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With the advancement of remote-sensed imaging large volumes of very high resolution land cover images can now be obtained. Automation of object recognition in these 2D images, however, is still a key issue. High intra-class variance and low…
In this article we study high-dimensional approximation capacities of shallow and deep artificial neural networks (ANNs) with the rectified linear unit (ReLU) activation. In particular, it is a key contribution of this work to reveal that…
We study training of Convolutional Neural Networks (CNNs) with ReLU activations and introduce exact convex optimization formulations with a polynomial complexity with respect to the number of data samples, the number of neurons, and data…
This paper is concerned with convergence estimates for fully discrete tree tensor network approximations of high-dimensional functions from several model classes. For functions having standard or mixed Sobolev regularity, new estimates…
Two dimensional (2D) peak finding is a common practice in data analysis for physics experiments, which is typically achieved by computing the local derivatives. However, this method is inherently unstable when the local landscape is…
Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the performance in tasks with complex-valued inputs, such as in…
Deep neural networks (DNNs), especially deep convolutional neural networks (CNNs), have emerged as the powerful technique in various machine learning applications. However, the large model sizes of DNNs yield high demands on computation…
This paper introduces a novel representation of convolutional Neural Networks (CNNs) in terms of 2-D dynamical systems. To this end, the usual description of convolutional layers with convolution kernels, i.e., the impulse responses of…
Neural networks, especially convolutional neural networks (CNN), are one of the most common tools these days used in computer vision. Most of these networks work with real-valued data using real-valued features. Complex-valued convolutional…
Convolutional neural networks (CNNs), one of the key architectures of deep learning models, have achieved superior performance on many machine learning tasks such as image classification, video recognition, and power systems. Despite their…
Deep Convolutional Neural Network (CNN) is a special type of Neural Networks, which has shown exemplary performance on several competitions related to Computer Vision and Image Processing. Some of the exciting application areas of CNN…
Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) are useful for many practical tasks in machine learning. Synaptic weights, as well as neuron activation functions within the deep network are typically stored with…
Lung cancer remains one of the leading causes of cancer-related mortality worldwide, with early and accurate diagnosis playing a pivotal role in improving patient outcomes. Automated detection of pulmonary nodules in computed tomography…
Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…
In this paper, we provide a theoretical analysis of the inductive biases in convolutional neural networks (CNNs). We start by examining the universality of CNNs, i.e., the ability to approximate any continuous functions. We prove that a…
Conventional 2D Convolutional Neural Networks (CNN) extract features from an input image by applying linear filters. These filters compute the spatial coherence by weighting the photometric information on a fixed neighborhood without taking…
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…
Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches,…
With the development of convolution neural network, more and more researchers focus their attention on the advantage of CNN for face recognition task. In this paper, we propose a deep convolution network for learning a robust face…
Learning acoustic models directly from the raw waveform data with minimal processing is challenging. Current waveform-based models have generally used very few (~2) convolutional layers, which might be insufficient for building high-level…