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Balanced Training for Sparse GANs

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arXiv 2023年

作者： Wang, Yite Wu, Jing Hovakimyan, Naira Sun, Ruoyu University of Illinois Urbana-Champaign United States School of Data Science The Chinese University of Hong Kong Shenzhen China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data China

Over the past few years, there has been growing interest in developing larger and deeper neural networks, including deep generative models like generative adversarial networks (GANs). However, GANs typically come with high computational complexity, leading researchers to explore methods for reducing the training and inference costs. One such approach gaining popularity in supervised learning is dynamic sparse training (DST), which maintains good performance while enjoying excellent training efficiency. Despite its potential benefits, applying DST to GANs presents challenges due to the adversarial nature of the training process. In this paper, we propose a novel metric called the balance ratio (BR) to study the balance between the sparse generator and discriminator. We also introduce a new method called balanced dynamic sparse training (ADAPT), which seeks to control the BR during GAN training to achieve a good trade-off between performance and computational cost. Our proposed method shows promising results on multiple datasets, demonstrating its effectiveness. Our code is available at https://***/YiteWang/ADAPT. Copyright © 2023, The Authors. All rights reserved.

关键词： Generative adversarial networks

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations

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arXiv 2023年

作者： Jentzen, Arnulf Riekert, Adrian von Wurstemberger, Philippe School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen [CUHK-Shenzhen China Applied Mathematics Institute for Analysis and Numerics University of Münster Germany School of Data Science The Chinese University of Hong Kong Shenzhen [CUHK-Shenzhen China Risklab Department of Mathematics ETH Zurich Switzerland

In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN) architectures in conjunction with specific ANN initialization schemes which are tailor-made for the particular approximation problem under consideration. In the proposed approach we combine efficient classical numerical approximation techniques with deep operator learning methodologies. Specifically, we introduce customized adaptions of existing ANN architectures together with specialized initializations for these ANN architectures so that at initialization we have that the ANNs closely mimic a chosen efficient classical numerical algorithm for the considered approximation problem. The obtained ANN architectures and their initialization schemes are thus strongly inspired by numerical algorithms as well as by popular deep learning methodologies from the literature and in that sense we refer to the introduced ANNs in conjunction with their tailor-made initialization schemes as Algorithmically Designed Artificial Neural Networks (ADANNs). We numerically test the proposed ADANN methodology in the case of several parametric PDEs. In the tested numerical examples the ADANN methodology significantly outperforms existing traditional approximation algorithms as well as existing deep operator learning methodologies from the literature. Copyright © 2023, The Authors. All rights reserved.

关键词： Neural networks

Extended calculations of energy levels, radiative properties, and lifetimes for phosphorus-like Se XX

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Atomic data and Nuclear data Tables 2025年 164卷

作者： Wang, Kai Bai, Xuan Chen, Chong Yang Yan, Jun Department of Physics and Anhui Key Laboratory of Optoelectric Materials Science and Technology Key Laboratory of Functional Molecular Solids Ministry of Education Anhui Normal University Wuhu241000 China Shanghai EBIT Lab Key Laboratory of Nuclear Physics and Ion-Beam Application Institute of Modern Physics Department of Nuclear Science and Technology Fudan University Shanghai200433 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

Highly accurate calculations are performed for the lowest 151 fine-structure levels arising from the 3s23p3, 3s3p4, 3s23p23d, 3s3p33d, 3p5 and 3s23p3d2 configurations in P-like Se XX using the multiconfiguration Dirac–Hartree–Fock and the relativistic configuration interaction methods. Complete and consistent atomic data, including excitation energies, wavelengths, E1, E2, M1, M2 line strengths, oscillator strengths, transition rates, and radiative lifetimes for these 151 levels, are provided. Our data set is compared with the NIST compiled values and other available results. The present data are accurate enough for identification and deblending of emission lines involving the n=3 levels and are also useful for modeling and diagnosing fusion plasmas. These data can be considered as a benchmark for other calculations. © 2025

关键词： Excitation energy

Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra osp (1|2): Exact solution for the quantum harmonic oscillator with a position-dependent mass

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arXiv 2025年

作者： Jafarov, E.I. Nagiyev, S.M. Van der Jeugt, J. Institute of Physics Ministry of Science and Education Javid av. 131 BakuAZ1143 Azerbaijan Department of Applied Mathematics Computer Science and Statistics Ghent University Krijgslaan 281-S9 Gent9000 Belgium

We propose a new deformation of the quantum harmonic oscillator Heisenberg-Weyl algebra with a parameter a > −1. This parameter is introduced through the replacement of the homogeneous mass m0 in the definition of the momentum operator pˆx as well as in the creation-annihilation operators â± with a mass varying with position x. The realization of such a deformation is shown through the exact solution of the corresponding Schrödinger equation for the non-relativistic quantum harmonic oscillator within the canonical approach. The obtained analytical expression of the energy spectrum consists of an infinite number of equidistant levels, whereas the wavefunctions of the stationary states of the problem under construction are expressed through the Hermite polynomials. Then, the Heisenberg-Weyl algebra deformation is generalized to the case of the Lie superalgebra osp (1|2). It is shown that the realization of such a generalized superalgebra can be performed for the parabose quantum harmonic oscillator problem, the mass of which possesses a behavior completely overlapping with the position-dependent mass of the canonically deformed harmonic oscillator problem. This problem is solved exactly for both even and odd stationary states. It is shown that the energy spectrum of the deformed parabose oscillator is still equidistant, however, both even and odd state wavefunctions are now expressed through the Laguerre polynomials. Some basic limit relations recovering the canonical harmonic oscillator with constant mass are also discussed *** Codes 17B81, 81Q37, 33C45 17B81 © 2025, CC BY.

关键词： Schrodinger equation

Feasibility of extracting the proton weak charge from quantum-control measurements of atomic parity violation on the 2s−3s or 2s−4s transition in hydrogen

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Physical Review A 2024年第1期109卷 012808-012808页

作者： Jiguang Li (李冀光) Andrei Derevianko D. S. Elliott Institute of Applied Physics and Computational Mathematics Beijing 100088 China Department of Physics University of Nevada Reno Nevada 89557 USA Department of Physics and Astronomy Purdue University West Lafayette Indiana 47907 USA School of Electrical and Computer Engineering Purdue University West Lafayette Indiana 47907 USA Purdue Quantum Science and Engineering Institute Purdue University West Lafayette Indiana 47907 USA

We explore the feasibility of extracting electroweak observables from a measurement of atomic parity violation in hydrogen. Our proposed quantum-control scheme focuses on the 2s−3s or 2s−4s transitions in hydrogen. This work is motivated by the recently observed anomaly in the W-boson mass, which may substantially modify the Standard Model value of the proton weak charge. We also study the accuracy of the previously employed approximations in computing parity-violating effects in hydrogen.

关键词： Atomic & molecular structure Coherent control W & Z bosons

NODE-Adapter: Neural Ordinary Differential Equations for Better Vision-Language Reasoning

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arXiv 2024年

作者： Zhang, Yi Cheng, Chun-Wun Yu, Ke He, Zhihai Schönlieb, Carola-Bibiane Aviles-Rivero, Angelica I. Harbin Institute of Technology Harbin China The Department of Electrical and Electronic Engineering Southern University of Science and Technology Shenzhen China The Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom

In this paper, we consider the problem of prototype-based vision-language reasoning problem. We observe that existing methods encounter three major challenges: 1) escalating resource demands and prolonging training times, 2) contending with excessive learnable parameters, and 3) fine-tuning based only on a single modality. These challenges will hinder their capability to adapt Vision-Language Models (VLMs) to downstream tasks. Motivated by this critical observation, we propose a novel method called NODE-Adapter, which utilizes Neural Ordinary Differential Equations for better vision-language reasoning. To fully leverage both visual and textual modalities and estimate class prototypes more effectively and accurately, we divide our method into two stages: cross-modal prototype construction and cross-modal prototype optimization using neural ordinary differential equations. Specifically, we exploit VLM to encode hand-crafted prompts into textual features and few-shot support images into visual features. Then, we estimate the textual prototype and visual prototype by averaging the textual features and visual features, respectively, and adaptively combine the textual prototype and visual prototype to construct the cross-modal prototype. To alleviate the prototype bias, we then model the prototype optimization process as an initial value problem with Neural ODEs to estimate the continuous gradient flow. Our extensive experimental results, which cover few-shot classification, domain generalization, and visual reasoning on human-object interaction, demonstrate that the proposed method significantly outperforms existing state-of-the-art approaches. Copyright © 2024, The Authors. All rights reserved.

关键词： Ordinary differential equations

Gas-Kinetic Scheme for Partially Ionized Plasma in Hydrodynamic Regime

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arXiv 2023年

作者： Pu, Zhigang Liu, Chang Xu, Kun Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong Institute of Applied Physics and Computational Mathematics Beijing China Shenzhen Research Institute Hong Kong University of Science and Technology Shenzhen China

Most plasmas are only partially ionized. To better understand the dynamics of these plasmas, the behaviors of a mixture of neutral species and plasma in ideal magnetohydrodynamic states are investigated. The current approach is about the construction of coupled kinetic models for the neutral gas, electron, and proton, and the development of the corresponding gas-kinetic scheme (GKS) for the solution in the continuum flow regime. The scheme is validated in the 1D Riemann problem for an enlarged system with the interaction from the Euler waves of the neutral gas and magnetohydrodynamic ones of the plasma. Additionally, the Orszag-Tang vortex problem across different ionized states is tested to examine the influence of neutrals on the MHD wave evolution. These tests demonstrate that the proposed scheme can capture the fundamental features of ideal partially ionized plasma, and a transition in the wave structure from the ideal MHD solution of the fully ionized plasma to the Euler solution of the neutral gas is obtained. Copyright © 2023, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

Bulk-Hole Correspondence and Inner Robust Boundary Modes in Singular Flatband Lattices

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Physical Review Letters 2025年第6期134卷 063803-063803页

作者： Limin Song Shenyi Gao Shiqi Xia Yongsheng Liang Liqin Tang Daohong Song Daniel Leykam Zhigang Chen The MOE Key Laboratory of Weak-Light Nonlinear Photonics TEDA Applied Physics Institute and School of Physics Nankai University Tianjin 300457 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi 030006 China Science Mathematics and Technology Cluster Singapore University of Technology and Design 8 Somapah Road 487372 Singapore Singapore

Topological entities based on bulk-boundary correspondence are ubiquitous, from conventional to higher-order topological insulators, where the protected states are typically localized at the outer boundaries (edges or corners). A less explored scenario involves protected states that are localized at the inner boundaries, sharing the same energy as the bulk states. Here, we propose and demonstrate what we refer to as the “bulk-hole correspondence’’—a relation between the inner robust boundary modes (RBMs) and the existence of multiple “holes” in singular flatband lattices, mediated by the immovable discontinuity of the bulk Bloch wave functions. We find that the number of independent flatband states always equals the sum of the number of independent compact localized states and the number of nontrivial inner RBMs, as captured by the Betti number that also counts the hole number from topological data analysis. This correspondence is universal for singular flatband lattices, regardless of the lattice shape and the hole shape. Using laser-written kagome lattices as a platform, we experimentally observe such inner RBMs, demonstrating their real-space topological nature and robustness. Our results may extend to other singular flatband systems beyond photonics, including non-Euclidean lattices, providing a new approach for understanding nontrivial flatband states and topology in hole-bearing lattice systems.

关键词： Topology

Partitioned Edge Learning over Fast Fading Channels

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IEEE Transactions on Vehicular Technology 2025年

作者： Jiang, Zhihui Wen, Dingzhu Liu, Shengli Zhu, Guangxu Yu, Guanding Zhejiang University College of Information Science and Electronic Engineering Hangzhou China ShanghaiTech University School of Information Science and Technology Shanghai China Shanghai University School of Communication and Information Engineering Shanghai China Shenzhen Research Institute of Big Data Shenzhen International Center for Industrial and Applied Mathematics Shenzhen China

The implementation of the partitioned edge learning (PARTEL) framework in practical fast-fading wireless systems with time-varying channels is investigated in this paper. By exploiting the benefit of only training and transmitting a light-size sub-model on devices, PARTEL enjoys both enhanced computation and communication efficiency compared to federated edge learning framework where each device needs to train and transmit all model parameters. In this work, we aim at further enhancing the learning efficiency via minimizing the training latency of each training round in practical fast fading channels, where each round includes multiple channel time-coherence time durations. The challenges arise from the unknown channel state information (CSI) of future durations and the coupling between load balancing and bandwidth allocation among devices. To this end, an equivalent Markov decision process (MDP) problem is derived, where each decision step corresponds to one channel coherence-time duration. The learning load balancing is first determined based on an existing design for static channels by using the expected channel gains. Then, the bandwidth allocation for uploading the local sub-model updates in each duration is sequentially determined by the proposed optimization algorithm. The spectrum efficiency is enhanced since the bandwidth is adaptively allocated to all devices according to their communication and computation statuses in each coherence-time duration. Finally, extensive simulations are conducted to show the superiority of our proposed algorithms over the existing benchmarks. Specifically, the proposed algorithm can reduce the one-round latency by up to 25.51% for the bandwidth of 70 MHz. © 1967-2012 IEEE.

关键词： Bandwidth