on a variety of natural language processing tasks. However, in most previous works, the models are learned based on single-task supervised objectives, which often suffer from…

Computation and Language · Computer Science 2016-05-18 Pengfei Liu , Xipeng Qiu , Xuanjing Huang

Deep learning is a subset of a broader family of machine learning methods based on learning data representations. These models are inspired by human biological nervous systems, even if there are various differences pertaining to the…

Neural and Evolutionary Computing · Computer Science 2019-05-22 Adriano Baldeschi , Raffaella Margutti , Adam Miller