arXiv subjects

Tao Luo

Publications and source records attributed to Tao Luo.

At least 181 records · Page 10Linked to original sources

arXiv2021

SG-PBFT: a Secure and Highly Efficient Blockchain PBFT Consensus Algorithm for Internet of Vehicles

The Internet of Vehicles (IoV) is an application of the Internet of things (IoT). It faces two main security problems: (1) the central server of the IoV may not be powerful enough to support the centralized authentication of the rapidly increasing connected vehicles, (2) the IoV itself may not be robust enough to single-node attacks. To solve these problems, this paper proposes SG-PBFT: a secure and highly efficient PBFT consensus algorithm for Internet of Vehicles, which is based on a distributed blockchain structure. The distributed structure can reduce the pressure on the central server and decrease the risk of single-node attacks. The SG-PBFT consensus algorithm improves the traditional PBFT consensus algorithm by using a score grouping mechanism to achieve a higher consensus efficiency. The experimental result shows that our method can greatly improve the consensus efficiency and prevent single-node attacks. Specifically, when the number of consensus nodes reaches 1000, the consensus time of our algorithm is only about 27% of what is required for the state-of-the-art consensus algorithm (PBFT). Our proposed SG-PBFT is versatile and can be used in other application scenarios which require high consensus efficiency.

cs.CR↗

arXiv2020

Adaptive Precision Training for Resource Constrained Devices

Learn in-situ is a growing trend for Edge AI. Training deep neural network (DNN) on edge devices is challenging because both energy and memory are constrained. Low precision training helps to reduce the energy cost of a single training iteration, but that does not necessarily translate to energy savings for the whole training process, because low precision could slows down the convergence rate. One evidence is that most works for low precision training keep an fp32 copy of the model during training, which in turn imposes memory requirements on edge devices. In this work we propose Adaptive Precision Training. It is able to save both total training energy cost and memory usage at the same time. We use model of the same precision for both forward and backward pass in order to reduce memory usage for training. Through evaluating the progress of training, APT allocates layer-wise precision dynamically so that the model learns quicker for longer time. APT provides an application specific hyper-parameter for users to play trade-off between training energy cost, memory usage and accuracy. Experiment shows that APT achieves more than 50% saving on training energy and memory usage with limited accuracy loss. 20% more savings of training energy and memory usage can be achieved in return for a 1% sacrifice in accuracy loss.

cs.LG↗

arXiv2020

Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory

The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solutions. A global minimizer corresponds to a neural network that solves the given PDE. In this paper, we show that the gradient descent method can identify a global minimizer of the least-squares optimization for solving second-order linear PDEs with two-layer neural networks under the assumption of over-parametrization. We also analyze the generalization error of the least-squares optimization for second-order linear PDEs and two-layer neural networks, when the right-hand-side function of the PDE is in a Barron-type space and the least-squares optimization is regularized with a Barron-type norm, without the over-parametrization assumption.

math.NA↗

arXiv2020

Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning

A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we propose a Fourier-domain variational formulation for supervised learning problem. This formulation circumvents the difficulty of imposing the constraints of given values on isolated data points in continuum modelling. Under a necessary and sufficient condition within our unified framework, we establish the well-posedness of the Fourier-domain variational problem, by showing a critical exponent depending on the data dimension. In practice, a neural network can be a convenient way to implement our formulation, which automatically satisfies the well-posedness condition.

math.NA↗

arXiv2020

On the exact computation of linear frequency principle dynamics and its generalization

Recent works show an intriguing phenomenon of Frequency Principle (F-Principle) that deep neural networks (DNNs) fit the target function from low to high frequency during the training, which provides insight into the training and generalization behavior of DNNs in complex tasks. In this paper, through analysis of an infinite-width two-layer NN in the neural tangent kernel (NTK) regime, we derive the exact differential equation, namely Linear Frequency-Principle (LFP) model, governing the evolution of NN output function in the frequency domain during the training. Our exact computation applies for general activation functions with no assumption on size and distribution of training data. This LFP model unravels that higher frequencies evolve polynomially or exponentially slower than lower frequencies depending on the smoothness/regularity of the activation function. We further bridge the gap between training dynamics and generalization by proving that LFP model implicitly minimizes a Frequency-Principle norm (FP-norm) of the learned function, by which higher frequencies are more severely penalized depending on the inverse of their evolution rate. Finally, we derive an \textit{a priori} generalization error bound controlled by the FP-norm of the target function, which provides a theoretical justification for the empirical results that DNNs often generalize well for low frequency functions.

cs.LG↗

arXiv2020

Phase diagram for two-layer ReLU neural networks at infinite-width limit

How neural network behaves during the training over different choices of hyperparameters is an important question in the study of neural networks. In this work, inspired by the phase diagram in statistical mechanics, we draw the phase diagram for the two-layer ReLU neural network at the infinite-width limit for a complete characterization of its dynamical regimes and their dependence on hyperparameters related to initialization. Through both experimental and theoretical approaches, we identify three regimes in the phase diagram, i.e., linear regime, critical regime and condensed regime, based on the relative change of input weights as the width approaches infinity, which tends to $0$, $O(1)$ and $+\infty$, respectively. In the linear regime, NN training dynamics is approximately linear similar to a random feature model with an exponential loss decay. In the condensed regime, we demonstrate through experiments that active neurons are condensed at several discrete orientations. The critical regime serves as the boundary between above two regimes, which exhibits an intermediate nonlinear behavior with the mean-field model as a typical example. Overall, our phase diagram for the two-layer ReLU NN serves as a map for the future studies and is a first step towards a more systematical investigation of the training behavior and the implicit regularization of NNs of different structures.

cs.LG↗

arXiv2020

Timing analysis of the black hole candidate EXO 1846-031 with Insight-HXMT monitoring

We present the observational results from a detailed timing analysis of the black hole candidate EXO 1846-031 during its outburst in 2019 with the observations of Insight-HXMT, NICER and MAXI. This outburst can be classfied roughly into four different states. Type-C quasi-periodic oscillations (QPOs) observed by NICER (about 0.1-6Hz) and Insight-HXMT (about 0.7-8Hz) are also reported in this work. Meanwhile, we study various physical quantities related to QPO frequency.The QPO rms-frequency relationship in three energy band 1-10 keV indicates that there is a turning pointing in frequency around 2 Hz,which is similar to that of GRS 1915+105. A possible hypothesis for the relationship above may be related to the inclination of the source, which may require a high inclination to explain it. The relationships between QPO frequency and QPO rms,hardness,total fractional rms and count rate have also been found in other transient sources, which can indicate that the origin of type-C QPOs is non-thermal.

astro-ph.HE↗

arXiv2020

Discovery of oscillations above 200 keV in a black hole X-ray binary with Insight-HXMT

Low-frequency quasi-periodic oscillations (LFQPOs) are commonly found in black hole X-ray binaries, and their origin is still under debate. The properties of LFQPOs at high energies (above 30 keV) are closely related to the nature of the accretion flow in the innermost regions, and thus play a crucial role in critically testing various theoretical models. The Hard X-ray Modulation Telescope (Insight-HXMT) is capable of detecting emissions above 30 keV, and is therefore an ideal instrument to do so. Here we report the discovery of LFQPOs above 200 keV in the new black hole MAXI J1820+070 in the X-ray hard state, which allows us to understand the behaviours of LFQPOs at hundreds of kiloelectronvolts. The phase lag of the LFQPO is constant around zero below 30 keV, and becomes a soft lag (that is, the high-energy photons arrive first) above 30 keV. The soft lag gradually increases with energy and reaches ~0.9s in the 150-200 keV band. The detection at energies above 200 keV, the large soft lag and the energy-related behaviors of the LFQPO pose a great challenge for most currently existing models, but suggest that the LFQPO probably originates from the precession of a small-scale jet.

astro-ph.HE↗

arXiv2020

A regularized deep matrix factorized model of matrix completion for image restoration

It has been an important approach of using matrix completion to perform image restoration. Most previous works on matrix completion focus on the low-rank property by imposing explicit constraints on the recovered matrix, such as the constraint of the nuclear norm or limiting the dimension of the matrix factorization component. Recently, theoretical works suggest that deep linear neural network has an implicit bias towards low rank on matrix completion. However, low rank is not adequate to reflect the intrinsic characteristics of a natural image. Thus, algorithms with only the constraint of low rank are insufficient to perform image restoration well. In this work, we propose a Regularized Deep Matrix Factorized (RDMF) model for image restoration, which utilizes the implicit bias of the low rank of deep neural networks and the explicit bias of total variation. We demonstrate the effectiveness of our RDMF model with extensive experiments, in which our method surpasses the state of art models in common examples, especially for the restoration from very few observations. Our work sheds light on a more general framework for solving other inverse problems by combining the implicit bias of deep learning with explicit regularization.

cs.LG↗

arXiv2020

Deep Learning for Optimal Deployment of UAVs with Visible Light Communications

In this paper, the problem of dynamical deployment of unmanned aerial vehicles (UAVs) equipped with visible light communication (VLC) capabilities for optimizing the energy efficiency of UAV-enabled networks is studied. In the studied model, the UAVs can simultaneously provide communications and illumination to service ground users. Since ambient illumination increases the interference over VLC links while reducing the illumination threshold of the UAVs, it is necessary to consider the illumination distribution of the target area for UAV deployment optimization. This problem is formulated as an optimization problem which jointly optimizes UAV deployment, user association, and power efficiency while meeting the illumination and communication requirements of users. To solve this problem, an algorithm that combines the machine learning framework of gated recurrent units (GRUs) with convolutional neural networks (CNNs) is proposed. Using GRUs and CNNs, the UAVs can model the long-term historical illumination distribution and predict the future illumination distribution. Given the prediction of illumination distribution, the original nonconvex optimization problem can be divided into two sub-problems and is then solved using a low-complexity, iterative algorithm. Then, the proposed algorithm enables UAVs to determine the their deployment and user association to minimize the total transmit power. Simulation results using real data from the Earth observations group (EOG) at NOAA/NCEI show that the proposed approach can achieve up to 68.9% reduction in total transmit power compared to a conventional optimal UAV deployment that does not consider the illumination distribution and user association.

eess.SP↗

arXiv2020

EDCompress: Energy-Aware Model Compression for Dataflows

Edge devices demand low energy consumption, cost and small form factor. To efficiently deploy convolutional neural network (CNN) models on edge device, energy-aware model compression becomes extremely important. However, existing work did not study this problem well because the lack of considering the diversity of dataflow types in hardware architectures. In this paper, we propose EDCompress, an Energy-aware model compression method for various Dataflows. It can effectively reduce the energy consumption of various edge devices, with different dataflow types. Considering the very nature of model compression procedures, we recast the optimization process to a multi-step problem, and solve it by reinforcement learning algorithms. Experiments show that EDCompress could improve 20X, 17X, 37X energy efficiency in VGG-16, MobileNet, LeNet-5 networks, respectively, with negligible loss of accuracy. EDCompress could also find the optimal dataflow type for specific neural networks in terms of energy consumption, which can guide the deployment of CNN models on hardware systems.

cs.LG↗

arXiv2020

Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)

Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite width limit trained by gradient descent can be described by the Neural Tangent Kernel (NTK) introduced in \cite{Jacot2018Neural}. In this paper, we study dynamics of the NTK for finite width Deep Residual Network (ResNet) using the neural tangent hierarchy (NTH) proposed in \cite{Huang2019Dynamics}. For a ResNet with smooth and Lipschitz activation function, we reduce the requirement on the layer width $m$ with respect to the number of training samples $n$ from quartic to cubic. Our analysis suggests strongly that the particular skip-connection structure of ResNet is the main reason for its triumph over fully-connected network.

cs.LG↗

arXiv2020

A type of generalization error induced by initialization in deep neural networks

How initialization and loss function affect the learning of a deep neural network (DNN), specifically its generalization error, is an important problem in practice. In this work, by exploiting the linearity of DNN training dynamics in the NTK regime \citep{jacot2018neural,lee2019wide}, we provide an explicit and quantitative answer to this problem. Focusing on regression problem, we prove that, in the NTK regime, for any loss in a general class of functions, the DNN finds the same \emph{global} minima---the one that is nearest to the initial value in the parameter space, or equivalently, the one that is closest to the initial DNN output in the corresponding reproducing kernel Hilbert space. Using these optimization problems, we quantify the impact of initial output and prove that a random non-zero one increases the generalization error. We further propose an antisymmetrical initialization (ASI) trick that eliminates this type of error and accelerates the training. To understand whether the above results hold in general, we also perform experiments for DNNs in the non-NTK regime, which demonstrate the effectiveness of our theoretical results and the ASI trick in a qualitative sense. Overall, our work serves as a baseline for the further investigation of the impact of initialization and loss function on the generalization of DNNs, which can potentially guide and improve the training of DNNs in practice.

cs.LG↗

arXiv2020

Energy Scaling and Asymptotic Properties of One-Dimensional Discrete System with Generalized Lennard--Jones $(m,n)$ Interaction

It is well known that elastic effects can cause surface instability. In this paper, we analyze a one-dimensional discrete system which can reveal pattern formation mechanism resembling the "step-bunching" phenomena for epitaxial growth on vicinal surfaces. The surface steps are subject to long-range pairwise interactions taking the form of a general Lennard--Jones (LJ) type potential. It is characterized by two exponents $m$ and $n$ describing the singular and decaying behaviors of the interacting potential at small and large distances, and henceforth are called generalized LJ $(m,n)$ potential. We provide a systematic analysis of the asymptotic properties of the step configurations and the value of the minimum energy, in particular, their dependence on $m$ and $n$ and an additional parameter $α$ indicating the interaction range. Our results show that there is a phase transition between the bunching and non-bunching regimes. Moreover, some of our statements are applicable for any critical points of the energy, not necessarily minimizers. This work extends the technique and results of [Luo et al, SIAM MMS, 2016] which concentrates on the case of LJ (0,2) potential (originated from the elastic force monopole and dipole interactions between the steps). As a by-product, our result also leads to the well-known fact that the classical LJ (6,12) potential does not demonstrate step-bunching type phenomena.

math.CA↗

arXiv2020

The Background Model of the Medium Energy X-ray telescope of Insight-HXMT

The Medium Energy X-ray Telescope (ME) is one of the main payloads of the Hard X-ray Modulation Telescope (dubbed as Insight-HXMT). The background of Insight-HXMT/ME is mainly caused by the environmental charged particles and the background intensity is modulated remarkably by the geomagnetic field, as well as the geographical location. At the same geographical location, the background spectral shape is stable but the intensity varies with the level of the environmental charged particles. In this paper, we develop a model to estimate the ME background based on the ME database that is established with the two-year blank sky observations of the high Galactic latitude. In this model, the entire geographical area covered by Insight-HXMT is divided into grids of $5^{\circ}\times5^{\circ}$ in geographical coordinate system. For each grid, the background spectral shape can be obtained from the background database and the intensity can be corrected by the contemporary count rate of the blind FOV detectors. Thus the background spectrum can be obtained by accumulating the background of all the grids passed by Insight-HXMT during the effective observational time. The model test with the blank sky observations shows that the systematic error of the background estimation in $8.9-44.0$ keV is $\sim1.3\%$ for a pointing observation with an average exposure $\sim5.5$ ks. We also find that the systematic error is anti-correlated with the exposure, which indicates the systematic error is partly contributed by the statistical error of count rate measured by the blind FOV detectors.

astro-ph.IM↗

arXiv2020

Discovery of Extended Structures around Two Evolved Planetary Nebulae M 2-55 and Abell 2

We report a multi-wavelength study of two evolved planetary nebulae (PNs) M 2-55 and Abell 2. Deep optical narrow-band images ([O III], H?, and [N II]) of M 2-55 reveal two pairs of bipolar lobes and a new faint arc-like structure. This arc-shaped filament around M 2-55 appears a well-defined boundary from southwest to southeast, strongly suggesting that this nebula is in interaction with its surrounding interstellar medium. From the imaging data of Wide-field Infrared Survey Explorer (WISE) all-sky survey, we discovered extensive mid-infrared halos around these PNs, which are approximately twice larger than their main nebulae seen in the visible. We also present a mid-resolution optical spectrum of M 2-55, which shows that it is a high-excitation evolved PN with a low electron density of 250 cm^-3. Furthermore, we investigate the properties of these nebulae from their spectral energy distributions (SEDs) by means of archival data.

astro-ph.SR↗

arXiv2019

Well-posedness for the Linearized Free Boundary Problem of Incompressible Ideal Magnetohydrodynamics Equations

We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors in the Lagrangian coordinates, and substitute the magnetic field into the momentum equation to get an equation of the velocity in which the initial magnetic field serves only as a parameter. Then, we linearize this equation with respect to the position vector field whose time derivative is the velocity, and obtain the local-in-time well-posedness of the solution by using energy estimates of the tangential derivatives and the curl with the help of Lie derivatives and the smooth-out approximation.

math.AP↗

arXiv2019

Polarization in $Ξ_c^0$ decays

Measurements on the weak decay asymmetry parameters of charmed baryon, say $Ξ_c$, provide more information on the $W$-emission and $W$-exchange mechanisms controlled by the strong and weak interactions. Taking advantage of the spin polarization in the charmed baryon decays, we investigate the possibility to measure the weak decay asymmetry parameters in the $e^{+}e^{-}\to Ξ_c^0\barΞ_c^0$ process. We analyze the transverse polarization spontaneously produced in this process and spin transfer in the subsequent $Ξ_c$ decays. The sensitivity to measure the asymmetry parameters are estimated for the decay $Ξ_c\toΞπ$.

hep-ex↗