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37th Annual Conference on Learning Theory, COLT 2024

作者： Parkinson, Suzanna Ongie, Greg Willett, Rebecca Shamir, Ohad Srebro, Nathan Committee on Computational and Applied Mathematics University of Chicago United States Department of Mathematical and Statistical Sciences Marquette University United States Department of Statistics Department of Computer Science University of Chicago United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Israel Toyota Technological Institute Chicago United States

We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared 2-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results focused on separation in terms of width, such results do not give insight into whether depth determines if it is possible to learn a network that generalizes well even when the network width is unbounded. Here, we study separation in terms of the sample complexity required for learnability. Specifically, we show that there are functions that are learnable with sample complexity polynomial in the input dimension by norm-controlled depth-3 ReLU networks, yet are not learnable with sub-exponential sample complexity by norm-controlled depth-2 ReLU networks (with any value for the norm). We also show that a similar statement in the reverse direction is not possible: any function learnable with polynomial sample complexity by a norm-controlled depth-2 ReLU network with infinite width is also learnable with polynomial sample complexity by a norm-controlled depth-3 ReLU network. © 2024 S. Parkinson, G. Ongie, R. Willett, O. Shamir & N. Srebro.

关键词： Source separation

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Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods

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Communications on applied mathematics and Computation 2024年第3期6卷 1860-1898页

作者： Andrés M.Rueda-Ramírez Benjamin Bolm Dmitri Kuzmin Gregor J.Gassner Department of Mathematics and Computer Science University of CologneWeyertal 86-90Cologne 50931Germany Institute of Applied Mathematics(LS Ⅲ) TU Dortmund UniversityVogelpothsweg 87Dortmund 44227Germany Center for Data and Simulation Science University of CologneWeyertal 86-90Cologne 50931Germany

We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution *** to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellﬂux *** a highorder spatial semi-discretization in terms of intermediate states,we performﬂux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant *** addition,local bounds may be imposed on scalar quantities of *** contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearﬂux approximations that are independent of the time-step size and can be further modiﬁed to enforce entropy *** demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedﬂows.

关键词： Structure-preserving schemes Subcellﬂux limiting Monolithic convex limiting(MCL) Discontinuous Galerkin spectral-element methods(DGSEMS) Legendre-Gauss-Lobatto(LGL)nodes

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An algorithm with optimal dimension-dependence for zero-order nonsmooth nonconvex stochastic optimization

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2024年第1期25卷 5918-5931页

作者： Guy Kornowski Ohad Shamir Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel

We study the complexity of producing (δ, ε)-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order algorithms that solve this task, all of which suffer from a dimension-dependence of Ω(d3/2) where d is the dimension of the problem, which was conjectured to be optimal. We refute this conjecture by providing a faster algorithm that has complexity O(dδ-1ε-3), which is optimal (up to numerical constants) with respect to d and also optimal with respect to the accuracy parameters δ, ε, thus solving an open question due to Lin et al. (2022). Moreover, the convergence rate achieved by our algorithm is also optimal for smooth objectives, proving that in the nonconvex stochastic zero-order setting, nonsmooth optimization is as easy as smooth optimization. We provide algorithms that achieve the aforementioned convergence rate in expectation as well as with high probability. Our analysis is based on a simple yet powerful lemma regarding the Goldstein-subdifferential set, which allows utilizing recent advancements in first-order nonsmooth nonconvex optimization.

关键词： nonsmooth nonconvex optimization stochastic optimization zero-order gradient-free Goldstein subdifferential

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Calculation of Deflagration Appearence in Hydrogen-Air Mixtures Flows in Regions with Obstacles 12

Calculation of Deflagration Appearence in Hydrogen-Air Mixtu...

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12th International Conference on Mathematical Modeling in Physical sciences, IC-MSQUARE 2023

作者： Martyushov, S.N. Computer Science and Applied Mathematics Faculty Moscow Aviation Institute - National Research University 4 Volokolamskoye Shosse Moscow125993 Russia

Many researches devoted to deflagration appearance in hydrogen-air mixes and transition it to detonation. Preference of hydrogen as a fuel is detonation fuel cycle which is more energetic preferable in comparing with ordinary fuel cycle. In connection with this preference problem of hydrogen detonation engine constructing is extreme actual. Essential part of investigations in this field is developing and improving of mathematical methods for numerical simulation of deflagration initiation and transition it to stable detonation. In real physical experiments this deflagration initiation in flows appears via sudden hot spot appearance or near an obstacle on boarding surface. In this paper numerically investigated flows of reactive gas mixes in channels with obstacles with purpose to define regims of deflagration initiation. © 2024 institute of Physics Publishing. All rights reserved.

关键词： Detonation

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Approbation of Asymptotic Method for Queue with an Unlimited Number of Servers and State-Dependent Service Rate 1

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26th International Conference on Distributed computer and Communication Networks: Control, Computation, Communications, DCCN 2023

作者： Nazarov, Anatoly Lapatin, Ivan Lizyura, Olga Institute of Applied Mathematics and Computer Science National Research Tomsk State University 36 Lenina ave. Tomsk634050 Russia

ISBN: (数字)9783031504822

ISBN: (纸本)9783031504815

The article discusses a model of the operation of a computing processor in the form of a queuing system with an unlimited number of servers and degradation of service rate. Degradation of service rate is the functional dependence of the service rate on the total number of requests (customers) in the system. Such function allows us to take into account the decrease in processor performance as the load on it increases. As a result of modification and application of the asymptotic analysis method, a Gaussian approximation of the probability distribution of the number of customers in the system was obtained, which corresponds to the distribution of simultaneously executed tasks by the processor. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Asymptotic analysis

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Convergence analysis of a Legendre spectral collocation method for nonlinear Fredholm integral equations in multidimensions

Convergence analysis of a Legendre spectral collocation meth...

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作者： Zaky, Mahmoud A. Hendy, Ahmed S. Department of Applied Mathematics National Research Centre Cairo Egypt Department of Mathematics Faculty of Science Benha University Benha Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University Yekaterinburg Russia

It is a very challenging task to solve a nonlinear integral equation in multidimensions. The main purpose of this paper is to develop and analyze a spectral collocation method for a class of nonlinear Fredholm integral equations of the second kind in multidimensions. The proposed spectral collocation method is based on a multivariate Legendre approximation in the frequency space. It is shown by both theory and numerics that the proposed spectral collocation scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations. © 2020 John Wiley & Sons, Ltd.

关键词： Fredholm integral equations

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Paradoxical roles of inhibitory autapse and excitatory synapse in formation of counterintuitive anticipated synchronization

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Chinese Physics B 2023年第8期32卷 499-509页

作者：丁学利古华光李玉叶贾雁兵 Department of Public Basic Education Fuyang Institute of TechnologyFuyang 236031China School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China College of Mathematics and Computer Science Chifeng UniversityChifeng 024000China School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471000China

Different from the common delayed synchronization(DS)in which response appears after stimulation,anticipated synchronization(AS)in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which response of the receiver neuron appears before stimulation of the sender neuron,showing an interesting function of brain to anticipate the *** dynamical mechanism for the AS remains unclear due to complex dynamics of inhibitory and excitatory *** this article,the paradoxical roles of excitatory synapse and inhibitory autapse in the formation of AS are ***,in addition to the common roles such that inhibitory modulation delays and excitatory modulation advances spike,paradoxical roles of excitatory stimulation to delay spike via type-II phase response and of inhibitory autapse to advance spike are obtained in suitable parameter regions,extending the dynamics and functions of the excitatory and inhibitory ***,AS is related to the paradoxical roles of the excitatory and inhibitory modulations,presenting deep understandings to the *** autapse induces spike of the receiver neuron advanced to appear before that of the sender neuron at first,and then excitatory synapse plays a delay role to prevent the spike further advanced,resulting in the AS as the advance and delay effects realize a dynamic ***,inhibitory autapse with strong advance,middle advance,and weak advance and delay effects induce phase drift(spike of the receiver neuron advances continuously),AS,and DS,respectively,presenting comprehensive relationships between AS and other *** results present potential measures to modulate AS related to brain function.

关键词： anticipated synchronization inhibitory autapse excitatory synapse paradoxical firing

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Algebraic Properties for Molecular Structure of Magnesium Iodide

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computer Modeling in Engineering & sciences 2023年第5期135卷 1131-1146页

作者： Ali N.A.Koam Ali Ahmad Muhammad Azeem Muhammad Kamran Siddiqui Department of Mathematics College of ScienceNew CampusJazan UniversityJazanSaudi Arabia College of Computer Science and Information Technology Jazan UniversityJazanSaudi Arabia Department of Mathematics Riphah Institute of Computing and Applied SciencesRiphah International UniversityLahorePakistan Department of Mathematics COMSATS University IslamabadLahorePakistan

As an inorganic chemical,magnesium iodide has a significant crystalline *** is a complex and multifunctional substance that has the potential to be used in a wide range of medical *** graph theory,on the other hand,provides a sufficient and cost-effective method of investigating chemical structures and networks.M-polynomial is a relatively new method for studying chemical networks and structures in molecular graph *** displays numerical descriptors in algebraic form and highlights molecular features in the form of a polynomial *** present a polynomials display of magnesium iodide structure and calculate several M-polynomials in this paper,particularly the M-polynomials of the augmented Zagreb index,inverse sum index,hyper Zagreb index and for the symmetric division index.

关键词： Magnesium iodide M-polynomials algebraic properties of magnesium iodide algebraic formation of numerics of magnesium iodide

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HS–WOA–MANET: a hybrid meta-heuristic approach-based multi-objective constraints for energy efficient routing protocol in mobile ad hoc networks

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Journal of Reliable Intelligent Environments 2024年第2期10卷 151-176页

作者： Goswami, Subhrananda Mondal, Sukumar Johardar, Subhankar Das, Chandan Bikash Research Centre of Natural and Applied Sciences Department of Computer Science Raja Narendra Lal Khan Women’s College Affiliated to Vidyasagar University Midnapore India Department of Mathematics Raja Narendra Lal Khan Women’s College Midnapore India Department of Computer Science Haldia Institute of Technology Haldia India Department of Mathematics Tamralipta Mahavidyalaya Tamluk India

A self-organizing, reconfigurable, and structure-less wireless network that provides intended communications without any radio infrastructure is called the mobile ad hoc network (MANETs). It is generally utilized in special outside occasions, locations, military surgeries, and natural disasters. In MANET, providing security is the primary issue because of the adoption of network structures. Moreover, the modifications in dynamic topologies expose the strike selection, such as routing, eavesdropping, and alteration of several programs. If MANET has several privacy and security issues, then it may surpass the quality of services (QoS). Hence, the security in MANET is guaranteed by using intrusion tracking approaches. This intrusion tracking system regulates the MANET in recognizing some other violation weaknesses. High protections are provided by detecting intrusions from the entire network, which includes attacks that are beyond the network layer. The nodes are not merely altered by the power collapse in the system, but it is also capable of transferring the packets in the network, which depends on the total system life. An effective routing protocol is designed to select the optimal paths for enhancing navigation in MANETs. Moreover, the terms secure routing and energy efficiency are critical problems when changing the network topology and limiting resources with this kind of network. A hybridized optimization-aided routing strategy is offered in this research work to provide an energy-efficient routing protocol. At the initial stage, the experimentation is conducted based on the sensor nodes in MANET. Since the existing models are ineffective in achieving high energy efficiency, the new routing protocol is developed by proposing the hybrid optimization algorithm. Accordingly, the suggested work is regarded for optimizing the shortest path in the routing model by using the Hybrid Sailfish Optimizer and Whale Optimization Algorithm (HS-WOA). To validate the network e

关键词： Mobile ad hoc networks

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IMPROVING OUT-OF-DISTRIBUTION GENERALIZATION WITH INDIRECTION REPRESENTATIONS 11

IMPROVING OUT-OF-DISTRIBUTION GENERALIZATION WITH INDIRECTIO...

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11th International Conference on Learning Representations, ICLR 2023

作者： Pham, Kha Le, Hung Ngo, Man Tran, Truyen Applied Artificial Intelligence Institute Deakin University Australia Faculty of Mathematics and Computer Science VNUHCM-University of Science Viet Nam

We propose a generic module named Indirection Layer (InLay), which leverages indirection and data internal relationships to effectively construct symbolic indirect representations to improve out-of-distribution generalization capabilities of various neural architectures. InLay receives data input in the form of a sequence of objects, treats it as a complete weighted graph whose vertices are the objects and edge weights are scalars representing relationships between vertices. The input is first mapped via indirection to a symbolic graph with data-independent and trainable vertices. This symbolic graph is then propagated, resulting in new vertex features whose indirection will be used for prediction steps afterward. Theoretically, we show that the distances between indirection representations are bounded by the distances between corresponding graphs, implying that unseen samples with very different surface statistics can still be close in the representation space to the seen samples if they share similar internal relationships. We demonstrate that InLay is consistently effective in improving out-of-distribution generalization throughout a comprehensive suite of experiments, including IQ problems, distorted image classification, and few-shot domain adaptation NLP classification. We also conduct ablation studies to verify different design choices of InLay. © 2023 11th International Conference on Learning Representations, ICLR 2023. All rights reserved.

关键词： Image enhancement

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