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11th International Conference on Learning Representations, ICLR 2023

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

Pruning neural networks before training has received increasing interest due to its potential to reduce training time and memory. One popular method is to prune the connections based on a certain metric, but it is not entirely clear what metric is the best choice. Recent advances in neural tangent kernel (NTK) theory suggest that the training dynamics of large enough neural networks is closely related to the spectrum of the NTK. Motivated by this finding, we propose to prune the connections that have the least influence on the spectrum of the NTK. This method can help maintain the NTK spectrum, which may help align the training dynamics to that of its dense counterpart. However, one possible issue is that the fixed-weight-NTK corresponding to a given initial point can be very different from the NTK corresponding to later iterates during the training phase. We further propose to sample multiple realizations of random weights to estimate the NTK spectrum. Note that our approach is weight-agnostic, which is different from most existing methods that are weight-dependent. In addition, we use random inputs to compute the fixed-weight-NTK, making our method data-agnostic as well. We name our foresight pruning algorithm Neural Tangent Kernel Spectrum-Aware Pruning (NTK-SAP). Empirically, our method achieves better performance than all baselines on multiple datasets. Our code is available at https://***/YiteWang/NTK-SAP. © 2023 11th International Conference on Learning Representations, ICLR 2023. All rights reserved.

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Augmented Lagrangian Methods for Convex Matrix Optimization Problems

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Journal of the Operations Research Society of China 2022年第2期10卷 305-342页

作者： Ying Cui Chao Ding Xu-Dong Li Xin-Yuan Zhao Department of Industrial and Systems Engineering University of MinnesotaMinneapolis 55411USA Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Data Science Fudan UniversityShanghai 200433China Shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433China College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In this paper,we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems(cMOP).Specifically,we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral *** a mild quadratic growth condition on the dual of cMOP,we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker(KKT)residuals of the sequence generated by the augmented Lagrangian methods(ALM)for solving convex matrix optimization *** details of the ALM for solving core convex matrix optimization problems are also provided.

关键词： Matrix optimization Spectral functions Quadratic growth conditions Metric subregularity Augmented Lagrangian methods Fast convergence rates Semismooth Newton methods

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TSENG-TYPE SUBGRADIENT METHODS FOR SOLVING NONMONOTONE VARIATIONAL INEQUALITIES

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UPB Scientific Bulletin, Series A: applied mathematics and physics 2023年第2期85卷 3-16页

作者： Li, Xiangyao Zhu, Li-Jun Postolache, Mihai School of Mathematics and Information Science North Minzu University Yinchuan750021 China Health Big Data Research Institute of North Minzu University Yinchuan750021 China The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province North Minzu University Yinchuan750021 China Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy Bucharest050711 Romania University "Politehnica" of Bucharest Department of Mathematics and Informatics Bucharest060042 Romania

In this article, we introduce two new approaches for solving variational inequalities without monotonicity. The first algorithm simplifies the projection region of each iteration in Ye and He [Comput. Optim. Appl., 60 (2015), 141-150], that is, it becomes the intersection of multiple half-spaces and no longer needs to be intersected with the feasible set. By a selection technique, the second algorithm replaces the projection on the common region of the feasible set and multiple half-spaces with a specific half-spaces in each iteration. The strong convergence of these two algorithms have been demonstrated under the assumption that the Minty variational inequality has a solution. Finally, some numerical examples are given to illustrate the advantages of the proposed algorithms. © 2023, Politechnica University of Bucharest. All rights reserved.

关键词： Variational techniques

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Mechanism of magnetic phase transition in correlated magnetic metal: insight into itinerant ferromagnet Fe3−δGeTe2

arXiv

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arXiv 2024年

作者： Xu, Yuanji Wang, Yue-Chao Jin, Xintao Liu, Haifeng Liu, Yu Song, Haifeng Tian, Fuyang Institute for Applied Physics University of Science and Technology Beijing Beijing100083 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China

Developing a comprehensive magnetic theory for correlated itinerant magnets poses challenges due to the difficulty in reconciling both local moments and itinerant electrons. In this work, we investigate the microscopic process of magnetic phase transition in ferromagnetic metal Fe3−δGeTe2. We find that Hund’s coupling is crucial for establishing ferromagnetic order. During the ferromagnetic transition, we observe the formation of quasiparticle flat bands and an opposing tendency in spectral weight transfer, primarily between the lower and upper Hubbard bands, across the two spin channels. Moreover, our results indicate that one of the inequivalent Fe sites exhibits Mott physics, while the other Fe site exhibits Hund’s physics, attributable to their distinct atomic environments. We suggest that ferromagnetic order reduces spin fluctuations and makes flat bands near the Fermi level more distinct. The hybridization between the distinctly flat bands and other itinerant bands offers a possible way to form heavy fermion behavior in ferromagnets. The complex interactions of competing orders drive correlated magnetic metals to a new frontier for discovering outstanding quantum states. © 2024, CC BY.

关键词： Ferromagnetism

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Error Exponent and Strong Converse for Quantum Soft Covering

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IEEE Transactions on Information Theory 2024年第5期70卷 3499-3511页

作者： Cheng, Hao-Chung Gao, Li The Graduate Institute of Communication Engineering The Institute of Applied Mathematical Sciences National Taiwan University Center for Quantum Science and Engineering The Department of Electrical Engineering The Department of Mathematics Taipei10617 Taiwan National Center for Theoretical Sciences Physics Division Taipei10617 Taiwan Quantum Computing Center New Taipei City236 Taiwan University of Houston Department of Mathematics HoustonTX77204 United States

How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem, which uses a pairwise-independent random codebook to approximate the target output state of a quantum channel. We establish a one-shot error exponent bound and a one-shot strong converse bound on the approximation error measured in terms of the expected trace distance between the codebook-induced state and the true channel output state. When using independent and identically-distributed random codebook with a rate above the quantum mutual information I(X:B)ρ , we prove that the error decays exponentially with its error exponent expressed by the sandwiched Rényi information. On the other hand, when the rate of the codebook size is below the quantum mutual information, the error converges to one exponentially fast. Similar results are obtained using a random constant composition codebook, whereas the sandwiched Augustin information gives the error exponent. In addition to the above large deviation analysis, our results also hold in the moderate deviation regime. © 1963-2012 IEEE.

关键词： Signal encoding

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Fine-tune chiroptical activity in discrete chiral Au nanorods

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Nano Research 2022年第7期15卷 6574-6581页

作者： Guangchao Zheng Sulin Jiao Wei Zhang Shenli Wang Qinghua Zhang Lin Gu Weixiang Ye Junjun Li Xiaochen Ren Zhicheng Zhang Kwok-yin Wong School of Physics and Microelectronics Zhengzhou UniversityZhengzhou 450001China State Key Laboratory of Chemical Biology and Drug Discovery Department of Applied Biology and Chemical TechnologyThe Hong Kong Polytechnic UniversityKowloonHong KongChina Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Food Science and Engineering Henan University of TechnologyZhengzhou 450001China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China Department of Applied Physics School of ScienceHainan UniversityHaikou 570228China Tianjin Key Laboratory of Molecular Optoelectronic Sciences Department of ChemistrySchool of ScienceTianjin University&Collaborative Innovation Center of Chemical Science and EngineeringTianjin 300072China

Accurate researches on the surface plasmon resonance(SPR)-based applications of chiral plasmonic metal nanoparticles(NPs)still remain a great ***,a series of chiral plasmonic metal NPs,e.g.,chiral Au nanorods(c-Au NRs),c-Au@Ag core–shell,and c-Au@TiO_(2) core–shell NRs,with different chiroptical activities have been *** circular dichroism(PCD)bands of c-Au NRs can be precisely tailored by tuning the longitudinal SPR(LSPR)and amount of Au NRs as ***,a shift of PCD bands within ultraviolet–visible–near infrared ray(UV–vis–NIR)region can also be achieved through the functionalization of a shell of another metal or ***,chirality transfer from c-Au core to Ag shell leads to new PCD bands at the near-UV *** tuning of PCD bands and chirality transfer are confirmed by our developed theoretical *** chiral Au NRs-based chiral plasmonic nanomaterials with tunable chiroptical activities will be helpful to understand the structure-direct PCD and to extend circularly polarized-based applications.

关键词： chiral Au nanorods(c-Au NRs) surface plasmon resonance optical activity chirality transfer

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Estimating the Probability of Falling Share Price Below the Minimum Level 9

Estimating the Probability of Falling Share Price Below the ...

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9th International Conference on Control, Decision and Information Technologies, CoDIT 2023

作者： Semakov, Sergei L. Moscow Institute of Physics and Technology Faculty of Control and Applied Mathematics Russia Moscow Automobile and Road Construction Institute Department of Mathematics Russia Federal Research Center 'Computer Science and Control' of the Russian Academy of Sciences Russia

ISBN: (纸本)9798350311402

A technology is proposed for estimating the probability that a share price will fall below the minimum level. The exact expression is obtained for the required probability under the assumption that the behavior of the share price is described by the well-known model of Samuelson, according to which the relative change in price is the sum of the non-random trend and the Wiener process. The obtained result is qualitatively analyzed for various relations of the problem parameters. © 2023 IEEE.

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THE GEOMETRICAL-CONVEXITY OF A FUNCTION RELATED TO THE MINC-SATHRE RATIO

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UPB Scientific Bulletin, Series A: applied mathematics and physics 2024年第4期86卷 3-10页

作者： Mortici, Cristinel Postolache, Mihai Valahia University of Târgovişte Târgovişte Romania National University of Science & Technology Politehnica Bucharest Department of Mathematics and Informatics Bucharest060042 Romania Academy of Romanian Scientists 3 Ilfov Bucharest050044 Romania Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy Bucharest050711 Romania The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province and Health Big Data Research Institute North Minzu University Yinchuan750021 China

In this paper we give a new proof for the fact that the function Γ (x)1 x−1 is geometrically convex. As an application, we give an improvement of Minc-Sathre inequality. © 2024, Politechnica University of Buchar... 详细信息

关键词： Choquet integral

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Optimizing over Multiple Distributions under Generalized Quasar-Convexity Condition 38

Optimizing over Multiple Distributions under Generalized Qua...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Ding, Shihong Yang, Long Luo, Luo Fang, Cong State Key Lab of General AI School of Intelligence Science and Technology Peking University China School of Data Science Fudan University China Institute for Artificial Intelligence Peking University China Shanghai Key Laboratory for Contemporary Applied Mathematics China

We study a typical optimization model where the optimization variable is composed of multiple probability distributions. Though the model appears frequently in practice, such as for policy problems, it lacks specific analysis in the general setting. For this optimization problem, we propose a new structural condition/landscape description named generalized quasar-convexity (GQC) beyond the realms of convexity. In contrast to original quasar-convexity [24], GQC allows an individual quasar-convex parameter γi for each variable block i and the smaller of γi implies less block-convexity. To minimize the objective function, we consider a generalized oracle termed as the internal function that includes the standard gradient oracle as a special case. We provide optimistic mirror descent (OMD) for multiple distributions and prove that the algorithm can achieve an adaptive (Equation presented) iteration complexity to find an Ε-suboptimal global solution without pre-known the exact values of γi when the objective admits "polynomial-like" structural. Notably, it achieves iteration complexity that does not explicitly depend on the number of distributions and strictly faster (Equation presented) than mirror decent methods. We also extend GQC to the minimax optimization problem proposing the generalized quasar-convexity-concavity (GQCC) condition and a decentralized variant of OMD with regularization. Finally, we show the applications of our algorithmic framework on discounted Markov Decision Processes problem and Markov games, which bring new insights on the landscape analysis of reinforcement learning. © 2024 Neural information processing systems foundation. All rights reserved.

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EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li Center for Data Science Peking University Zuse Institute Berlin Department of Mathematics and Computer Science Freie Universit?t Berlin Laboratory of Mathematics and Applied Mathematics(LMAM)and School of Mathematical Sciences Peking University Center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

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