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Universality of explosive percolation under product and sum rule

Physical Review E 2023年第3期108卷 034108-034108页

作者： Ziting Luo Wei Chen Jan Nagler LMIB and School of Mathematical Sciences Beihang University Beijing 100191 China Institute of Artificial Intelligence Beihang University Beijing 100191 China Zhongguancun Laboratory Beijing 100094 People's Republic of China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing 100191 China Deep Dynamics Centre for Human and Machine Intelligence Frankfurt School of Finance and Management Frankfurt am Main 60322 Germany

We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M−1 candidate edges are being discarded. These two rules are prototypical “explosive” percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., M=2. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with M larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for M from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed M.

关键词： Percolation phase transition

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Coupled Alternating Neural Networks for Solving Multi-Population High-Dimensional Mean-Field Games with Stochasticity

TechRxiv

引用

TechRxiv 2022年

作者： Wang, Guofang Yao, Wang Zhang, Xiao Niu, Zijia The School of Mathematical Sciences Beihang University Beijing100191 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Ministry of Education Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing100191 China Peng Cheng Laboratory Guangdong Shenzhen518055 China The Institute of Artificial Intelligence Beihang University Beijing100191 China Key Laboratory of Mathematics Informatics and Behavioral Semantics Ministry of Education Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing100191 China

Multi-population mean-field game is a critical subclass of mean-field games (MFGs). It is a theoretically feasible multi-agent model for simulating and analyzing the game between multiple heterogeneous populations of interacting massive agents. Due to the factors of game complexity, dimensionality disaster and disturbances should be taken into account simultaneously, how to solve the multi-population high-dimensional stochastic MFG problem is faced with great challenges. We present CA-Net, a coupled alternating neural network approach for tractably solving multi-population high-dimensional MFGs in the stochastic case. First, we provide a universal modeling framework for large-scale heterogeneous multi-agent game systems, which is strictly expressed as a multi-population MFG problem. Next, we generalize the potential variational primal-dual structure that MFGs exhibit, then phrase the multi-population MFG problem as a convex-concave saddle-point problem. Last but not least, we design a generative adversarial network (GAN) with multiple generators and multiple discriminators—the solving network, which parameterizes the value functions and the density functions of multiple populations by two sets of neural networks, respectively. Moreover, numerical experiments demonstrate the feasibility and effectiveness of our approach. © 2022, CC BY.

关键词： Generative adversarial networks

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BiKT: Unleashing the potential of GNNs via Bi-directional Knowledge Transfer

arXiv

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arXiv 2023年

作者： Zheng, Shuai Liu, Zhizhe Zhu, Zhenfeng Zhang, Xingxing Li, Jianxin Zhao, Yao The Institute of Information Science Beijing Jiaotong University Beijing100044 China The Beijing Key Laboratory of Advanced Information Science and Network Technology Beijing100044 China Qiyuan Lab Beijing China The Beijing Advanced Innovation Center for Big Data and Brain Computing School of Computer Science and Engineering Beihang University Beijing100083 China

Based on the message-passing paradigm, there has been an amount of research proposing diverse and impressive feature propagation mechanisms to improve the performance of GNNs. However, less focus has been put on feature transformation, another major operation of the message-passing framework. In this paper, we first empirically investigate the performance of the feature transformation operation in several typical GNNs. Unexpectedly, we notice that GNNs do not completely free up the power of the inherent feature transformation operation. By this observation, we propose the Bi-directional Knowledge Transfer (BiKT), a plug-and-play approach to unleash the potential of the feature transformation operations without modifying the original architecture. Taking the feature transformation operation as a derived representation learning model that shares parameters with the original GNN, the direct prediction by this model provides a topological-agnostic knowledge feedback that can further instruct the learning of GNN and the feature transformations therein. On this basis, BiKT not only allows us to acquire knowledge from both the GNN and its derived model but promotes each other by injecting the knowledge into the other. In addition, a theoretical analysis is further provided to demonstrate that BiKT improves the generalization bound of the GNNs from the perspective of domain adaption. An extensive group of experiments on up to 7 datasets with 5 typical GNNs demonstrates that BiKT brings up to 0.5% - 4% performance gain over the original GNN, which means a boosted GNN is obtained. Meanwhile, the derived model also shows a powerful performance to compete with or even surpass the original GNN, enabling us to flexibly apply it independently to some other specific downstream tasks. Copyright © 2023, The Authors. All rights reserved.

关键词： Message passing

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Realizing Emotional Interactions to Learn User Experience and Guide Energy Optimization for Mobile Architectures 22

Realizing Emotional Interactions to Learn User Experience an...

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Proceedings of the 55th Annual IEEE/ACM International Symposium on Microarchitecture

作者： Xueliang Li Zhuobin Shi Junyang Chen Yepang Liu National Engineering Laboratory for Big Data System Computing Technology Shenzhen University China College of Computer Science and Software Engineering Shenzhen University China Research Institute of Trustworthy Autonomous Systems Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation and Department of Computer Science and Engineering Southern University of Science and Technology China

ISBN: (纸本)9781665462723

In the age of AI, mobile architectures such as smartphones are still "cold machines"; machines do not feel. If the architecture is able to feel users' feelings and runtime user experience (UX), it will accordingly adapt performance/energy to find the optimal system-operating state that consumes the least energy to satisfy users. In this paper, we will utilize users' facial expressions (FEs) to learn their runtime UX. We know that FEs are the natural and direct way for humans to convey their emotions and feelings. Our study reveals that FEs also reflect UX. Our research for the first time quantifies the link between FEs and UX. Leveraging this link, the architecture will be able to use the front camera to see FEs and feel users' UX. Based on UX, the architecture can appropriately provision computing resources. We propose Vi-energy system to realize the above idea. Our evaluation shows that Vi-energy reduces energy consumption by 52.9% at maximum and secures UX.

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MG-DVD: A real-time framework for malware variant detection based on dynamic heterogeneous graph learning

arXiv

引用

arXiv 2021年

作者： Liu, Chen Li, Bo Zhao, Jun Su, Ming Liu, Xu-Dong School of Computer Science and Engineering Beihang University Beijing China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University China

Detecting the newly emerging malware variants in real time is crucial for mitigating cyber risks and proactively blocking intrusions. In this paper, we propose MG-DVD, a novel detection framework based on dynamic heterogeneous graph learning, to detect malware variants in real time. Particularly, MG-DVD first models the fine-grained execution event streams of malware variants into dynamic heterogeneous graphs and investigates real-world meta-graphs between malware objects, which can effectively characterize more discriminative malicious evolutionary patterns between malware and their variants. Then, MG-DVD presents two dynamic walk-based heterogeneous graph learning methods to learn more comprehensive representations of malware variants, which significantly reduces the cost of the entire graph retraining. As a result, MG-DVD is equipped with the ability to detect malware variants in real time, and it presents better interpretability by introducing meaningful meta-graphs. Comprehensive experiments on large-scale samples prove that our proposed MG-DVD outperforms state-of-the-art methods in detecting malware variants in terms of effectiveness and efficiency. Copyright © 2021, The Authors. All rights reserved.

关键词： Malware

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On the Chordality of Simple Decomposition in Top-Down Style 8th

On the Chordality of Simple Decomposition in Top-Down Style

引用

8th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2019

作者： Mou, Chenqi Lai, Jiahua LMIB–School of Mathematical Sciences Beihang University Beijing100191 China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing100191 China

ISBN: (纸本)9783030431198

Simple decomposition of polynomial sets computes conditionally squarefree triangular sets or systems with certain zero or ideal relationships with the polynomial sets. In this paper we study the chordality of polynomial sets occurring in the process of simple decomposition in top-down style. We first reformulate Wang’s algorithm for simple decomposition in top-down style so that the decomposition process can be described in an inductive way. Then we prove that for a polynomial set whose associated graph is chordal, all the polynomial sets in the process of Wang’s algorithm for computing simple decomposition of this polynomial set have associated graphs which are subgraphs of the input chordal graph. © 2020, Springer Nature Switzerland AG.

关键词： Polynomials

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Self-organization Preserved Graph Structure Learning with Principle of Relevant Information

arXiv

引用

arXiv 2022年

作者： Sun, Qingyun Li, Jianxin Yang, Beining Fu, Xingcheng Peng, Hao Yu, Philip S. Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing100191 China School of Computer Science and Engineering Beihang University Beijing100191 China Department of Computer Science University of Illinois at Chicago Chicago United States

Most Graph Neural Networks follow the message-passing paradigm, assuming the observed structure depicts the ground-truth node relationships. However, this fundamental assumption cannot always be satisfied, as real-world graphs are always incomplete, noisy, or redundant. How to reveal the inherent graph structure in a unified way remains under-explored. We proposed PRI-GSL, a Graph Structure Learning framework guided by the Principle of Relevant Information, providing a simple and unified framework for identifying the self-organization and revealing the hidden structure. PRI-GSL learns a structure that contains the most relevant yet least redundant information quantified by von Neumann entropy and Quantum Jensen-Shannon divergence. PRI-GSL incorporates the evolution of quantum continuous walk with graph wavelets to encode node structural roles, showing in which way the nodes interplay and self-organize with the graph structure. Extensive experiments demonstrate the superior effectiveness and robustness of PRI-GSL. Copyright © 2022, The Authors. All rights reserved.

关键词： Graphic methods

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A local enhanced spatiotemporal tensor decomposition for missing travel time completion

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Smart and Resilient Transportation 2022年第3期4卷 194-208页

作者： Yilong Ren Jianbin Wang School of Transportation Science and Engineering Beihang University Beijing China Zhongguancun Laboratory Beijing China and Beihang Hangzhou Innovation Institute Yuhang Hangzhou China School of Transportation Science and Engineering Beihang University Beijing China and Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing China

Purpose The missing travel time data for roads is a common problem encountered by traffic management departments. Tensor decomposition, as one of the most widely used method for completing missing traffic data, plays a significant role in the intelligent transportation system (ITS). However, existing methods of tensor decomposition focus on the global data structure, resulting in relatively low accuracy in fibrosis missing scenarios. Therefore, this paper aims to propose a novel tensor decomposition model which further considers the local spatiotemporal similarity for fibrosis missing to improve travel time completion accuracy. Design/methodology/approach The proposed model can aggregate road sections with similar physical attributes by spatial clustering, and then it calculates the temporal association of road sections by the dynamic longest common subsequence. A similarity relationship matrix in the temporal dimension is constructed and incorporated into the tensor completion model, which can enhance the local spatiotemporal relationship of the missing parts of the fibrosis type. Findings The experiment shows that this method is superior and robust. Compared with other baseline models, this method has the smallest error and maintains good completion results despite high missing rates. Originality/value This model has higher accuracy for the fibrosis missing and performs good convergence effects in the case of the high missing rate.

关键词： Travel time data completion Fibrosis missing scenarios Tensor decomposition

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Differentiable top-k with optimal transport 34

Differentiable top-k with optimal transport

引用

34th Conference on Neural Information Processing Systems, NeurIPS 2020

作者： Xie, Yujia Dai, Hanjun Chen, Minshuo Dai, Bo Zhao, Tuo Zha, Hongyuan Wei, Wei Pfister, Tomas College of Computing Georgia Tech United States Google Brain College of Engineering Georgia Tech United States School of Data Science Shenzhen Research Institute of Big Data CUHK Shenzhen China Google Cloud AI

The top-k operation, i.e., finding the k largest or smallest elements from a collection of scores, is an important model component, which is widely used in information retrieval, machine learning, and data mining. However, if the top-k operation is implemented in an algorithmic way, e.g., using bubble algorithm, the resulting model cannot be trained in an end-to-end way using prevalent gradient descent algorithms. This is because these implementations typically involve swapping indices, whose gradient cannot be computed. Moreover, the corresponding mapping from the input scores to the indicator vector of whether this element belongs to the top-k set is essentially discontinuous. To address the issue, we propose a smoothed approximation, namely the SOFT (Scalable Optimal transport-based diFferenTiable) top-k operator. Specifically, our SOFT top-k operator approximates the output of the top-k operation as the solution of an Entropic Optimal Transport (EOT) problem. The gradient of the SOFT operator can then be efficiently approximated based on the optimality conditions of EOT problem. We apply the proposed operator to the k-nearest neighbors and beam search algorithms, and demonstrate improved performance. © 2020 Neural information processing systems foundation. All rights reserved.

关键词： data mining

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Two-stage Generative Adversarial Recovery Network for MR brain Images Containing Tumors 9

Two-stage Generative Adversarial Recovery Network for MR Bra...

引用

9th International Conference on Bioinformatics and Biomedical Science, ICBBS 2020

作者： Kong, Meng Zhao, Haifeng Zhang, Shaojie Tang, Zhenyu School of Computer Science and Technology Anhui University HefeiAnhui230601 China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing100191 China

ISBN: (纸本)9781450388658

brain image registration (BIR) plays an important role in neuroscience. However, for the registration of brain image containing tumors, the existence of tumor could cause great influence to BIR. One possible solution for getting rid of such influence is to recover the tumor brain image to "normal"appearance brain image (no tumor). Most of existing methods for tumor brain image recovery are based on low-rank, which is time consuming and low recovery quality. In this paper, wepropose a novel deep-learning based method for tumor brain image recovery. Specifically, a two-stage generative adversarial network comprising a region recovery stage and an image recovery stage is presented. For the input tumor brain image, the region recovery stage first generates a recovered brain region image containing three different regions (i.e., the gray matter, the white matter and the cerebrospinal fluid). The recovered brain region image is used in the image recovery stage as priori information to get the final "normal"appearance brain image. Both stages are trained under the generative adversarial framework. The experimental results demonstrate that the registration accuracy of tumor brain images can be significantly enhanced by our network as compared to the state-of-the-art image recovery methods. © 2020 ACM.

关键词： Tumors

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