Related papers: Nonparametric Functional Approximation with Delaun…
Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…
Backpropagation is the foundational algorithm for training neural networks and a key driver of deep learning's success. However, its biological plausibility has been challenged due to three primary limitations: weight symmetry, reliance on…
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…
In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…
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…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
In this paper, we address the problem of discovering maximal Lyapunov functions, as a means of determining the region of attraction of a dynamical system. To this end, we design a novel neural network architecture, which we prove to be a…
Non-Independent and Identically Distributed (non- IID) data distribution among clients is considered as the key factor that degrades the performance of federated learning (FL). Several approaches to handle non-IID data such as personalized…
In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…
This paper analyzes multi-step temporal difference (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…
We present a Deep Differentiable Simplex Layer (DDSL) for neural networks for geometric deep learning. The DDSL is a differentiable layer compatible with deep neural networks for bridging simplex mesh-based geometry representations (point…
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…
A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating \emph{sweep-hull} (sequentially created from the radially sorted set of 2D…
Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…
We propose a deep neural network architecture and a training algorithm for computing approximate Lyapunov functions of systems of nonlinear ordinary differential equations. Under the assumption that the system admits a compositional…
Multi-step temporal-difference (TD) learning, where the update targets contain information from multiple time steps ahead, is one of the most popular forms of TD learning for linear function approximation. The reason is that multi-step…
Deep Reinforcement Learning (DRL) is emerging as a promising approach to generate adaptive behaviors for robotic platforms. However, a major drawback of using DRL is the data-hungry training regime that requires millions of trial and error…
Distributionally robust reinforcement learning (DRRL) focuses on designing policies that achieve good performance under model uncertainties. The goal is to maximize the worst-case long-term discounted reward, where the data for RL comes…