Related papers: Partition of unity networks: deep hp-approximation

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…

Radial basis function neural networks (\emph{RBFNN}) are {well-known} for their capability to approximate any continuous function on a closed bounded set with arbitrary precision given enough hidden neurons. In this paper, we introduce the…

Hardware implementations of complex functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

In recent years, deep convolutional neural network-based segmentation methods have achieved state-of-the-art performance for many medical analysis tasks. However, most of these approaches rely on optimizing the U-Net structure or adding new…

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be…

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition…

Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. While most research has focused on modeling the entire dynamics of interconnected systems, the…

We propose an optimization method for the automatic design of approximate multipliers, which minimizes the average error according to the operand distributions. Our multiplier achieves up to 50.24% higher accuracy than the best reproduced…

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks. The approach balances model size and tightness by partitioning node inputs into a number of groups and forming the convex hull over the partitions…

Graded posets frequently arise throughout combinatorics, where it is natural to try to count the number of elements of a fixed rank. These counting problems are often $\#\textbf{P}$-complete, so we consider approximation algorithms for…

We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…

Recent advances in geometric deep-learning introduce complex computational challenges for evaluating the distance between meshes. From a mesh model, point clouds are necessary along with a robust distance metric to assess surface quality or…

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…

In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…

This paper proposes a new deep convolutional neural network (DCNN) architecture that learns pixel embeddings, such that pairwise distances between the embeddings can be used to infer whether or not the pixels lie on the same region. That…

We propose a highly structured neural network architecture for semantic segmentation with an extremely small model size, suitable for low-power embedded and mobile platforms. Specifically, our architecture combines i) a Haar wavelet-based…

In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields…

This paper studies the universal approximation property of deep neural networks for representing probability distributions. Given a target distribution $\pi$ and a source distribution $p_z$ both defined on $\mathbb{R}^d$, we prove under…