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In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…

Real-world face detection and alignment demand an advanced discriminative model to address challenges by pose, lighting and expression. Illuminated by the deep learning algorithm, some convolutional neural networks based face detection and…

We investigate how a residual network can learn to predict the dynamics of interacting shapes purely as an image-to-image regression task. With a simple 2d physics simulator, we generate short sequences composed of rectangles put in motion…

Automated surface segmentation is important and challenging in many medical image analysis applications. Recent deep learning based methods have been developed for various object segmentation tasks. Most of them are a classification based…

Due to object detection's close relationship with video analysis and image understanding, it has attracted much research attention in recent years. Traditional object detection methods are built on handcrafted features and shallow trainable…

Shape learning, or the ability to leverage shape information, could be a desirable property of convolutional neural networks (CNNs) when target objects have specific shapes. While some research on the topic is emerging, there is no…

Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

Deep convolutional neural networks have achieved impressive performance on a broad range of problems, beating prior art on established benchmarks, but it often remains unclear what are the representations learnt by those systems and how…

The fast growing deep learning technologies have become the main solution of many machine learning problems for medical image analysis. Deep convolution neural networks (CNNs), as one of the most important branch of the deep learning…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

We propose methodologies to train highly accurate and efficient deep convolutional neural networks (CNNs) for image super resolution (SR). A cascade training approach to deep learning is proposed to improve the accuracy of the neural…

For image classification problems, various neural network models are commonly used due to their success in yielding high accuracies. Convolutional Neural Network (CNN) is one of the most frequently used deep learning methods for image…

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…

Arbitrary shape text detection is a challenging task due to the high variety and complexity of scenes texts. In this paper, we propose a novel unified relational reasoning graph network for arbitrary shape text detection. In our method, an…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

Porting state of the art deep learning algorithms to resource constrained compute platforms (e.g. VR, AR, wearables) is extremely challenging. We propose a fast, compact, and accurate model for convolutional neural networks that enables…