Related papers: Nonparametric Functional Approximation with Delaun…

In this work, we propose a Triangle based approach to classify flower images. Initially, flowers are segmented using whorl based region merging segmentation. Skeleton of a flower is obtained from the segmented flower using a skeleton…

Subset selection is central to many wireless communication problems, including link scheduling, power allocation, and spectrum management. However, these problems are often NP-complete, because of which heuristic algorithms applied to solve…

Temporal difference (TD) learning is a widely used method to evaluate policies in reinforcement learning. While many TD learning methods have been developed in recent years, little attention has been paid to preserving privacy and most of…

Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets.…

This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge flippings from an initial triangulation until the Delaunay property is achieved. To describe…

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…

Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…

We propose a new representation of visual data that disentangles object position from appearance. Our method, termed Deep Latent Particles (DLP), decomposes the visual input into low-dimensional latent ``particles'', where each particle is…

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

Training deep neural networks (DNNs) in large-cluster computing environments is increasingly necessary, as networks grow in size and complexity. Local memory and processing limitations require robust data and model parallelism for crossing…

One of the biggest challenges for deep learning algorithms in medical image analysis is the indiscriminate mixing of image properties, e.g. artifacts and anatomy. These entangled image properties lead to a semantically redundant feature…

In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…

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…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

The predictive accuracy of density functional theory (DFT) for alloy formation enthalpies is often limited by intrinsic energy resolution errors, particularly in ternary phase stability calculations. In this work, we present a machine…

The past decade has seen increasing interest in applying Deep Learning (DL) to Computational Science and Engineering (CSE). Driven by impressive results in applications such as computer vision, Uncertainty Quantification (UQ), genetics,…

A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extended to point clouds equipped with an $\mathbb{R}$-valued…

This paper analyzes multi-step TD-learning algorithms within the `deadly triad' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms…

Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…