Related papers: Intrinsic stationarity for vector quantization: Fo…
The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics, including the problem of quantum measurement. The current study compares between some possible methods that can be used to…
Quantizing images into discrete representations has been a fundamental problem in unified generative modeling. Predominant approaches learn the discrete representation either in a deterministic manner by selecting the best-matching token or…
We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform…
We present a deterministic local routing algorithm that is guaranteed to find a path between any pair of vertices in a half-$\theta_6$-graph (the half-$\theta_6$-graph is equivalent to the Delaunay triangulation where the empty region is an…
The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph-minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The…
Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…
A new procedure for coarse-graining dynamical triangulations is presented. The procedure provides a meaning for the relevant value of observables when "probing at large scales", e.g. the average scalar curvature. The scheme may also be…
Quantization techniques applied to the inference of deep neural networks have enabled fast and efficient execution on resource-constraint devices. The success of quantization during inference has motivated the academic community to explore…
Quantization of deep neural networks is a promising approach that reduces the inference cost, making it feasible to run deep networks on resource-restricted devices. Inspired by existing methods, we propose a new framework to learn the…
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
Quantization of Convolutional Neural Networks (CNNs) is a common approach to ease the computational burden involved in the deployment of CNNs, especially on low-resource edge devices. However, fixed-point arithmetic is not natural to the…
In this report, we propose a novel quantum diagonalization algorithm based on the optimization of variational quantum circuits. Diagonalizing a quantum state is a fundamental yet computationally challenging task in quantum information…
An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi/Delaunay meshes appropriate for general…
Irregularly sampling a spatially stationary random field does not yield a graph stationary signal in general. Based on this observation, we build a definition of graph stationarity based on intrinsic stationarity, a less restrictive…
The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, though, critical phenomena have so far been only investigated on the Delaunay triangulation, the dual of a Voronoi graph. In this…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…
Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale…