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arXiv 2019年

作者： Bai, Ruipu Hou, Shuai Kang, Chuangchuang College of Mathematics and Information Science Hebei University Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province Baoding071002 China College of Mathematics and Information Science Hebei University Baoding071002 China

In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if A is an m-dimensional 3-Lie algebra with an involutive derivation D, then there exists a compatible 3-pre-Lie algebra (A, -⋯ }D) such that A is the sub-adjacent 3-Lie algebra, and there is a local cocycle 3-Lie bialgebraic structure on the 2m-dimensional semi- direct product 3-Lie algebra A ad∗ A∗, which is associated to the adjoint representation (A, ad). By means of involutive derivations, the skew-symmetric solution of the 3-Lie classical Yang- Baxter equation in the 3-Lie algebra A ad∗ A∗, a class of 3-pre-Lie algebras, and eight and ten dimensional local cocycle 3-Lie bialgebras are constructed. Copyright © 2019, The Authors. All rights reserved.

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3-lie-rinehart algebras

arXiv

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arXiv 2019年

作者： BAI, RUIPU LI, XIAOJUAN WU, YINGLI College of Mathematics and Information Science Hebei University Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province Baoding071002 China College of Mathematics and Information Science Hebei University Baoding071002 China

In this paper, we define a class of 3-algebraswhich are called 3-Lie-Rinehart algebras. A 3-Lie-Rinehart algebra is a triple (L, A, ρ), where A is a commutative associative algebra, L is an A-module, (A, ρ) is a 3-Lie algebra L-module and ρ(L, L) ⊆ Der(A). We discuss the basic structures, actions and crossed modules of 3-Lie-Rinehart algebras and construct 3-Lie-Rinehart algebras from given algebras, we also study the derivations from 3-Lie-Rinehart algebras to 3-Lie A-algebras. From the study, we see that there is much difference between 3-Lie algebras and 3-Lie-Rinehart algebras. Copyright © 2019, The Authors. All rights reserved.

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MANIN TRIPLES OF 3-LIE ALGEBRAS INDUCED BY INVOLUTIVE DERIVATIONS

arXiv

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arXiv 2019年

作者： Hou, Shuai Bai, Ruipu College of Mathematics and Information Science Hebei University Baoding071002 China College of Mathematics and Information Science Hebei University Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province Baoding071002 China

For any n-dimensional 3-Lie algebra A over a field of characteristic zero with an involutive derivation D, we investigate the structure of the 3-Lie algebra B1 = A ad∗ A∗ associated with the coadjoint representation (A∗, ad∗). We then discuss the structure of the dual 3-Lie algebra B2 of the local cocycle 3-Lie bialgebra (A ad∗ A∗, ∆). By means of the involutive derivation D, we construct the 4n-dimensional Manin triple (B1 B2, [·, ·, ·]1, [·, ·, ·]2, B1, B2) of 3-Lie algebras, and provide concrete multiplication in a special basis Π1 ∪ Π2. We also construct a sixteen dimensional Manin triple (B, [·, ·, ·]) with dim B1 = 12 using an involutive derivation on a four dimensional 3-Lie algebra A with dim A1 = 2. Copyright © 2019, The Authors. All rights reserved.

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Multimodal Representation learning: Advances, Trends and Challenges

Multimodal Representation Learning: Advances, Trends and Cha...

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International Conference on machine learning and Cybernetics (ICMLC)

作者： Su-Fang Zhang Jun-Hai Zhai Bo-Jun Xie Yan Zhan Xin Wang Hebei Branch of China Meteorological Administration Training Center China Meteorological Administration Baoding China Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding Hebei China

ISBN: (纸本)9781728128177

Representation learning is the base and crucial for consequential tasks, such as classification, regression, and recognition. The goal of representation learning is to automatically learning good features with deep models. Multimodal representation learning is a special representation learning, which automatically learns good features from multiple modalities, and these modalities are not independent, there are correlations and associations among modalities. Furthermore, multimodal data are usually heterogeneous. Due to the characteristics, multimodal representation learning poses many difficulties: how to combine multimodal data from heterogeneous sources; how to jointly learning features from multimodal data; how to effectively describe the correlations and associations, etc. These difficulties triggered great interest of researchers along with the upsurge of deep learning, many deep multimodal learning methods have been proposed by different researchers. In this paper, we present an overview of deep multimodal learning, especially the approaches proposed within the last decades. We provide potential readers with advances, trends and challenges, which can be very helpful to researchers in the field of machine, especially for the ones engaging in the study of multimodal deep machine learning.

关键词： Multimodal Representation learning machine learning Deep learning Multimodal deep learning learning machine learning Artificial intelligence AUTOMATIC Association (Psychology)

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DPA-2: a large atomic model as a multi-task learner

arXiv

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arXiv 2023年

作者： Zhang, Duo Liu, Xinzijian Zhang, Xiangyu Zhang, Chengqian Cai, Chun Bi, Hangrui Du, Yiming Qin, Xuejian Peng, Anyang Huang, Jiameng Li, Bowen Shan, Yifan Zeng, Jinzhe Zhang, Yuzhi Liu, Siyuan Li, Yifan Chang, Junhan Wang, Xinyan Zhou, Shuo Liu, Jianchuan Luo, Xiaoshan Wang, Zhenyu Jiang, Wanrun Wu, Jing Yang, Yudi Yang, Jiyuan Yang, Manyi Gong, Fu-Qiang Zhang, Linshuang Shi, Mengchao Dai, Fu-Zhi York, Darrin M. Liu, Shi Zhu, Tong Zhong, Zhicheng Lv, Jian Cheng, Jun Jia, Weile Chen, Mohan Ke, Guolin Weinan, E. Zhang, Linfeng Wang, Han AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China CAS Key Laboratory of Magnetic Materials and Devices Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of Sciences Ningbo315201 China School of Electronics Engineering and Computer Science Peking University Beijing100871 China Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development School of Chemistry and Molecular Engineering East China Normal University Shanghai200062 China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States Department of Chemistry Princeton University PrincetonNJ08540 United States College of Chemistry and Molecular Engineering Peking University Beijing100871 China Yuanpei College Peking University Beijing100871 China School of Electrical Engineering and Electronic Information Xihua University Chengdu610039 China State Key Laboratory of Superhard Materials College of Physics Jilin University Changchun130012 China Key Laboratory of Material Simulation Methods & Software of Ministry of Education College of Physics Jilin University Changchun130012 China International Center of Future Science Jilin University Changchun130012 China Key Laboratory for Quantum Materials of Zhejiang Province Department of Physics School of Science Westlake University Zhejiang Hangzhou310030 China Atomistic Simulations Italia

The rapid advancements in artificial intelligence (AI) are catalyzing transformative changes in atomic modeling, simulation, and design. AI-driven potential energy models have demonstrated the capability to conduct large-scale, long-duration simulations with the accuracy of ab initio electronic structure methods. However, the model generation process remains a bottleneck for large-scale applications. We propose a shift towards a model-centric ecosystem, wherein a large atomic model (LAM), pre-trained across multiple disciplines, can be efficiently fine-tuned and distilled for various downstream tasks, thereby establishing a new framework for molecular modeling. In this study, we introduce the DPA-2 architecture as a prototype for LAMs. Pre-trained on a diverse array of chemical and materials systems using a multi-task approach, DPA-2 demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning methodologies. Our approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research. Copyright © 2023, The Authors. All rights reserved.

关键词： Multi-task learning

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An Acceleration Method for Computing Dominace Classes in Ordered Information System

An Acceleration Method for Computing Dominace Classes in Ord...

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International Conference on machine learning and Cybernetics (ICMLC)

作者： Yan Li Jing Zhang Qiang He Siyuan Liu Lujing Huo School of Applied Mathematics Beijing Normal University Zhuhai Zhuhai China Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding Hebei China School of Science Beijing University of Civil Engineering and Architecture Beijing China

ISBN: (纸本)9781728128177

In rough set theory, two crisp sets (i.e., the lower and upper approximates of a target concept) is used to describe uncertainties in given information systems. However, the traditional rough set models are built based on equivalence relations which do not consider the preference relationship of attribute values. Dominance relation-based rough set approach effectively solve this problem which uses dominance relations to substitute equivalence relations to deal with ordered data. In this kind of approach, the computing of dominance class is a necessary step to attribute reduction which is very time-consuming. In order to reduce the computational cost in calculating dominance classes, this paper presents a method to compute dominance classes by gradually reducing the search space in the domain. The corresponding algorithm is proposed. In each step of the algorithm, the inferior classes of the objects in a given information system are removed in the universe with the increase of the attributes. Experiments using six UCI data show that the proposed method improves the efficiency of computing dominance classes with the increasing of attributes and objects.

关键词： Rough set Dominance relation Dominance class Rough sets Computer based information systems Equivalence relation dominance ordered data acceleration information Classes

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Rotation Based Ensemble of One-Class Support Vector machines

Rotation Based Ensemble of One-Class Support Vector Machines

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International Conference on machine learning and Cybernetics (ICMLC)

作者： Wei-Tao Liu Hong-Jie Xing Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information Science Hebei University Baoding China

ISBN: (纸本)9781538652152

One-class support vector machine (OCSVM) is regarded as an important one-class classification method for tackling the problem of extreme class imbalance. However, combining several OCSVMs by the traditional ensemble approaches may not improve the performance of the single OCSVM because it is known as a strong classifier. In the paper, a rotation based ensemble method is proposed for integrating OCSVMs., The training data of different OCSVMs in the ensemble is transformed by different rotation matrices. Therefore, the diversity of training data for the ensemble of OCSVMs can be guaranteed. Experiments conducted on ten benchmark data sets to validate the effectiveness of the proposed ensemble strategy.

关键词： Training Support vector machines Training data Bagging Principal component analysis Forestry Diversity reception

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Adaptive-weighted One-Class Support Vector machine for Outlier Detection 29

Adaptive-weighted One-Class Support Vector Machine for Outli...

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第29届中国控制与决策会议

作者： Man Ji Hong-Jie Xing Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information ScienceHebei University

ISBN: (纸本)9781509046584

The classification performances of the traditional one-class support vector machine(OCSVM) and its variants are often not satisfying when outliers are *** deal with this case,assigning smaller weights to these outliers may alleviate their influence upon the classification boundary and enhance the robustness of *** this paper,a novel adaptive-weighted one-class support vector machine(AWOCSVM) is proposed for dealing with the outlier detection *** appropriate weights are assigned to training samples by considering both their local densities and distances between them to their *** results on two synthetic data sets and eight benchmark data sets demonstrate that the proposed AWOCSVM achieves more compact classification boundary and superior performance in comparison with the traditional OCSVM and one related approach.

关键词： One-Class Support Vector machine Classification Boundary Weighted One-Class Support Vector machine Support Vector machine

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Locality Correlation Preserving Based One-Class Support Vector machine 29

Locality Correlation Preserving Based One-Class Support Vect...

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第29届中国控制与决策会议

作者： Jian-Di Chang Hong-Jie Xing Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information ScienceHebei University

ISBN: (纸本)9781509046584

In order to fully utilize the local geometric information of the given training set consisting of the normal data,locality correlation preserving(LCP) is introduced into the traditional one-class support vector machine(OCSVM).The proposed method,named as locality correlation preserving based one-class support vector machine(LCP-OCSVM),inherits the merits of LCP and *** can keep locality correlation of the normal data and margin maximization between the normal data and the origin in the high-dimensional feature *** results on one synthetic data set and ten benchmark data sets demonstrate that the proposed method is superior to the traditional OCSVM and two related approaches.

关键词： Locality Correlation Preserving One-Class Support Vector machine One-Class Classification Local Geometric Structure

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Structure of n-Lie algebras with involutive derivations

引用

International Journal of Mathematics and Mathematical Sciences 2018年第1期2018卷 1-9页

作者： Bai, Ruipu Hou, Shuai Gao, Yansha College of Mathematics and Information Science Hebei University Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province Baoding 071002 China College of Mathematics and Information Science Hebei University Baoding 071002 China

We study the structure of n-Lie algebras with involutive derivations for n≥2. We obtain that a 3-Lie algebra A is a two-dimensional extension of Lie algebras if and only if there is an involutive derivation D on A=A1 A-1 such that dimA1=2 or dimA-1=2, where A1 and A-1 are subspaces of A with eigenvalues 1 and-1, respectively. We show that there does not exist involutive derivations on nonabelian n-Lie algebras with n=2s for s≥1. We also prove that if A is a (2s+2)-dimensional (2s+1)-Lie algebra with dimA1=r, then there are involutive derivations on A if and only if r is even, or r satisfies 1≤r≤s+2. We discuss also the existence of involutive derivations on (2s+3)-dimensional (2s+1)-Lie algebras. © 2018 Ruipu Bai et al.

关键词： LIE algebras NONABELIAN groups MATHEMATICAL proofs DERIVATIVES (Mathematics) SUBSPACES (Mathematics)

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