Tootfinder

Quasi-Monte Carlo hyperinterpolation
Congpei An, Mou Cai, Takashi Goda
https://arxiv.org/abs/2506.11622 https://arxiv.org/pdf/2506.11…

Quasi-Monte Carlo hyperinterpolation
This paper studies a generalization of hyperinterpolation over the high-dimensional unit cube. Hyperinterpolation of degree \( m \) serves as a discrete approximation of the \( L_2 \)-orthogonal projection of the same degree, using Fourier coefficients evaluated by a positive-weight quadrature rule that exactly integrates all polynomials of degree up to \( 2m \). Traditional hyperinterpolation methods often depend on exact quadrature assumptions, which can be impractical in high-dimensional con…

Quantum mixture-density network for multimodal probabilistic prediction
Jaemin Seo
https://arxiv.org/abs/2506.09497 https://arxiv.org…

Quantum mixture-density network for multimodal probabilistic prediction
Multimodal probability distributions are common in both quantum and classical systems, yet modeling them remains challenging when the number of modes is large or unknown. Classical methods such as mixture-density networks (MDNs) scale poorly, requiring parameter counts that grow quadratically with the number of modes. We introduce a Quantum Mixture-Density Network (Q-MDN) that employs parameterized quantum circuits to efficiently model multimodal distributions. By representing an exponential nu…

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
E. Alper Yildirim
https://arxiv.org/abs/2506.09892

Relaxations of KKT Conditions do not Strengthen Finite RLT and SDP-RLT Bounds for Nonconvex Quadratic Programs
We consider linear and semidefinite programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT relaxation), and the Shor relaxation combined with the RLT relaxation (SDP-RLT relaxation). By incorporating the first-order optimality conditions, a quadratic program can be formulated as an optimization problem with complementarity constraints. We investigate the effect of incorporating optimality conditions on the strength of the RLT and SDP-RLT …

On-the-Fly Adaptive Distillation of Transformer to Dual-State Linear Attention
Yeonju Ro, Zhenyu Zhang, Souvik Kundu, Zhangyang Wang, Aditya Akella
https://arxiv.org/abs/2506.09316

On-the-Fly Adaptive Distillation of Transformer to Dual-State Linear Attention
Large language models (LLMs) excel at capturing global token dependencies via self-attention but face prohibitive compute and memory costs on lengthy inputs. While sub-quadratic methods (e.g., linear attention) can reduce these costs, they often degrade accuracy due to overemphasizing recent tokens. In this work, we first propose \textit{dual-state linear attention} (\textbf{\dsla}), a novel design that maintains two specialized hidden states-one for preserving historical context and one for tr…

Automatic differentiation for Lax-Wendroff-type discretizations
Arpit Babbar, Valentin Churavy, Michael Schlottke Lakemper, Hendrik Ranocha
https://arxiv.org/abs/2506.11719

Automatic differentiation for Lax-Wendroff-type discretizations
Lax-Wendroff methods combined with discontinuous Galerkin/flux reconstruction spatial discretization provide a high-order, single-stage, quadrature-free method for solving hyperbolic conservation laws. In this work, we introduce automatic differentiation (AD) in the element-local time average flux computation step (the predictor step) of Lax-Wendroff methods. The application of AD is similar for methods of any order and does not need positivity corrections during the predictor step. This contra…

Efficient Task Graph Scheduling for Parallel QR Factorization in SLSQP
Soumyajit Chatterjee, Rahul Utkoor, Uppu Eshwar, Sathya Peri, V. Krishna Nandivada
https://arxiv.org/abs/2506.09463

Efficient Task Graph Scheduling for Parallel QR Factorization in SLSQP
Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming (SLSQP) for solving non-linear programming (NLP) problems. QR factorization decomposes a matrix into an orthogonal matrix Q and an upper triangular matrix R, which are essential for solving systems of linear equations arising from optimization problems. SLSQP uses …

Large Time Behavior of the Klein-Gordon-Schr\"{o}digner system
Chanjin You
https://arxiv.org/abs/2506.09863 https://arxiv.org/pd…

Large Time Behavior of the Klein-Gordon-Schrödigner system
We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schrödinger system in three dimensions. The system consists of coupled semilinear Schrödinger and Klein-Gordon equations with quadratic nonlinearities. This model is motivated by the study of plasma oscillations arising from the Hartree equation near a translation-invariant equilibrium with the Coulomb potential. Our proof relies on the space-time resonance method. The main difficulty comes …

Second-Order Linear Relaxation Schemes for Time-Fractional Phase-Field Models
Hui Yu, Zhaoyang Wang, Ping Lin
https://arxiv.org/abs/2506.11817 https://

Second-Order Linear Relaxation Schemes for Time-Fractional Phase-Field Models
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable is introduced to approximate the nonlinear term by solving an algebraic equation rather than a differential equation as in the invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches. The proposed semi-discrete scheme is linear, se…

Transformed Diffusion-Wave fPINNs: Enhancing Computing Efficiency for PINNs Solving Time-Fractional Diffusion-Wave Equations
Jing Li, Zhengqi Zhang
https://arxiv.org/abs/2506.11518

Transformed Diffusion-Wave fPINNs: Enhancing Computing Efficiency for PINNs Solving Time-Fractional Diffusion-Wave Equations
We propose transformed Diffsuion-Wave fractional Physics-Informed Neural Networks (tDWfPINNs) for efficiently solving time-fractional diffusion-wave equations with fractional order $α\in(1,2)$. Conventional numerical methods for these equations often compromise the mesh-free advantage of Physics-Informed Neural Networks (PINNs) or impose high computational costs when computing fractional derivatives. The proposed method avoids first-order derivative calculations at quadrature points by introdu…

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
Hongwei Mei, Rui Wang, Jiongmin Yong
https://arxiv.org/abs/2506.09337

Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike properties for the optimal pairs. The key is to prove a proper convergence of the solutions to the differential Riccati equations to the algebraic Riccati equation. Even for the problems without regime switchings, our result provides a refined estimate compared to t…