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How deep convolutional neural networks lose spatial information with training

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Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Universal Approximation Property of Hamiltonian Deep Neural Networks

Giancarlo Ferrari Trecate, Muhammad Zakwan

This letter investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs enjoy, by design, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Improving the Training of Compact Neural Networks for Visual Recognition

Shuxuan Guo

During the Artificial Intelligence (AI) revolution of the past decades, deep neural networks have been widely used and have achieved tremendous success in visual recognition. Unfortunately, deploying deep models is challenging because of their huge model s ...

EPFL2022

Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu, Yongtao Wu

Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incomplete for neural networks with Hadamar ...

2022

Sharp asymptotics on the compression of two-layer neural networks

Marco Mondelli

In this paper, we study the compression of a target two-layer neural network with N nodes into a compressed network with M < N nodes. More precisely, we consider the setting in which the weights of the target network are i.i.d. sub-Gaussian, and we minimiz ...

IEEE2022

Impulsive noise removal via a blind CNN enhanced by an iterative post-processing

Hatef Otroshi Shahreza, Seyedeh Sahar Sadrizadeh

In digital imaging, especially in the process of data acquisition and transmission, images are often affected by impulsive noise. Therefore, it is essential to remove impulsive noise from images before any further processing. Due to the remarkable performa ...

ELSEVIER2022

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Developing energy-saving neural network models is a topic of rapidly increasing interest in the artificial intelligence community. Spiking neural networks (SNNs) are biologically inspired models that strive to leverage the energy efficiency stemming from a ...

IEEE2022

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions and that use commonly adopt ...

AMER PHYSICAL SOC2022

A Machine Learning-based Framework for Forecasting Sales of New Products With Short Life Cycles Using Deep Neural Networks

Ralf Seifert, Yara Kayyali El Alem

Demand forecasting is becoming increasingly important as firms launch new products with short life cycles more frequently. This paper provides a framework based on state-of-the-art techniques that enables firms to use quantitative methods to forecast sales ...

2022

GALET: A deep learning image segmentation model for drone-based grain size analysis of gravel bars

Giovanni De Cesare, Christian Mörtl

In this study, we present the deep learning image segmentation model for drone-based grain size analysis of gravel bars called GALET. The objectives are to quantify the performance of the code and to test its applicability in river research and management. ...

International Association for Hydro-Environment Engineering and Research (IAHR)2022