arXiv subjects

Xiang Cheng

Publications and source records attributed to Xiang Cheng.

At least 163 records · Page 9Linked to original sources

arXiv2020

Stochastic Gradient and Langevin Processes

We prove quantitative convergence rates at which discrete Langevin-like processes converge to the invariant distribution of a related stochastic differential equation. We study the setup where the additive noise can be non-Gaussian and state-dependent and the potential function can be non-convex. We show that the key properties of these processes depend on the potential function and the second moment of the additive noise. We apply our theoretical findings to studying the convergence of Stochastic Gradient Descent (SGD) for non-convex problems and corroborate them with experiments using SGD to train deep neural networks on the CIFAR-10 dataset.

cs.LG↗

arXiv2020

Distilling a Deep Neural Network into a Takagi-Sugeno-Kang Fuzzy Inference System

Deep neural networks (DNNs) demonstrate great success in classification tasks. However, they act as black boxes and we don't know how they make decisions in a particular classification task. To this end, we propose to distill the knowledge from a DNN into a fuzzy inference system (FIS), which is Takagi-Sugeno-Kang (TSK)-type in this paper. The model has the capability to express the knowledge acquired by a DNN based on fuzzy rules, thus explaining a particular decision much easier. Knowledge distillation (KD) is applied to create a TSK-type FIS that generalizes better than one directly from the training data, which is guaranteed through experiments in this paper. To further improve the performances, we modify the baseline method of KD and obtain good results.

cs.AI↗

arXiv2020

Finite Meta-Dynamic Neurons in Spiking Neural Networks for Spatio-temporal Learning

Spiking Neural Networks (SNNs) have incorporated more biologically-plausible structures and learning principles, hence are playing critical roles in bridging the gap between artificial and natural neural networks. The spikes are the sparse signals describing the above-threshold event-based firing and under-threshold dynamic computation of membrane potentials, which give us an alternative uniformed and efficient way on both information representation and computation. Inspired from the biological network, where a finite number of meta neurons integrated together for various of cognitive functions, we proposed and constructed Meta-Dynamic Neurons (MDN) to improve SNNs for a better network generalization during spatio-temporal learning. The MDNs are designed with basic neuronal dynamics containing 1st-order and 2nd-order dynamics of membrane potentials, including the spatial and temporal meta types supported by some hyper-parameters. The MDNs generated from a spatial (MNIST) and a temporal (TIDigits) datasets first, and then extended to various other different spatio-temporal tasks (including Fashion-MNIST, NETtalk, Cifar-10, TIMIT and N-MNIST). The comparable accuracy was reached compared to other SOTA SNN algorithms, and a better generalization was also achieved by SNNs using MDNs than that without using MDNs.

cs.NE↗

arXiv2020

Answering Multi-Dimensional Range Queries under Local Differential Privacy

In this paper, we tackle the problem of answering multi-dimensional range queries under local differential privacy. There are three key technical challenges: capturing the correlations among attributes, avoiding the curse of dimensionality, and dealing with the large domains of attributes. None of the existing approaches satisfactorily deals with all three challenges. Overcoming these three challenges, we first propose an approach called Two-Dimensional Grids (TDG). Its main idea is to carefully use binning to partition the two-dimensional (2-D) domains of all attribute pairs into 2-D grids that can answer all 2-D range queries and then estimate the answer of a higher dimensional range query from the answers of the associated 2-D range queries. However, in order to reduce errors due to noises, coarse granularities are needed for each attribute in 2-D grids, losing fine-grained distribution information for individual attributes. To correct this deficiency, we further propose Hybrid-Dimensional Grids (HDG), which also introduces 1-D grids to capture finer-grained information on distribution of each individual attribute and combines information from 1-D and 2-D grids to answer range queries. To make HDG consistently effective, we provide a guideline for properly choosing granularities of grids based on an analysis of how different sources of errors are impacted by these choices. Extensive experiments conducted on real and synthetic datasets show that HDG can give a significant improvement over the existing approaches.

cs.CR↗

arXiv2020

Sharp convergence rates for Langevin dynamics in the nonconvex setting

We study the problem of sampling from a distribution $p^*(x) \propto \exp\left(-U(x)\right)$, where the function $U$ is $L$-smooth everywhere and $m$-strongly convex outside a ball of radius $R$, but potentially nonconvex inside this ball. We study both overdamped and underdamped Langevin MCMC and establish upper bounds on the number of steps required to obtain a sample from a distribution that is within $ε$ of $p^*$ in $1$-Wasserstein distance. For the first-order method (overdamped Langevin MCMC), the iteration complexity is $\tilde{\mathcal{O}}\left(e^{cLR^2}d/ε^2\right)$, where $d$ is the dimension of the underlying space. For the second-order method (underdamped Langevin MCMC), the iteration complexity is $\tilde{\mathcal{O}}\left(e^{cLR^2}\sqrt{d}/ε\right)$ for an explicit positive constant $c$. Surprisingly, the iteration complexity for both these algorithms is only polynomial in the dimension $d$ and the target accuracy $ε$. It is exponential, however, in the problem parameter $LR^2$, which is a measure of non-log-concavity of the target distribution.

stat.ML↗

arXiv2019

Explosion cratering in 3D granular media

Sudden release of energy in explosion creates craters in granular media. In comparison with well-studied impact cratering in granular media, our understanding of explosion cratering is still primitive. Here, we study low-energy lab-scale explosion cratering in 3D granular media using controlled pulses of pressurized air. We identify four regimes of explosion cratering at different burial depths, which are associated with distinct explosion dynamics and result in different crater morphologies. We propose a general relation between the dynamics of granular flows and the surface structures of resulting craters. Moreover, we measure the diameter of explosion craters as a function of explosion pressures, durations and burial depths. We find that the size of craters is non-monotonic with increasing burial depths, reaching a maximum at an intermediate burial depth. In addition, the crater diameter shows a weak dependence on explosion pressures and durations at small burial depths. We construct a simple model to explain this finding. Finally, we explore the scaling relations of the size of explosion craters. Despite the huge difference in energy scales, we find that the diameter of explosion craters in our experiments follows the same cube root energy scaling as explosion cratering at high energies. We also discuss the dependence of rescaled crater sizes on the inertial numbers of granular flows. These results shed light onto the rich dynamics of 3D explosion cratering and provide new insights into the general physical principles governing granular cratering processes.

cond-mat.soft↗

arXiv2019

Estimating Doubly-Selective Channels for Hybrid mmWave Massive MIMO Systems: A Doubly-Sparse Approach

In mmWave massive multiple-input multiple-output (mMIMO) systems, hybrid digital/analog beamforming has been recognized as an economic means to overcome the severe mmWave propagation loss. To facilitate beamforming for mmWace mMIMO, there is a great urgency to acquire accurate channel state information. To this end, a novel doubly-sparse approach is proposed to estimate doubly-selective mmWave channels under hybrid mMIMO. Via the judiciously designed training pattern, the well-known beamspace sparsity along with the under-investigated delay-domain sparsity that mmWave channels exhibit can be jointly exploited to assist channel estimation. Thanks to our careful two-stage (random-probing and steering-probing) design, the proposed channel estimator possesses strong robustness against the double (frequency and time) selectivity whilst enjoying the benefits brought by the exploitation of double sparsity. Compared with existing alternatives, our proposed channel estimator not only proves to be more general, but also largely reduces the training overhead, storage demand as well as computational complexity.

eess.SP↗

arXiv2019

Cooperative Reasoning on Knowledge Graph and Corpus: A Multi-agentReinforcement Learning Approach

Knowledge-graph-based reasoning has drawn a lot of attention due to its interpretability. However, previous methods suffer from the incompleteness of the knowledge graph, namely the interested link or entity that can be missing in the knowledge graph(explicit missing). Also, most previous models assume the distance between the target and source entity is short, which is not true on a real-world KG like Freebase(implicit missing). The sensitivity to the incompleteness of KG and the incapability to capture the long-distance link between entities have limited the performance of these models on large KG. In this paper, we propose a model that leverages the text corpus to cure such limitations, either the explicit or implicit missing links. We model the question answering on KG as a cooperative task between two agents, a knowledge graph reasoning agent and an information extraction agent. Each agent learns its skill to complete its own task, hopping on KG or select knowledge from the corpus, via maximizing the reward for correctly answering the question. The reasoning agent decides how to find an equivalent path for the given entity and relation. The extraction agent provide shortcut for long-distance target entity or provide missing relations for explicit missing links with messages from the reasoning agent. Through such cooperative reward design, our model can augment the incomplete KG strategically while not introduce much unnecessary noise that could enlarge the search space and lower the performance.

cs.CL↗

arXiv2019

Learning to Order Sub-questions for Complex Question Answering

Answering complex questions involving multiple entities and relations is a challenging task. Logically, the answer to a complex question should be derived by decomposing the complex question into multiple simple sub-questions and then answering those sub-questions. Existing work has followed this strategy but has not attempted to optimize the order of how those sub-questions are answered. As a result, the sub-questions are answered in an arbitrary order, leading to larger search space and a higher risk of missing an answer. In this paper, we propose a novel reinforcement learning(RL) approach to answering complex questions that can learn a policy to dynamically decide which sub-question should be answered at each stage of reasoning. We lever-age the expected value-variance criterion to enable the learned policy to balance between the risk and utility of answering a sub-question. Experiment results show that the RL approach can substantially improve the optimality of ordering the sub-questions, leading to improved accuracy of question answering. The proposed method for learning to order sub-questions is general and can thus be potentially combined with many existing ideas for answering complex questions to enhance their performance.

cs.CL↗

arXiv2019

Tunable single photon and two-photon emission in a four-level quantum dot-bimodal cavity system

We investigate the generation of single photons and photon pairs in a cavity quantum electrodynamics system of a four-level quantum dot coupled to bimodal cavity. By tuning frequencies and intensity ratio of the driving lasers, sub-Poissonian and super-Poissonian photon statistics are obtained in each nondegenerate cavity mode respectively. Single photon emission is characterized as zero-delay second-order correlation function g^2(0)~0.15. Photon pair emission under the two-photon resonance excitation is quantified by Mandel parameter as Q~0.04. The mean cavity photon number in both scenarios can maintain large around 0.1. As a result, single photon emission and two-photon emission can be integrated in our proposed system only by tuning the external parameters of the driving lasers.

quant-ph↗

arXiv2019

Unconventional Photon blockade in a Photonic Molecule Containing a Quantum Dot

We propose a scheme to realize strong photon antibunching with lower photon nonlinearity in a photonic molecule consisting of two photonic cavities, one of which contains a quantum dot (QD). This strong photon antibunching is attributed to destructive quantum interference effect which suppresses the two-photon excitation of the cavity field. That g^2 (0)~10^(-4) can be achieved with modest QD-cavity coupling strength g=1.1k and cavity tunneling strength J=3k when the system is driven by single laser field. To further reduce the requisite tunneling and make the system tunable, two laser fields are applied to the system. The strong photon antibunching (g^2 (0)~10^(-3)) can be achieved with a relatively large intracavity photon number by optimizing the phase between two driving laser fields when J=0.9k. Moreover, the system shows a strong robustness of maintaining strong photon antibunching within a large parameter variation under the optimal phase condition. Our scheme provides a flexible and efficient method for solid state quantum single photon sources.

quant-ph↗

arXiv2019

Design of spontaneous parametric down-conversion in integrated hybrid SixNy-PPLN waveguides

High-efficient and high-purity photon sources are highly desired for quantum information processing. We report the design of a chip-scale hybrid SixNy and thin film periodically-poled lithium niobate waveguide for generating high-purity type-II spontaneous parametric down conversion (SPDC) photons in telecommunication band. The modeled second harmonic generation efficiency of 225% W^(-1)*cm^(-2) is obtained at 1560nm. Joint spectral analysis is performed to estimate the frequency correlation of SPDC photons, yielding intrinsic purity with up to 95.17%. The generation rate of these high-purity photon pairs is estimated to be 2.87 * 10^7 pairs/s/mW within the bandwidth of SPDC. Our chip-scale hybrid waveguide design has the potential for large scale on-chip quantum information processing and integrated photon-efficient quantum key distribution through high-dimensional time-energy encoding.

physics.optics↗

arXiv2019

Is There an Analog of Nesterov Acceleration for MCMC?

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an underdamped form of the Langevin algorithm performs accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm.

stat.ML↗

arXiv2019

Quantitative Weak Convergence for Discrete Stochastic Processes

In this paper, we quantitative convergence in $W_2$ for a family of Langevin-like stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the iterates of these stochastic processes converge to an invariant distribution at a rate of $\tilde{O}\lrp{1/\sqrt{k}}$ where $k$ is the number of steps; this rate is provably tight up to log factors. Our result reduces to a quantitative form of the classical Central Limit Theorem in the special case when the potential is quadratic.

math.ST↗

arXiv2019

Rheology of bacterial suspensions under confinement

As a paradigmatic model of active fluids, bacterial suspensions show intriguing rheological responses drastically different from their counterpart colloidal suspensions. Although the flow of bulk bacterial suspensions has been extensively studied, the rheology of bacterial suspensions under confinement has not been experimentally explored. Here, using a microfluidic viscometer, we systematically measure the rheology of dilute E. coli suspensions under different degrees of confinement. Our study reveals a strong confinement effect: the viscosity of bacterial suspensions decreases substantially when the confinement scale is comparable or smaller than the run length of bacteria. Moreover, we also investigate the microscopic dynamics of bacterial suspensions including velocity profiles, bacterial density distributions and single bacterial dynamics in shear flows. These measurements allow us to construct a simple heuristic model based on the boundary layer of upstream swimming bacteria near confining walls, which qualitatively explains our experimental observations. Our study sheds light on the influence of the boundary layer of collective bacterial motions on the flow of confined bacterial suspensions. Our results provide a benchmark for testing different rheological models of active fluids and are useful for understanding the transport of microorganisms in confined geometries.

cond-mat.soft↗

arXiv2019

Long-wavelength fluctuations and static correlations in quasi-2D colloidal suspensions

Dimensionality strongly affects thermal fluctuations and critical dynamics of equilibrium systems. These influences persist in amorphous systems going through the nonequilibrium glass transition. Here, we experimentally study the glass transition of quasi-2D suspensions of spherical and ellipsoidal particles under different degrees of circular confinement. We show that the strength of the long-wavelength fluctuations increases logarithmically with system sizes and displays the signature of the Mermin-Wagner fluctuations. Moreover, using confinement as a tool, we also measure static structural correlations and extract a growing static correlation length in 2D supercooled liquids. Finally, we explore the influence of the Mermin-Wagner fluctuations on the translational and orientational relaxations of 2D ellipsoidal suspensions, which leads to a new interpretation of the two-step glass transition and the orientational glass phase of anisotropic particles. Our study reveals the importance of long-wavelength fluctuations in 2D supercooled liquids and provides new insights into the role of dimensionality in the glass transition.

cond-mat.soft↗

arXiv2018

Approximation of A Class of Non-Zero-Sum Investment and Reinsurance Games for Regime-Switching Jump-Diffusion Models

This work develops an approximation procedure for a class of non-zero-sum stochastic differential investment and reinsurance games between two insurance companies. Both proportional reinsurance and excess-of loss reinsurance policies are considered. We develop numerical algorithms to obtain the Nash equilibrium by adopting the Markov chain approximation methodology and applying the dynamical programming principle for the nonlinear integro-differential Hamilton-Jacobi-Isaacs (HJI) equations. Furthermore, we establish the convergence of the approximation sequences and the approximation to the value functions. Numerical examples are presented to illustrate the applicability of the algorithms.

math.OC↗

arXiv2018

Effect of edge disturbance on shear banding in polymeric solutions

Edge instabilities are believed to be one of the possible causes of shear banding in entangled polymeric fluids. Here, we investigate the effect of edge disturbance on the shear-induced dynamics of well-entangled DNA solutions. Using a custom high-aspect-ratio planar-Couette cell, we systematically measure the velocity profiles of sheared DNA samples at different distances away from the edge of the shear cell. Under a weak oscillatory shear with the corresponding Weissenberg number (Wi) smaller than 1, where DNA solutions exhibit linear velocity profiles with strong wall slip, the penetration depth of the edge disturbance is on the order of the gap thickness of the shear cell, consistent with the behavior of Newtonian fluids. However, under a strong oscillatory shear with Wi > 1 that produces shear-banding flows, the penetration depth is an order of magnitude larger than the gap thickness and becomes spatially anisotropic. Moreover, we find that the shear-banding flows persist deep inside the sheared sample, where the effect of edge disturbance diminishes. Hence, our experiments demonstrate an abnormally long penetration depth of edge disturbance and illustrate the bulk nature of shear-banding flows of entangled polymeric fluids under time-dependent oscillatory shear.

cond-mat.soft↗