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Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…

Classical Analysis and ODEs · Mathematics 2022-11-22 Matthew Thorpe , Yves van Gennip

Stochastic differential equations can describe a wide range of dynamical systems, and obtaining the governing equations of these systems is the premise of studying the nonlinear dynamic behavior of the system. Neural networks are currently…

Dynamical Systems · Mathematics 2023-04-25 Xiao-Kai An , Lin Du , Zi-Chen Deng , Yu-jia Zhang

In this work, we leverage advances in sparse coding techniques to reduce the number of trainable parameters in a fully connected neural network. While most of the works in literature impose $\ell_1$ regularization, DropOut or DropConnect…

Machine Learning · Computer Science 2019-07-04 Arman Hasanzadeh , Nagaraj T. Janakiraman , Vamsi K. Amalladinne , Krishna R. Narayanan

In this paper, we introduce the problem of jointly learning feed-forward neural networks across a set of relevant but diverse datasets. Compared to learning a separate network from each dataset in isolation, joint learning enables us to…

Machine Learning · Computer Science 2019-06-12 Zaiwei Zhang , Xiangru Huang , Qixing Huang , Xiao Zhang , Yuan Li

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

Machine Learning · Computer Science 2023-11-21 Andrea Apicella , Francesco Isgrò , Roberto Prevete

Machine learning is advancing towards a data-science approach, implying a necessity to a line of investigation to divulge the knowledge learnt by deep neuronal networks. Limiting the comparison among networks merely to a predefined…

Computer Vision and Pattern Recognition · Computer Science 2019-03-13 Arash Akbarinia , Karl R. Gegenfurtner

Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states which produce inconsistent predictions of the same test…

Dynamical Systems · Mathematics 2021-06-16 Mohammed Eslami , Hamed Eramian , Marcio Gameiro , William Kalies , Konstantin Mischaikow

This work presents a novel Convolutional Neural Network (CNN) architecture and a training procedure to enable robust and accurate pose estimation of a noncooperative spacecraft. First, a new CNN architecture is introduced that has scored a…

Computer Vision and Pattern Recognition · Computer Science 2019-09-04 Tae Ha Park , Sumant Sharma , Simone D'Amico

Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their…

Machine Learning · Computer Science 2018-10-26 Cem Tarhan , Gozde Bozdagi Akar

We describe Swapout, a new stochastic training method, that outperforms ResNets of identical network structure yielding impressive results on CIFAR-10 and CIFAR-100. Swapout samples from a rich set of architectures including dropout,…

Computer Vision and Pattern Recognition · Computer Science 2016-05-23 Saurabh Singh , Derek Hoiem , David Forsyth

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is…

Machine Learning · Computer Science 2017-12-25 Pierre Baldi , Peter Sadowski , Zhiqin Lu

Implicit neural networks, a.k.a., deep equilibrium networks, are a class of implicit-depth learning models where function evaluation is performed by solving a fixed point equation. They generalize classic feedforward models and are…

Machine Learning · Computer Science 2022-01-27 Saber Jafarpour , Alexander Davydov , Anton V. Proskurnikov , Francesco Bullo

Many types of neural network layers rely on matrix properties such as invertibility or orthogonality. Retaining such properties during optimization with gradient-based stochastic optimizers is a challenging task, which is usually addressed…

Machine Learning · Statistics 2020-12-02 Andreas Krämer , Jonas Köhler , Frank Noé

Deep neural networks have achieved substantial achievements in several computer vision areas, but have vulnerabilities that are often fooled by adversarial examples that are not recognized by humans. This is an important issue for security…

Computer Vision and Pattern Recognition · Computer Science 2021-01-29 Hakmin Lee , Hong Joo Lee , Seong Tae Kim , Yong Man Ro

This work proposes the first strategy to make distributed training of neural networks resilient to computing errors, a problem that has remained unsolved despite being first posed in 1956 by von Neumann. He also speculated that the…

Information Theory · Computer Science 2019-03-05 Sanghamitra Dutta , Ziqian Bai , Tze Meng Low , Pulkit Grover

Recent studies have shown that many important aspects of neural network learning take place within the very earliest iterations or epochs of training. For example, sparse, trainable sub-networks emerge (Frankle et al., 2019), gradient…

Machine Learning · Computer Science 2020-02-25 Jonathan Frankle , David J. Schwab , Ari S. Morcos

Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of…

Computer Vision and Pattern Recognition · Computer Science 2021-11-23 Woochul Kang , Daeyeon Kim

Convolutional neural networks (CNN's) are powerful and widely used tools. However, their interpretability is far from ideal. One such shortcoming is the difficulty of deducing a network's ability to generalize to unseen data. We use…

Computer Vision and Pattern Recognition · Computer Science 2019-10-21 Rickard Brüel Gabrielsson , Gunnar Carlsson

Conditional computation and modular networks have been recently proposed for multitask learning and other problems as a way to decompose problem solving into multiple reusable computational blocks. We propose a new approach for learning…

Machine Learning · Computer Science 2021-07-26 Andrey Zhmoginov , Dina Bashkirova , Mark Sandler

Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-the-art, model-based methods for…

Machine Learning · Computer Science 2022-12-22 Maksym Neyra-Nesterenko , Ben Adcock