检索结果-内蒙古大学图书馆

ROBUSTIFYING STATE-SPACE MODELS FOR LONG SEQUENCES VIA APPROXIMATE DIAGONALIZATION 12

学校读者我要写书评

暂无评论

ROBUSTIFYING STATE-SPACE MODELS FOR LONG SEQUENCES VIA APPRO...

12th International Conference on Learning Representations, ICLR 2024

作者： Yu, Annan Nigmetov, Arnur Morozov, Dmitriy Mahoney, Michael W. Erichson, N. Benjamin Center for Applied Mathematics Cornell University IthacaNY14853 United States Lawrence Berkeley National Laboratory BerkeleyCA94720 United States International Computer Science Institute BerkeleyCA94704 United States Department of Statistics University of California at Berkeley BerkeleyCA94720 United States

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges;and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Deep learning

Conditional Parametric Armax Models For Observed Hourly Heat-Load Dynamics in Apartment Buildings

学校读者我要写书评

暂无评论

SSRN

SSRN 2023年

作者： Smertinas, Justinas Bacher, Peder Lindström, Erik Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Centre for Mathematical Sciences Lund University Sweden

This paper presents a methodology for estimation of physically interpretable building characteristics such as heat loss coefficient, azimuth angle dependent solar gain, and diurnal periodicity in heat-demand. The models are demonstrated on case-study with hourly observations of district-heating connected apartment buildings in Denmark. The weather model inputs are obtained from re-analysis climate data, hence no local climate station is necessary. The estimates are thus achieved without directly observing internal climate of the buildings, making the applications scalable and less prone to errors from *** characteristics are extracted from ARX and ARMAX models extended via B-splines to capture non-linear effects. Interactions of the B-splines with solar radiation are used for approximating varying solar gain factor and periodic B-splines are included to capture the diurnal effect. Same model is applied independently for each building, such that the parameter estimates can be directly *** quality of estimates for solar and diurnal effect are substantially improved when employing the higher complexity ARMAX models over the simpler ARX. This investigation observes a consistent underestimation of heat loss coefficient from ARX models. Lastly, solar gain estimates are physically interpretable and show dependence on directionality of the buildings' facades. The periodical diurnal characteristics are markedly different between buildings with residential and commercial uses. © 2023, The Authors. All rights reserved.

关键词： Climate models

INJECTIVE ENVELOPES FOR LOCALLY C∗-ALGEBRAS

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Joit, Maria A. Şimon, Gheorghe-Ionut Department of Mathematics Faculty of Applied Sciences University Po-litehnica of Bucharest 313 Spl. Independentei Bucharest060042 Romania Department of Mathematics Faculty of Mathematics and Computer Science University of Bucharest Str. Academiei nr. 14 Bucharest Romania

We introduce the notion of admissible injective envelope for a locally C∗-algebra and show that each object in the category whose objects are unital Fréchet locally C∗-algebras and whose morphisms are unital admissible local completely positive maps has a unique admissible injective envelope. The concept of admissible injectivity is stronger than that of injectivity. As a consequence, we show that a unital Fréchet locally W∗-algebras is injective if and only if the C∗-algebras from its Arens-Michael decomposition are injective. Copyright © 2025, The Authors. All rights reserved.

关键词： Algebra

CLEARING SECTIONS OF LATTICE LIABILITY NETWORKS

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Riess, Hans Department of Mathematics and Electrical & Systems Engineering University of Pennsylvania Philadelphia PA Department of Mathematics University of Pennsylvania Philadelphia PA Applied Mathematics & Computational Science University of Pennsylvania Philadelphia PA School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA

Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present a mathematical framework that unifies and extends these scenarios by recasting the classical Eisenberg-Noe model of financial clearing in terms of lattice liability networks. Each node in the network carries a complete lattice of possible states, while edges encode nominal liabilities. Our framework generalizes the scalar-valued clearing vectors of the classical model to lattice-valued clearing sections, preserving the elegant fixed-point structure while dramatically expanding its descriptive power. Our main theorem establishes that such networks possess clearing sections that themselves form a complete lattice under the product order. This structure theorem enables tractable analysis of equilibria in diverse domains, including multi-currency financial systems, decentralized finance with automated market makers, supply chains with resource transformation, and permission networks with complex authorization structures. We further extend our framework to chain-complete lattices for term structure models and multivalued mappings for complex negotiation systems. Our results demonstrate how lattice theory provides a natural language for understanding complex network dynamics across multiple domains, creating a unified mathematical foundation for analyzing systemic risk, resource allocation, and network *** Codes 91G40, 06B23, 91D30, 68Q85 Copyright © 2025, The Authors. All rights reserved.

关键词： Lattice theory

Massively Winning Configurations in the Convex Grabbing Game on the Plane 33

学校读者我要写书评

暂无评论

Massively Winning Configurations in the Convex Grabbing Game...

33rd Canadian Conference on Computational Geometry, CCCG 2021

作者： Dvorak, Martin Nicholson, Sara Department of Theoretical Computer Science and Mathematical Logic Faculty of Mathematics and Physics Charles University Institute of Science and Technology Austria Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Czech Republic

The convex grabbing game is a game where two players, Alice and Bob, alternate taking extremal points from the convex hull of a point set on the plane. Rational weights are given to the points. The goal of each player is to maximize the total weight over all points that they obtain. We restrict the setting to the case of binary weights. We show a construction of an arbitrarily large odd-sized point set that allows Bob to obtain almost 3/4 of the total weight. This construction answers a question asked by Matsumoto, Nakamigawa, and Sakuma in [Graphs and Combinatorics, 36/1 (2020)]. We also present an arbitrarily large even-sized point set where Bob can obtain the entirety of the total weight. Finally, we discuss conjectures about optimum moves in the convex grabbing game for both players in general. © 2021 Meng He and Don Sheehy.

关键词： Combinatorial mathematics

The Geometry and Well-Posedness of Sparse Regularized Linear Regression

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Everink, Jasper M. Dong, Yiqiu Andersen, Martin S. Department of Applied Mathematics and Computer Science Technical University of Denmark Richard Petersens Plads Building 324 LyngbyDK-2800 Kgs. Denmark

In this work, we study the well-posedness of certain sparse regularized linear regression problems, i.e., the existence, uniqueness and continuity of the solution map with respect to the data. We focus on regularization functions that are convex piecewise linear, i.e., whose epigraph is polyhedral. This includes total variation on graphs and polyhedral constraints. We provide a geometric framework for these functions based on their connection to polyhedral sets and apply this to the study of the well-posedness of the corresponding sparse regularized linear regression problem. Particularly, we provide geometric conditions for well-posedness of the regression problem, compare these conditions to those for smooth regularization, and show the computational difficulty of verifying these *** Codes 52B99, 62J05, 90C31 © 2024, CC BY.

关键词： Linear regression

Diabetes Prediction Using Machine Learning

学校读者我要写书评

暂无评论

Diabetes Prediction Using Machine Learning

2023 IEEE World Conference on Communication and Computing, WCONF 2023

作者： Bhatia, Sandeep Goel, Amit Kumar Naib, Bharat Bhushan Singh, Khushwant Yadav, Mohit Saini, Ashish Galgotias University Department of CSE Uttar Pradesh Greater Noida India Maharshi Dayanand University U.I.E.T Department of Computer Science & Engineering Rohtak124001 India Maharshi Dayanand University U.I.E.T Department of Applied Sciences Mathematics Rohtak124001 India Maharshi Dayanand University U.I.E.T Department of Computer Science & Applications Rohtak124001 India

ISBN: (纸本)9798350311204

Patient's Infirmity Assumption system is a psychological gauge structure which predicts an infection in light of the information or signs went into the system and gives the specific happens. We suggest a creative replacement for the traditional methodology that resolves the drawn-out issues with expert course of action arranging. This approach is the remedy if one isn't too certifiable and simply has to retain what kind of illness they are dealing with. It very well may be a structure that gives the client urging on the most proficient method to keep their prosperity system with everything looking good and offers a strategy to recognize disease using this expectation. The prosperity section is indispensable to the treatment of patients' diseases, so it is furthermore a casing of help to the medical services portion that the client will be taught and helped inside the event that the individual decides not to visit a center or other facility, allowing the client to remember around their condition by entering the incidental effects and some other fitting information. © 2023 IEEE.

关键词： Diseases

Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Ding, Zhiyan Junge, Marius Schleich, Philipp Wu, Peixue Department of Mathematics University of California Berkeley United States Department of Mathematics University of Illinois at Urbana and Champaign United States Department of Computer Science University of Toronto Canada Department of Applied Mathematics University of Waterloo Canada Institute for Quantum Computing University of Waterloo Canada

Simulating quantum dynamics is one of the most promising applications of quantum computers. While the upper bound of the simulation cost has been extensively studied through various quantum algorithms, much less work has focused on establishing the lower bound, particularly for the simulation of open quantum system dynamics. In this work, we present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Given a fixed accessible unitary set, we introduce the concept of convexified circuit depth to quantify the quantum simulation cost and analyze the necessary circuit depth to construct a quantum simulation scheme that achieves a specific order. Our framework can be applied to both unital and non-unital quantum dynamics, and the tightness of our lower bound technique is illustrated by showing that the upper and lower bounds coincide in several examples. © 2024, CC BY.

关键词： Quantum computers

Visualization of Syntax and Semantics for Simple Functional Language of Natural Numbers and Boolean Values 10

学校读者我要写书评

暂无评论

Visualization of Syntax and Semantics for Simple Functional ...

10th IEEE Jubilee International Conference on Computational Cybernetics and Cyber-Medical Systems, ICCC 2022

作者： Perháč, Ján Ferencsik, Michal Zhukovskyy, Viktor Zhukovska, Nataliia Shatnyi, Serhii Technical University of Košice Faculty of Electrical Engineering and Informatics Department of Computers and Informatics Košice Slovakia National University of Water and Environmental Engineering Department of Computer Science and Applied Mathematics Rivne Ukraine

ISBN: (数字)9781665481779

ISBN: (纸本)9781665481779

Building an abstract syntax tree is an integral part of compilers. We analyze a few of the popular techniques providing such analysis in the web environment. Based on the analysis of these solutions, we deal with the implementation of our parser solution, which also provides a graphical representation of abstract syntax trees as well as proof trees. This solution is then used in our application designed to interpret the expressions of the simple teaching functional language of natural numbers and boolean values. In addition, the application supports the evaluation (semantics) of expressions (step by step), and also their individual properties: the depth of the syntax tree, syntax tree nodes count, and the constants used in the expression. © 2022 IEEE.

关键词： Semantics