Related papers: Two-Dimensional Deep ReLU CNN Approximation for Ko…
In today's digital age, Convolutional Neural Networks (CNNs), a subset of Deep Learning (DL), are widely used for various computer vision tasks such as image classification, object detection, and image segmentation. There are numerous types…
We study the necessary and sufficient complexity of ReLU neural networks---in terms of depth and number of weights---which is required for approximating classifier functions in $L^2$. As a model class, we consider the set $\mathcal{E}^\beta…
We show that deep convolutional neural networks (CNN) can massively outperform traditional densely-connected neural networks (both deep or shallow) in predicting eigenvalue problems in mechanics. In this sense, we strike out in a new…
We represent 3D shape by structured 2D representations of fixed length making it feasible to apply well investigated 2D convolutional neural networks (CNN) for both discriminative and geometric tasks on 3D shapes. We first provide a general…
The paper briefy reviews several recent results on hierarchical architectures for learning from examples, that may formally explain the conditions under which Deep Convolutional Neural Networks perform much better in function approximation…
We present ApproxConv, a novel method for compressing the layers of a convolutional neural network. Reframing conventional discrete convolution as continuous convolution of parametrised functions over space, we use functional approximations…
We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as…
Computer Aided Diagnosis has emerged as an indispensible technique for validating the opinion of radiologists in CT interpretation. This paper presents a deep 3D Convolutional Neural Network (CNN) architecture for automated CT scan-based…
There is an increasing interest in applying deep learning to 3D mesh segmentation. We observe that 1) existing feature-based techniques are often slow or sensitive to feature resizing, 2) there are minimal comparative studies and 3)…
This paper quantitatively characterizes the approximation power of deep feed-forward neural networks (FNNs) in terms of the number of neurons. It is shown by construction that ReLU FNNs with width $\mathcal{O}\big(\max\{d\lfloor…
Previous works proved that the combination of the linear neuron network with nonlinear activation functions (e.g. ReLu) can achieve nonlinear function approximation. However, simply widening or deepening the network structure will introduce…
Recognizing objects and scenes are two challenging but essential tasks in image understanding. In particular, the use of RGB-D sensors in handling these tasks has emerged as an important area of focus for better visual understanding.…
Deep Convolutional Neural Networks (CNNs) have significantly advanced deep learning, driving breakthroughs in computer vision, natural language processing, medical diagnosis, object detection, and speech recognition. Architectural…
Building large models with parameter sharing accounts for most of the success of deep convolutional neural networks (CNNs). In this paper, we propose doubly convolutional neural networks (DCNNs), which significantly improve the performance…
During the last decade, Convolutional Neural Networks (CNNs) have become the de facto standard for various Computer Vision and Machine Learning operations. CNNs are feed-forward Artificial Neural Networks (ANNs) with alternating…
We study the expressive power of deep ReLU neural networks for approximating functions in dilated shift-invariant spaces, which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are…
We study ReLU deep neural networks (DNNs) by investigating their connections with the hierarchical basis method in finite element methods. First, we show that the approximation schemes of ReLU DNNs for $x^2$ and $xy$ are composition…
This paper develops simple feed-forward neural networks that achieve the universal approximation property for all continuous functions with a fixed finite number of neurons. These neural networks are simple because they are designed with a…
In this paper, we present an application of 2-D convolutional neural networks (2-D CNNs) designed to perform both feature extraction and classification stages as a single organism to solve the highlighted problems. The method uses a network…
The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome the curse of…