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Convex functions and their gradients play a critical role in mathematical imaging, from proximal optimization to Optimal Transport. The successes of deep learning has led many to use learning-based methods, where fixed functions or…
Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are…
Convolutional Neural Network (CNN)-based machine learning systems have made breakthroughs in feature extraction and image recognition tasks in two dimensions (2D). Although there is significant ongoing work to apply CNN technology to…
We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For non-smooth initial conditions, the solutions of these PDEs…
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
Traditional Convolutional Neural Networks (CNNs) typically use the same activation function (usually ReLU) for all neurons with non-linear mapping operations. For example, the deep convolutional architecture Inception-v4 uses ReLU. To…
This paper addresses the problem of nearly optimal Vapnik--Chervonenkis dimension (VC-dimension) and pseudo-dimension estimations of the derivative functions of deep neural networks (DNNs). Two important applications of these estimations…
We propose a local modelling approach using deep convolutional neural networks (CNNs) for fine-grained image classification. Recently, deep CNNs trained from large datasets have considerably improved the performance of object recognition.…
Recent radiomic studies have witnessed promising performance of deep learning techniques in learning radiomic features and fusing multimodal imaging data. Most existing deep learning based radiomic studies build predictive models in a…
Convolutional neural networks (CNNs) are a widely used form of deep neural networks, introducing state-of-the-art results for different problems such as image classification, computer vision tasks, and speech recognition. However, CNNs are…
In this paper, we develop a 2D and 3D segmentation pipelines for fully automated cardiac MR image segmentation using Deep Convolutional Neural Networks (CNN). Our models are trained end-to-end from scratch using the ACD Challenge 2017…
Lacunes of presumed vascular origin (lacunes) are associated with an increased risk of stroke, gait impairment, and dementia and are a primary imaging feature of the small vessel disease. Quantification of lacunes may be of great importance…
Deep networks are often considered to be more expressive than shallow ones in terms of approximation. Indeed, certain functions can be approximated by deep networks provably more efficiently than by shallow ones, however, no tractable…
The work presented in this paper is to propose a reliable high-quality system of Convolutional Neural Network (CNN) for brain tumor segmentation with a low computation requirement. The system consists of a CNN for the main processing for…
Deep learning techniques have become prominent in modern fault diagnosis for complex processes. In particular, convolutional neural networks (CNNs) have shown an appealing capacity to deal with multivariate time-series data by converting…
Recently, convolutional neural networks (CNNs) have been used as a powerful tool to solve many problems of machine learning and computer vision. In this paper, we aim to provide insight on the property of convolutional neural networks, as…
In this era of artificial intelligence, deep neural networks like Convolutional Neural Networks (CNNs) have emerged as front-runners, often surpassing human capabilities. These deep networks are often perceived as the panacea for all…
Most of existing statistical theories on deep neural networks have sample complexities cursed by the data dimension and therefore cannot well explain the empirical success of deep learning on high-dimensional data. To bridge this gap, we…
Convolutional Neural Networks (CNNs) have been recently employed to solve problems from both the computer vision and medical image analysis fields. Despite their popularity, most approaches are only able to process 2D images while most…