相关论文: Deep Signatures -- Learning Invariants of Planar C…

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…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

In this work, we used deep neural networks (DNNs) to solve a fundamental problem in differential geometry. One can find many closed-form expressions for calculating curvature, length, and other geometric properties in the literature. As we…

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated…

In the past decade, deep neural networks (DNNs) came to the fore as the leading machine learning algorithms for a variety of tasks. Their raise was founded on market needs and engineering craftsmanship, the latter based more on trial and…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

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…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…

We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods. For nonparametric regression problems, it is well known that many standard methods attain the minimax…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

We investigate deep morphological neural networks (DMNNs). We demonstrate that despite their inherent non-linearity, "linear" activations are essential for DMNNs. To preserve their inherent sparsity, we propose architectures that constraint…

This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular…

Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been…

Deep neural networks (DNNs) have achieved unprecedented performance on a wide range of complex tasks, rapidly outpacing our understanding of the nature of their solutions. This has caused a recent surge of interest in methods for rendering…

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…