arXiv subjects

Zhuo Liu

Publications and source records attributed to Zhuo Liu.

51 records · Page 3Linked to original sources

arXiv2024

A new characterization of $L^2$-domains of holomorphy with null thin complements via $L^2$-optimal conditions

In this paper, we show that the $L^2$-optimal condition implies the $L^2$-divisibility of $L^2$-integrable holomorphic functions. As an application, we offer a new characterization of bounded $L^2$-domains of holomorphy with null thin complements using the $L^2$-optimal condition, which appears to be advantageous in addressing a problem proposed by Deng-Ning-Wang. Through this characterization, we show that a domain in a Stein manifold with a null thin complement, admitting an exhaustion of complete Kähler domains, remains Stein. By the way, we construct an $L^2$-optimal domain that does not admit any complete Kähler metric.

math.CV↗

arXiv2024

Multiplier Submodule Sheaves and a problem of Lempert

In this article, we establish an $L^2$ extension theorem for Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles, and the strong openness and stability properties of the multiplier submodule sheaves associated to Nakano semi-positive singular Hermitian metrics on holomorphic vector bundles. We solve affirmatively a question of Lempert on the preservation of Nakano semi-positivity under limit of an increasing metrics based on Deng-Ning-Wang-Zhou's characterization of Nakano positivity.

math.CV↗

arXiv2024

A Le Potier-type isomorphism twisted with multiplier submodule sheaves

In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semipositive singular Hermitian metric to the tautological line bundle with the induced metric. As applications, we obtain a Kollár-type injectivity theorem, a Nadel-type vanishing theorem, and a singular holomorphic Morse inequality for holomorphic vector bundles and so on.

math.CV↗

arXiv2024

Approximated Likelihood Ratio: A Forward-Only and Parallel Framework for Boosting Neural Network Training

Efficient and biologically plausible alternatives to backpropagation in neural network training remain a challenge due to issues such as high computational complexity and additional assumptions about neural networks, which limit scalability to deeper networks. The likelihood ratio method offers a promising gradient estimation strategy but is constrained by significant memory consumption, especially when deploying multiple copies of data to reduce estimation variance. In this paper, we introduce an approximation technique for the likelihood ratio (LR) method to alleviate computational and memory demands in gradient estimation. By exploiting the natural parallelism during the backward pass using LR, we further provide a high-performance training strategy, which pipelines both the forward and backward pass, to make it more suitable for the computation on specialized hardware. Extensive experiments demonstrate the effectiveness of the approximation technique in neural network training. This work underscores the potential of the likelihood ratio method in achieving high-performance neural network training, suggesting avenues for further exploration.

cs.LG↗

arXiv2024

CoRMF: Criticality-Ordered Recurrent Mean Field Ising Solver

We propose an RNN-based efficient Ising model solver, the Criticality-ordered Recurrent Mean Field (CoRMF), for forward Ising problems. In its core, a criticality-ordered spin sequence of an $N$-spin Ising model is introduced by sorting mission-critical edges with greedy algorithm, such that an autoregressive mean-field factorization can be utilized and optimized with Recurrent Neural Networks (RNNs). Our method has two notable characteristics: (i) by leveraging the approximated tree structure of the underlying Ising graph, the newly-obtained criticality order enables the unification between variational mean-field and RNN, allowing the generally intractable Ising model to be efficiently probed with probabilistic inference; (ii) it is well-modulized, model-independent while at the same time expressive enough, and hence fully applicable to any forward Ising inference problems with minimal effort. Computationally, by using a variance-reduced Monte Carlo gradient estimator, CoRFM solves the Ising problems in a self-train fashion without data/evidence, and the inference tasks can be executed by directly sampling from RNN. Theoretically, we establish a provably tighter error bound than naive mean-field by using the matrix cut decomposition machineries. Numerically, we demonstrate the utility of this framework on a series of Ising datasets.

stat.ML↗

arXiv2024

A Two-dimensional Numerical Study of Ion-Acoustic Turbulence

We investigate the linear and nonlinear evolution of the ion-acoustic instability in a collisionless plasma via two-dimensional (2D2V) Vlasov-Poisson numerical simulations. We initialize the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding super-critical initial conditions that are physically unrealizable. The nonlinear evolution of ion-acoustic turbulence (IAT) is characterized in detail, including the particles' distribution functions, particle heating, (two-dimensional) wave spectrum, and the resulting anomalous resistivity. An important result is that no steady saturated nonlinear state is ever reached in our simulations: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived. Electron-acoustic waves (EAWs) are triggered during the late nonlinear evolution of the system, caused by strong modifications to the particle distribution induced by IAT.

physics.plasm-ph↗

arXiv2023

Scalable CP Decomposition for Tensor Learning using GPU Tensor Cores

CP decomposition is a powerful tool for data science, especially gene analysis, deep learning, and quantum computation. However, the application of tensor decomposition is largely hindered by the exponential increment of the computational complexity and storage consumption with the size of tensors. While the data in our real world is usually presented as trillion- or even exascale-scale tensors, existing work can only support billion-scale scale tensors. In our work, we propose the Exascale-Tensor to mitigate the significant gap. Specifically, we propose a compression-based tensor decomposition framework, namely the exascale-tensor, to support exascale tensor decomposition. Then, we carefully analyze the inherent parallelism and propose a bag of strategies to improve computational efficiency. Last, we conduct experiments to decompose tensors ranging from million-scale to trillion-scale for evaluation. Compared to the baselines, the exascale-tensor supports 8,000x larger tensors and a speedup up to 6.95x. We also apply our method to two real-world applications, including gene analysis and tensor layer neural networks, of which the numeric results demonstrate the scalability and effectiveness of our method.

cs.LG↗

arXiv2022

Intermittency and electron heating in kinetic-Alfvén-wave turbulence

We report analytical and numerical investigations of sub-ion-scale turbulence in low-beta plasmas, focusing on the spectral properties of the fluctuations and electron heating. In the isothermal limit, the numerical results strongly support a description of the turbulence as a critically-balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by Boldyrev & Perez (Astrophys. J. Lett. 758, L44 (2012)) to include intermittent effects. When the constraint of isothermality is removed (i.e., with the inclusion of electron kinetic physics), the energy spectrum is found to steepen due to electron Landau damping, which is enabled by the local weakening of advective nonlinearities around current sheets, and yields significant energy dissipation via a velocity-space cascade. The use of a Hermite-polynomial representation to express the velocity-space dependence of the electron distribution function allows us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.

astro-ph.HE↗

arXiv2021

Model-Free Prediction of Chaotic Systems Using High Efficient Next-generation Reservoir Computing

To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving model-free predication for both low-dimensional and very large spatiotemporal chaotic systems. Compared with traditional reservoir computing models, it is more efficient in terms of predication length, training data set required and computational expense. By taking the Lorenz and Kuramoto-Sivashinsky equations as two classical examples of dynamical systems, numerical simulations are conducted, and the results show our model excels at predication tasks than the latest reservoir computing methods.

cs.NE↗

arXiv2021

From Chaos to Pseudo-Randomness: A Case Study on the 2D Coupled Map Lattice

Applying chaos theory for secure digital communications is promising and it is well acknowledged that in such applications the underlying chaotic systems should be carefully chosen. However, the requirements imposed on the chaotic systems are usually heuristic, without theoretic guarantee for the resultant communication scheme. Among all the primitives for secure communications, it is well-accepted that (pseudo) random numbers are most essential. Taking the well-studied two-dimensional coupled map lattice (2D CML) as an example, this paper performs a theoretical study towards pseudo-random number generation with the 2D CML. In so doing, an analytical expression of the Lyapunov exponent (LE) spectrum of the 2D CML is first derived. Using the LEs, one can configure system parameters to ensure the 2D CML only exhibits complex dynamic behavior, and then collect pseudo-random numbers from the system orbits. Moreover, based on the observation that least significant bit distributes more evenly in the (pseudo) random distribution, an extraction algorithm E is developed with the property that, when applied to the orbits of the 2D CML, it can squeeze uniform bits. In implementation, if fixed-point arithmetic is used in binary format with a precision of $z$ bits after the radix point, E can ensure that the deviation of the squeezed bits is bounded by $2^{-z}$ . Further simulation results demonstrate that the new method not only guide the 2D CML model to exhibit complex dynamic behavior, but also generate uniformly distributed independent bits. In particular, the squeezed pseudo random bits can pass both NIST 800-22 and TestU01 test suites in various settings. This study thereby provides a theoretical basis for effectively applying the 2D CML to secure communications.

cs.CR↗

arXiv2021

Identification of 27 abnormalities from multi-lead ECG signals: An ensembled Se-ResNet framework with Sign Loss function

Cardiovascular disease is a major threat to health and one of the primary causes of death globally. The 12-lead ECG is a cheap and commonly accessible tool to identify cardiac abnormalities. Early and accurate diagnosis will allow early treatment and intervention to prevent severe complications of cardiovascular disease. In the PhysioNet/Computing in Cardiology Challenge 2020, our objective is to develop an algorithm that automatically identifies 27 ECG abnormalities from 12-lead ECG recordings.

eess.SP↗

arXiv2020

A Comprehensive Survey of Grammar Error Correction

Grammar error correction (GEC) is an important application aspect of natural language processing techniques. The past decade has witnessed significant progress achieved in GEC for the sake of increasing popularity of machine learning and deep learning, especially in late 2010s when near human-level GEC systems are available. However, there is no prior work focusing on the whole recapitulation of the progress. We present the first survey in GEC for a comprehensive retrospect of the literature in this area. We first give the introduction of five public datasets, data annotation schema, two important shared tasks and four standard evaluation metrics. More importantly, we discuss four kinds of basic approaches, including statistical machine translation based approach, neural machine translation based approach, classification based approach and language model based approach, six commonly applied performance boosting techniques for GEC systems and two data augmentation methods. Since GEC is typically viewed as a sister task of machine translation, many GEC systems are based on neural machine translation (NMT) approaches, where the neural sequence-to-sequence model is applied. Similarly, some performance boosting techniques are adapted from machine translation and are successfully combined with GEC systems for enhancement on the final performance. Furthermore, we conduct an analysis in level of basic approaches, performance boosting techniques and integrated GEC systems based on their experiment results respectively for more clear patterns and conclusions. Finally, we discuss five prospective directions for future GEC researches.

cs.CL↗

arXiv2016

$SU(3)_{F}$ Gauge Family Model and New Symmetry Breaking Scale From FCNC Processes

Based on the $SU(3)_{F}$ gauge family symmetry model which was proposed to explain the observed mass and mixing pattern of neutrinos, we investigate the symmetry breaking, the mixing pattern in quark and lepton sectors, and the contribution of the new gauge bosons to some flavour changing neutral currents (FCNC) processes at low energy. With the current data of the mass differences in the neutral pseudo-scalar $P^{0}-\bar{P}^{0}$ systems, we find that the $SU(3)_{F}$ symmetry breaking scale can be as low as 300TeV and the mass of the lightest gauge boson be about $100$TeV. Other FCNC processes, such as the lepton flavour number violation process $μ^{-}\rightarrow e^{-}e^{+}e^{-}$ and the semi-leptonic rare decay $K\rightarrow π\barν ν$, contain contributions via the new gauge bosons exchanging. With the constrains got from $P^0-\bar{P}^0$ system, we estimate that the contribution of the new physics is around $10^{-16}$, far below the current experimental bounds.

hep-ph↗

arXiv2014

Leptonic CP Violation and Wolfenstein Parametrization for Lepton Mixing

We investigate a general structure of lepton mixing matrix resulting from the SU$_F$(3) gauge family model with an appropriate vacuum structure of SU$_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase $δ_e$ and the leptonic Wolfenstein parameters $λ_e$, $A_e$, $ρ_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the leptonic Wolfenstein parameters. It is found that the phase $δ_e$ is strongly constrained and only a large or nearly maximal leptonic CP-violating phase $|δ_e| \simeq 3π/4 \sim π/2$ is favorable when $λ_e > 0.15 $. In particular, when taking $λ_e$ to be the Cabbibo angle $\gl_e\simeq λ\simeq 0.225$, a sensible result for leptonic Wolfenstein parameters and CP violation is obtained with $ A_e=1.40$, $ρ_e=0.20$, $δ_{e}\sim 101.76\;^o$, which is compatible with the one in quark sector. An interesting correlation between leptons and quarks is observed, which indicates a possible common origin of masses and mixing for the charged-leptons and quarks.

hep-ph↗

arXiv2010

Deterministic creation and stabilization of entanglement in circuit QED by homodyne-mediated feedback control

In the solid-state circuit QED system and based on the homodyne measurement in dispersive regime, we demonstrate that a homodyne-current-based feedback can create and stabilize highly entangled two-qubit states in the presence of moderate noisy environment. Particularly, we present an extended analysis for the current-based Markovian feedback, which leads to an improved filtered-current-based feedback scheme. We show that this is essential for us to achieve the desirable control effect in present system.

quant-ph↗