arXiv subjects

Hao Zhu

Publications and source records attributed to Hao Zhu.

At least 271 records · Page 15Linked to original sources

arXiv2019

Quantifying Similarity between Relations with Fact Distribution

We introduce a conceptually simple and effective method to quantify the similarity between relations in knowledge bases. Specifically, our approach is based on the divergence between the conditional probability distributions over entity pairs. In this paper, these distributions are parameterized by a very simple neural network. Although computing the exact similarity is in-tractable, we provide a sampling-based method to get a good approximation. We empirically show the outputs of our approach significantly correlate with human judgments. By applying our method to various tasks, we also find that (1) our approach could effectively detect redundant relations extracted by open information extraction (Open IE) models, that (2) even the most competitive models for relational classification still make mistakes among very similar relations, and that (3) our approach could be incorporated into negative sampling and softmax classification to alleviate these mistakes. The source code and experiment details of this paper can be obtained from https://github.com/thunlp/relation-similarity.

cs.AI↗

arXiv2019

Fast Nonconvex SDP Solvers for Large-scale Power System State Estimation

Fast power system state estimation (SE) solution is of paramount importance for achieving real-time decision making in power grid operations. Semidefinite programming (SDP) reformulation has been shown effective to obtain the global optimum for the nonlinear SE problem, while suffering from high computational complexity. Thus, we leverage the recent advances in nonconvex SDP approach that allows for the simple first-order gradient-descent (GD) updates. Using the power system model, we can verify that the SE objective function enjoys nice properties (strongly convex, smoothness) which in turn guarantee a linear convergence rate of the proposed GD-based SE method. To further accelerate the convergence speed, we consider the accelerated gradient descent (AGD) extension, as well as their robust versions under outlier data and a hybrid GD-based SE approach with additional synchrophasor measurements. Numerical tests on the IEEE 118-bus, 300-bus and the synthetic ACTIVSg2000-bus systems have demonstrated that FGD-SE and AGD-SE, can approach the near-optimal performance of the SDP-SE solution at significantly improved computational efficiency, especially so for AGD-SE.

eess.SP↗

arXiv2019

Detailed Human Shape Estimation from a Single Image by Hierarchical Mesh Deformation

This paper presents a novel framework to recover detailed human body shapes from a single image. It is a challenging task due to factors such as variations in human shapes, body poses, and viewpoints. Prior methods typically attempt to recover the human body shape using a parametric based template that lacks the surface details. As such the resulting body shape appears to be without clothing. In this paper, we propose a novel learning-based framework that combines the robustness of parametric model with the flexibility of free-form 3D deformation. We use the deep neural networks to refine the 3D shape in a Hierarchical Mesh Deformation (HMD) framework, utilizing the constraints from body joints, silhouettes, and per-pixel shading information. We are able to restore detailed human body shapes beyond skinned models. Experiments demonstrate that our method has outperformed previous state-of-the-art approaches, achieving better accuracy in terms of both 2D IoU number and 3D metric distance. The code is available in https://github.com/zhuhao-nju/hmd.git

cs.CV↗

arXiv2019

On the $j$-th Eigenvalue of Sturm-Liouville Problem and the Maslov Index

In the previous papers \cite{HLWZ,KWZ}, the jump phenomena of the $j$-th eigenvalue were completely characterized for Sturm-Liouville problems. In this paper, we show that the jump number of these eigenvalue branches is exactly the Maslov index for the path of corresponding boundary conditions. Then we determine the sharp range of the $j$-th eigenvalue on each layer of the space of boundary conditions. Finally, we prove that the graph of monodromy matrix tends to the Dirichlet boundary condition as the spectral parameter goes to $-\infty$.

math.FA↗

arXiv2019

Barotropic instability of shear flows

We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability conditions. We study the flow with Sinus profile in details and obtain the sharp stability boundary in the whole parameter space, which corrects previous results in the fluid literature. Our new results are confirmed by more accurate numerical computation. The addition of the Coriolis force is found to bring fundamental changes to the stability of shear flows. Moreover, we study dynamical behaviors near the shear flows, including the bifurcation of nontrivial traveling wave solutions and the linear inviscid damping. The first ingredient of our proof is a careful classification of the neutral modes. The second one is to write the linearized fluid equation in a Hamiltonian form and then use an instability index theory for general Hamiltonian PDEs. The last one is to study the singular and non-resonant neutral modes using Sturm-Liouville theory and hypergeometric functions.

math.AP↗

arXiv2019

Breaking the Spatio-Angular Trade-off for Light Field Super-Resolution via LSTM Modelling on Epipolar Plane Images

Light-field cameras (LFC) have received increasing attention due to their wide-spread applications. However, current LFCs suffer from the well-known spatio-angular trade-off, which is considered as an inherent and fundamental limit for LFC designs. In this paper, by doing a detailed geometrical optical analysis of the sampling process in an LFC, we show that the effective sampling resolution is generally higher than the number of micro-lenses. This contribution makes it theoretically possible to break the resolution trade-off. Our second contribution is an epipolar plane image (EPI) based super-resolution method, which can super-resolve the spatial and angular dimensions simultaneously. We prove that the light field is a 2D series, thus, a specifically designed CNN-LSTM network is proposed to capture the continuity property of the EPI. Rather than leveraging semantic information, our network focuses on extracting geometric continuity in the EPI. This gives our method an improved generalization ability and makes it applicable to a wide range of previously unseen scenes. Experiments on both synthetic and real light fields demonstrate the improvements over state-of-the-art, especially in large disparity areas.

cs.CV↗

arXiv2019

Graph Neural Networks with Generated Parameters for Relation Extraction

Recently, progress has been made towards improving relational reasoning in machine learning field. Among existing models, graph neural networks (GNNs) is one of the most effective approaches for multi-hop relational reasoning. In fact, multi-hop relational reasoning is indispensable in many natural language processing tasks such as relation extraction. In this paper, we propose to generate the parameters of graph neural networks (GP-GNNs) according to natural language sentences, which enables GNNs to process relational reasoning on unstructured text inputs. We verify GP-GNNs in relation extraction from text. Experimental results on a human-annotated dataset and two distantly supervised datasets show that our model achieves significant improvements compared to baselines. We also perform a qualitative analysis to demonstrate that our model could discover more accurate relations by multi-hop relational reasoning.

cs.CL↗

arXiv2019

Discrete Sturm-Liouville problems: singularity of the $n$-th eigenvalue with application to Atkinson type

In this paper, we characterize singularity of the $n$-th eigenvalue of self-adjoint discrete Sturm-Liouville problems in any dimension. For a fixed Sturm-Liouville equation, we completely characterize singularity of the $n$-th eigenvalue. For a fixed boundary condition, unlike in the continuous case, the $n$-th eigenvalue exhibits jump phenomena and we describe the singularity under a non-degenerate assumption. Compared with the continuous case in [8, 12], the singular set here is involved heavily with coefficients of the Sturm-Liouville equations. This, along with arbitrariness of the dimension, causes difficulty when dividing areas in layers of the considered space such that the $n$-th eigenvalue has the same singularity in any given area. We study the singularity by partitioning and analyzing the local coordinate systems, and provide a Hermitian matrix which can determine the areas' division. To prove the asymptotic behavior of the $n$-th eigenvalue, we generalize the method developed in [21] to any dimension. Finally, by transforming the Sturm-Liouville problem of Atkinson type in any dimension to a discrete one, we can not only determine the number of eigenvalues, but also apply our approach above to obtain the complete characterization of singularity of the $n$-th eigenvalue for the Atkinson type.

math.SP↗

arXiv2019

CrowdPose: Efficient Crowded Scenes Pose Estimation and A New Benchmark

Multi-person pose estimation is fundamental to many computer vision tasks and has made significant progress in recent years. However, few previous methods explored the problem of pose estimation in crowded scenes while it remains challenging and inevitable in many scenarios. Moreover, current benchmarks cannot provide an appropriate evaluation for such cases. In this paper, we propose a novel and efficient method to tackle the problem of pose estimation in the crowd and a new dataset to better evaluate algorithms. Our model consists of two key components: joint-candidate single person pose estimation (SPPE) and global maximum joints association. With multi-peak prediction for each joint and global association using graph model, our method is robust to inevitable interference in crowded scenes and very efficient in inference. The proposed method surpasses the state-of-the-art methods on CrowdPose dataset by 5.2 mAP and results on MSCOCO dataset demonstrate the generalization ability of our method. Source code and dataset will be made publicly available.

cs.CV↗

arXiv2019

Optimal Power Flow with Step-Voltage Regulators in Multi-Phase Distribution Networks

This paper develops a branch-flow based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed-delta, and open-delta step-voltage regulators (SVRs). SVRs are assumed ideal and their taps are represented by continuous decision variables. To tackle the non-linearity, the branch-flow semidefinite programming framework of traditional OPF is expanded to accommodate SVR edges. Three types of non-convexity are addressed: (a) rank-1 constraints on non-SVR edges, (b) nonlinear equality constraints on SVR power flows and taps, and (c) trilinear equalities on SVR voltages and taps. Leveraging a practical phase-separation assumption on the SVR secondary voltage, novel McCormick relaxations are provided for (c) and certain rank-1 constraints of (a), while dropping the rest. A linear relaxation based on conservation of power is used in place of (b). Numerical simulations on standard distribution test feeders corroborate the merits of the proposed convex formulation.

math.OC↗

arXiv2019

Dynamic Distribution State Estimation Using Synchrophasor Data

The increasing deployment of distribution-level phasor measurement units (PMUs) calls for dynamic distribution state estimation (DDSE) approaches that tap into high-rate measurements to maintain a comprehensive view of the distribution-system state in real time. Accordingly, this paper explores the development of a fast algorithmic framework by casting the DDSE task within the time-varying optimization realm. The time-varying formulation involves a time-varying robustified least-squares approach, and it naturally models optimal trajectories for the estimated states under streaming of measurements. The formulation is based on a linear surrogate of the AC power-flow equations, and it includes an element of robustness with respect to measurement outliers. The paper then leverages a first-order prediction-correction method to achieve simple online updates that can provably track the state variables from heterogeneous measurements. This online algorithm is computationally efficient as it relies on the Hessian of the cost function without computing matrix-inverse. Convergence and bounds on the estimation errors of proposed algorithm can be analytically established.

math.OC↗

arXiv2018

Language Modeling with Sparse Product of Sememe Experts

Most language modeling methods rely on large-scale data to statistically learn the sequential patterns of words. In this paper, we argue that words are atomic language units but not necessarily atomic semantic units. Inspired by HowNet, we use sememes, the minimum semantic units in human languages, to represent the implicit semantics behind words for language modeling, named Sememe-Driven Language Model (SDLM). More specifically, to predict the next word, SDLM first estimates the sememe distribution gave textual context. Afterward, it regards each sememe as a distinct semantic expert, and these experts jointly identify the most probable senses and the corresponding word. In this way, SDLM enables language models to work beyond word-level manipulation to fine-grained sememe-level semantics and offers us more powerful tools to fine-tune language models and improve the interpretability as well as the robustness of language models. Experiments on language modeling and the downstream application of headline gener- ation demonstrate the significant effect of SDLM. Source code and data used in the experiments can be accessed at https:// github.com/thunlp/SDLM-pytorch.

cs.CL↗

arXiv2018

FewRel: A Large-Scale Supervised Few-Shot Relation Classification Dataset with State-of-the-Art Evaluation

We present a Few-Shot Relation Classification Dataset (FewRel), consisting of 70, 000 sentences on 100 relations derived from Wikipedia and annotated by crowdworkers. The relation of each sentence is first recognized by distant supervision methods, and then filtered by crowdworkers. We adapt the most recent state-of-the-art few-shot learning methods for relation classification and conduct a thorough evaluation of these methods. Empirical results show that even the most competitive few-shot learning models struggle on this task, especially as compared with humans. We also show that a range of different reasoning skills are needed to solve our task. These results indicate that few-shot relation classification remains an open problem and still requires further research. Our detailed analysis points multiple directions for future research. All details and resources about the dataset and baselines are released on http://zhuhao.me/fewrel.

cs.LG↗

arXiv2018

Linear inviscid damping for the $β$-plane equation

In this paper, we study the linear inviscid damping for the linearized $β$-plane equation around shear flows. We develop a new method to give the explicit decay rate of the velocity for a class of monotone shear flows. This method is based on the space-time estimate and the vector field method in sprit of the wave equation. For general shear flows including the Sinus flow, we also prove the linear damping by establishing the limiting absorption principle, which is based on the compactness method introduced by Wei-Zhang-Zhao in \cite{WZZ2}. The main difficulty is that the Rayleigh-Kuo equation has more singular points due to the Coriolis effects so that the compactness argument becomes more involved and delicate.

math.AP↗

arXiv2018

Dense Light Field Reconstruction From Sparse Sampling Using Residual Network

A light field records numerous light rays from a real-world scene. However, capturing a dense light field by existing devices is a time-consuming process. Besides, reconstructing a large amount of light rays equivalent to multiple light fields using sparse sampling arises a severe challenge for existing methods. In this paper, we present a learning based method to reconstruct multiple novel light fields between two mutually independent light fields. We indicate that light rays distributed in different light fields have the same consistent constraints under a certain condition. The most significant constraint is a depth related correlation between angular and spatial dimensions. Our method avoids working out the error-sensitive constraint by employing a deep neural network. We solve residual values of pixels on epipolar plane image (EPI) to reconstruct novel light fields. Our method is able to reconstruct 2 to 4 novel light fields between two mutually independent input light fields. We also compare our results with those yielded by a number of alternatives elsewhere in the literature, which shows our reconstructed light fields have better structure similarity and occlusion relationship.

cs.CV↗

arXiv2018

A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systems

In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given for both continuous and discrete Hamiltonian systems. The method used in this paper also works for both endpoints are regular, or one endpoint is regular and the other is in the limit circle case.

math.SP↗

arXiv2018

Incorporating Chinese Characters of Words for Lexical Sememe Prediction

Sememes are minimum semantic units of concepts in human languages, such that each word sense is composed of one or multiple sememes. Words are usually manually annotated with their sememes by linguists, and form linguistic common-sense knowledge bases widely used in various NLP tasks. Recently, the lexical sememe prediction task has been introduced. It consists of automatically recommending sememes for words, which is expected to improve annotation efficiency and consistency. However, existing methods of lexical sememe prediction typically rely on the external context of words to represent the meaning, which usually fails to deal with low-frequency and out-of-vocabulary words. To address this issue for Chinese, we propose a novel framework to take advantage of both internal character information and external context information of words. We experiment on HowNet, a Chinese sememe knowledge base, and demonstrate that our framework outperforms state-of-the-art baselines by a large margin, and maintains a robust performance even for low-frequency words.

cs.CL↗

arXiv2018

Singularity of the $n$-th eigenvalue of high dimensional Sturm-Liouville problems

It is natural to consider continuous dependence of the $n$-th eigenvalue on $d$-dimensional ($d\geq2$) Sturm-Liouville problems after the results on $1$-dimensional case by Kong, Wu and Zettl [14]. In this paper, we find all the boundary conditions such that the $n$-th eigenvalue is not continuous, and give complete characterization of asymptotic behavior of the $n$-th eigenvalue. This renders a precise description of the jump phenomena of the $n$-th eigenvalue near such a boundary condition. Furthermore, we divide the space of boundary conditions into $2d+1$ layers and show that the $n$-th eigenvalue is continuously dependent on Sturm-Liouville equations and on boundary conditions when restricted into each layer. In addition, we prove that the analytic and geometric multiplicities of an eigenvalue are equal. Finally, we obtain derivative formula and positive direction of eigenvalues with respect to boundary conditions.

math.SP↗