arXiv subjects

Lei Yang

Publications and source records attributed to Lei Yang.

At least 415 records · Page 23Linked to original sources

arXiv2021

Birational geometry of blow-ups of projective spaces along points and lines

Consider the blow-up $X$ of $\mathbb{P}^3$ at 6 points in very general position and the 15 lines through the 6 points. We construct an infinite-order pseudo-automorphism $ϕ_X$ on $X$, induced by the complete linear system of a divisor of degree 13. The effective cone of $X$ has infinitely many extremal rays and hence, $X$ is not a Mori Dream Space. The threefold $X$ has a unique anticanonical section which is a Jacobian K3 Kummer surface $S$ of Picard number 17. The restriction of $ϕ_X$ on $S$ realizes one of Keum's 192 infinite-order automorphisms of Jacobian K3 Kummer surfaces. In general, we show the blow-up of $\mathbb{P}^n$ ($n\geq 3$) at $(n+3)$ very general points and certain 9 lines through them is not Mori Dream, with infinitely many extremal effective divisors. As an application, for $n\geq 7$, the blow-up of $\overline{M}_{0,n}$ at a very general point has infinitely many extremal effective divisors.

math.AG↗

arXiv2021

E-Tree Learning: A Novel Decentralized Model Learning Framework for Edge AI

Traditionally, AI models are trained on the central cloud with data collected from end devices. This leads to high communication cost, long response time and privacy concerns. Recently Edge empowered AI, namely Edge AI, has been proposed to support AI model learning and deployment at the network edge closer to the data sources. Existing research including federated learning adopts a centralized architecture for model learning where a central server aggregates the model updates from the clients/workers. The centralized architecture has drawbacks such as performance bottleneck, poor scalability and single point of failure. In this paper, we propose a novel decentralized model learning approach, namely E-Tree, which makes use of a well-designed tree structure imposed on the edge devices. The tree structure and the locations and orders of aggregation on the tree are optimally designed to improve the training convergency and model accuracy. In particular, we design an efficient device clustering algorithm, named by KMA, for E-Tree by taking into account the data distribution on the devices as well as the the network distance. Evaluation results show E-Tree significantly outperforms the benchmark approaches such as federated learning and Gossip learning under NonIID data in terms of model accuracy and convergency.

cs.NI↗

arXiv2021

Deferrable Load Scheduling under Demand Charge: A Block Model-Predictive Control Approach

Optimal scheduling of deferrable electrical loads can reshape the aggregated load profile to achieve higher operational efficiency and reliability. This paper studies deferrable load scheduling under demand charge that imposes a penalty on the peak consumption over a billing period. Such a terminal cost poses challenges in real-time dispatch when demand forecasts are inaccurate. A block model-predictive control approach is proposed by breaking demand charge into a sequence of stage costs. The problem of charging electric vehicles is used to illustrate the efficacy of the proposed approach. Numerical examples show that the block model-predictive control outperforms benchmark methods in various settings.

math.OC↗

arXiv2020

A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters

We consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the support points of the barycenter are pre-specified, this problem can be modeled as a linear programming (LP) problem whose size can be extremely large. To handle this large-scale LP, we analyse the structure of its dual problem, which is conceivably more tractable and can be reformulated as a well-structured convex problem with 3 kinds of block variables and a coupling linear equality constraint. We then adapt a symmetric Gauss-Seidel based alternating direction method of multipliers (sGS-ADMM) to solve the resulting dual problem and establish its global convergence and global linear convergence rate. As a critical component for efficient computation, we also show how all the subproblems involved can be solved exactly and efficiently. This makes our method suitable for computing a Wasserstein barycenter on a large-scale data set, without introducing an entropy regularization term as is commonly practiced. In addition, our sGS-ADMM can be used as a subroutine in an alternating minimization method to compute a barycenter when its support points are not pre-specified. Numerical results on synthetic data sets and image data sets demonstrate that our method is highly competitive for solving large-scale Wasserstein barycenter problems, in comparison to two existing representative methods and the commercial software Gurobi.

math.OC↗

arXiv2020

Winning property of badly approximable points on curves

In this paper we prove that badly approximable points on any analytic non-degenerate curve in $\mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching generalisation of Davenport's problem from the 1960s. Amongst various consequences of our main result is a solution to Bugeaud's problem on real numbers badly approximable by algebraic numbers of arbitrary degree. The proof relies on new ideas from fractal geometry and homogeneous dynamics.

math.NT↗

arXiv2020

Solving the Travelling Thief Problem based on Item Selection Weight and Reverse Order Allocation

The Travelling Thief Problem (TTP) is a challenging combinatorial optimization problem that attracts many scholars. The TTP interconnects two well-known NP-hard problems: the Travelling Salesman Problem (TSP) and the 0-1 Knapsack Problem (KP). Increasingly algorithms have been proposed for solving this novel problem that combines two interdependent sub-problems. In this paper, TTP is investigated theoretically and empirically. An algorithm based on the score value calculated by our proposed formulation in picking items and sorting items in the reverse order in the light of the scoring value is proposed to solve the problem. Different approaches for solving the TTP are compared and analyzed; the experimental investigations suggest that our proposed approach is very efficient in meeting or beating current state-of-the-art heuristic solutions on a comprehensive set of benchmark TTP instances.

cs.AI↗

arXiv2020

Edge Computing Assisted Autonomous Flight for UAV: Synergies between Vision and Communications

Autonomous flight for UAVs relies on visual information for avoiding obstacles and ensuring a safe collision-free flight. In addition to visual clues, safe UAVs often need connectivity with the ground station. In this paper, we study the synergies between vision and communications for edge computing-enabled UAV flight. By proposing a framework of Edge Computing Assisted Autonomous Flight (ECAAF), we illustrate that vision and communications can interact with and assist each other with the aid of edge computing and offloading, and further speed up the UAV mission completion. ECAAF consists of three functionalities that are discussed in detail: edge computing for 3D map acquisition, radio map construction from the 3D map, and online trajectory planning. During ECAAF, the interactions of communication capacity, video offloading, 3D map quality, and channel state of the trajectory form a positive feedback loop. Simulation results verify that the proposed method can improve mission performance by enhancing connectivity. Finally, we conclude with some future research directions.

cs.NI↗

arXiv2020

Bad($\mathbf{w}$) is hyperplane absolute winning

In 1998 Kleinbock conjectured that any set of weighted badly approximable $d\times n$ real matrices is a winning subset in the sense of Schmidt's game. In this paper we prove this conjecture in full for vectors in $\mathbf{R}^d$ in arbitrary dimensions by showing that the corresponding set of weighted badly approximable vectors is hyperplane absolute winning. The proof uses the Cantor potential game played on the support of Ahlfors regular absolutely decaying measures and the quantitative non-divergence estimate for a class of fractal measures due to Kleinbock, Lindenstrauss and Weiss. To establish the existence of a relevant winning strategy in the Cantor potential game we introduce a new approach using two independent diagonal actions on the space of lattices.

math.NT↗

arXiv2020

CoEdge: Cooperative DNN Inference with Adaptive Workload Partitioning over Heterogeneous Edge Devices

Recent advances in artificial intelligence have driven increasing intelligent applications at the network edge, such as smart home, smart factory, and smart city. To deploy computationally intensive Deep Neural Networks (DNNs) on resource-constrained edge devices, traditional approaches have relied on either offloading workload to the remote cloud or optimizing computation at the end device locally. However, the cloud-assisted approaches suffer from the unreliable and delay-significant wide-area network, and the local computing approaches are limited by the constrained computing capability. Towards high-performance edge intelligence, the cooperative execution mechanism offers a new paradigm, which has attracted growing research interest recently. In this paper, we propose CoEdge, a distributed DNN computing system that orchestrates cooperative DNN inference over heterogeneous edge devices. CoEdge utilizes available computation and communication resources at the edge and dynamically partitions the DNN inference workload adaptive to devices' computing capabilities and network conditions. Experimental evaluations based on a realistic prototype show that CoEdge outperforms status-quo approaches in saving energy with close inference latency, achieving up to 25.5%~66.9% energy reduction for four widely-adopted CNN models.

cs.NI↗

arXiv2020

Spiral wave chimeras in reaction-diffusion systems: phenomenon, mechanism and transitions

Spiral wave chimeras (SWCs), which combine the features of spiral waves and chimera states, are a new type of dynamical patterns emerged in spatiotemporal systems due to the spontaneous symmetry breaking of the system dynamics. In generating SWC, the conventional wisdom is that the dynamical elements should be coupled in a nonlocal fashion. For this reason, it is commonly believed that SWC is excluded from the general reaction-diffusion (RD) systems possessing only local couplings. Here, by an experimentally feasible model of three-component FitzHugh-Nagumo-type RD system, we demonstrate that, even though the system elements are locally coupled, stable SWCs can still be observed in a wide region in the parameter space. The properties of SWCs are explored, and the underlying mechanisms are analyzed from the point view of coupled oscillators. Transitions from SWC to incoherent states are also investigated, and it is found that SWCs are typically destabilized in two scenarios, namely core breakup and core expansion. The former is characterized by a continuous breakup of the single asynchronous core into a number of small asynchronous cores, whereas the latter is featured by the continuous expansion of the single asynchronous core to the whole space. Remarkably, in the scenario of core expansion, the system may develop into an intriguing state in which regular spiral waves are embedded in a completely disordered background. This state, which is named shadowed spirals, manifests from a new perspective the coexistence of incoherent and coherent states in spatiotemporal systems, generalizing therefore the traditional concept of chimera states. Our studies provide an affirmative answer to the observation of SWCs in RD systems, and pave a way to the realization of SWCs in experiments.

nlin.PS↗

arXiv2020

Deep Human Answer Understanding for Natural Reverse QA

This study focuses on a reverse question answering (QA) procedure, in which machines proactively raise questions and humans supply the answers. This procedure exists in many real human-machine interaction applications. However, a crucial problem in human-machine interaction is answer understanding. The existing solutions have relied on mandatory option term selection to avoid automatic answer understanding. However, these solutions have led to unnatural human-computer interaction and negatively affected user experience. To this end, the current study proposes a novel deep answer understanding network, called AntNet, for reverse QA. The network consists of three new modules, namely, skeleton attention for questions, relevance-aware representation of answers, and multi-hop based fusion. As answer understanding for reverse QA has not been explored, a new data corpus is compiled in this study. Experimental results indicate that our proposed network is significantly better than existing methods and those modified from classical natural language processing deep models. The effectiveness of the three new modules is also verified.

cs.CL↗

arXiv2020

Study of Quasi-two-body $B_{(s)}\to ϕ(f_0(980)/f_2(1270)\to)ππ$ Decays in Perturbative QCD Approach

In 2017, LHCb collaboration reported their first observation of the rare decays $B_s \to ϕ(f_0(980)$ $/f_2(1270) \to ) π^+π^-$ and the evidence of $B^0 \to ϕ(f_0(980)/f_2(1270)\to)π^+π^-$. Motivated by this, we study these quasi-two-body decays in the perturbative QCD approach. The branching fractions, $CP$ asymmetries and the polarization fractions are calculated. We find that within the appropriate two-meson wave functions, the calculated branching fractions are in agreement with the measurements of LHCb. Based on the narrow-width approximation, We also calculate the branching fractions of the quasi-two-body $B_{d,s}\to ϕ(f_0(980)/f_2(1270)\to) π^0π^0$ and $B_{d,s}\to ϕ(f_2(1270)\to) K^+K^-$, and hope the predictions to be tested in the ongoing LHCb and Belle II experiments. Moreover, the processes $B_{d,s}\to ϕf_2(1270)$ are also analyzed under this approximation. We note that the $CP$ asymmetries of these decays are very small, because these decays are either penguin dominant or pure penguin processes.

hep-ph↗

arXiv2020

$E_8$-singularity, invariant theory and modular forms

As an algebraic surface, the equation of $E_8$-singularity $x^5+y^3+z^2=0$ can be obtained from a quotient $C_Y/\text{SL}(2, 13)$ over the modular curve $X(13)$, where $Y \subset \mathbb{CP}^5$ is a complete intersection curve given by a system of $\text{SL}(2, 13)$-invariant polynomials and $C_Y$ is a cone over $Y$. It is different from the Kleinian singularity $\mathbb{C}^2/Γ$, where $Γ$ is the binary icosahedral group. This gives a negative answer to Arnol'd and Brieskorn's questions about the mysterious relation between the icosahedron and $E_8$, i.e., the $E_8$-singularity is not necessarily the Kleinian icosahedral singularity. In particular, the equation of $E_8$-singularity possesses infinitely many kinds of distinct modular parametrizations, and there are infinitely many kinds of distinct constructions of the $E_8$-singularity. They form a variation of the $E_8$-singularity structure over the modular curve $X(13)$, for which we give its algebraic version, geometric version, $j$-function version and the version of Poincaré homology $3$-sphere as well as its higher dimensional lifting, i.e., Milnor's exotic $7$-sphere. Moreover, there are variations of $Q_{18}$ and $E_{20}$-singularity structures over $X(13)$. Thus, three different algebraic surfaces, the equations of $E_8$, $Q_{18}$ and $E_{20}$-singularities can be realized from the same quotients $C_Y/\text{SL}(2, 13)$ over the modular curve $X(13)$ and have the same modular parametrizations.

math.NT↗

arXiv2020

Event Cause Analysis in Distribution Networks using Synchro Waveform Measurements

This paper presents a machine learning method for event cause analysis to enhance situational awareness in distribution networks. The data streams are captured using time-synchronized high sampling rates synchro waveform measurement units (SWMU). The proposed method is formulated based on a machine learning method, the convolutional neural network (CNN). This method is capable of capturing the spatiotemporal feature of the measurements effectively and perform the event cause analysis. Several events are considered in this paper to encompass a range of possible events in real distribution networks, including capacitor bank switching, transformer energization, fault, and high impedance fault (HIF). The dataset for our study is generated using the real-time digital simulator (RTDS) to simulate real-world events. The event cause analysis is performed using only one cycle of the voltage waveforms after the event is detected. The simulation results show the effectiveness of the proposed machine learning-based method compared to the state-of-the-art classifiers.

eess.SP↗

arXiv2020

Deep Neural Network based Wide-Area Event Classification in Power Systems

This paper presents a wide-area event classification in transmission power grids. The deep neural network (DNN) based classifier is developed based on the availability of data from time-synchronized phasor measurement units (PMUs). The proposed DNN is trained using Bayesian optimization to search for the best hyperparameters. The effectiveness of the proposed event classification is validated through the real-world dataset of the U.S. transmission grids. This dataset includes line outage, transformer outage, frequency event, and oscillation events. The validation process also includes different PMU outputs, such as voltage magnitude, angle, current magnitude, frequency, and rate of change of frequency (ROCOF). The simulation results show that ROCOF as input feature gives the best classification performance. In addition, it is shown that the classifier trained with higher sampling rate PMUs and a larger dataset has higher accuracy.

eess.SP↗

arXiv2020

Mapping in a cycle: Sinkhorn regularized unsupervised learning for point cloud shapes

We propose an unsupervised learning framework with the pretext task of finding dense correspondences between point cloud shapes from the same category based on the cycle-consistency formulation. In order to learn discriminative pointwise features from point cloud data, we incorporate in the formulation a regularization term based on Sinkhorn normalization to enhance the learned pointwise mappings to be as bijective as possible. Besides, a random rigid transform of the source shape is introduced to form a triplet cycle to improve the model's robustness against perturbations. Comprehensive experiments demonstrate that the learned pointwise features through our framework benefits various point cloud analysis tasks, e.g. partial shape registration and keypoint transfer. We also show that the learned pointwise features can be leveraged by supervised methods to improve the part segmentation performance with either the full training dataset or just a small portion of it.

cs.CV↗

arXiv2020

Learn to Propagate Reliably on Noisy Affinity Graphs

Recent works have shown that exploiting unlabeled data through label propagation can substantially reduce the labeling cost, which has been a critical issue in developing visual recognition models. Yet, how to propagate labels reliably, especially on a dataset with unknown outliers, remains an open question. Conventional methods such as linear diffusion lack the capability of handling complex graph structures and may perform poorly when the seeds are sparse. Latest methods based on graph neural networks would face difficulties on performance drop as they scale out to noisy graphs. To overcome these difficulties, we propose a new framework that allows labels to be propagated reliably on large-scale real-world data. This framework incorporates (1) a local graph neural network to predict accurately on varying local structures while maintaining high scalability, and (2) a confidence-based path scheduler that identifies outliers and moves forward the propagation frontier in a prudent way. Experiments on both ImageNet and Ms-Celeb-1M show that our confidence guided framework can significantly improve the overall accuracies of the propagated labels, especially when the graph is very noisy.

cs.CV↗

arXiv2020

Standing on the Shoulders of Giants: Hardware and Neural Architecture Co-Search with Hot Start

Hardware and neural architecture co-search that automatically generates Artificial Intelligence (AI) solutions from a given dataset is promising to promote AI democratization; however, the amount of time that is required by current co-search frameworks is in the order of hundreds of GPU hours for one target hardware. This inhibits the use of such frameworks on commodity hardware. The root cause of the low efficiency in existing co-search frameworks is the fact that they start from a "cold" state (i.e., search from scratch). In this paper, we propose a novel framework, namely HotNAS, that starts from a "hot" state based on a set of existing pre-trained models (a.k.a. model zoo) to avoid lengthy training time. As such, the search time can be reduced from 200 GPU hours to less than 3 GPU hours. In HotNAS, in addition to hardware design space and neural architecture search space, we further integrate a compression space to conduct model compressing during the co-search, which creates new opportunities to reduce latency but also brings challenges. One of the key challenges is that all of the above search spaces are coupled with each other, e.g., compression may not work without hardware design support. To tackle this issue, HotNAS builds a chain of tools to design hardware to support compression, based on which a global optimizer is developed to automatically co-search all the involved search spaces. Experiments on ImageNet dataset and Xilinx FPGA show that, within the timing constraint of 5ms, neural architectures generated by HotNAS can achieve up to 5.79% Top-1 and 3.97% Top-5 accuracy gain, compared with the existing ones.

cs.LG↗