arXiv subjects

Yi Zhou

Publications and source records attributed to Yi Zhou.

At least 505 records · Page 28Linked to original sources

arXiv2019

Electron-Nuclear Hyperfine Coupling in Quantum Kagome Antiferromagnets from First-Principles Calculation and a Reflection of the Defect Effect

The discovery of ideal spin-1/2 kagome antiferromagnets Herbertsmithite and Zn-doped Barlowite represents a breakthrough in the quest for quantum spin liquids (QSLs), and nuclear magnetic resonance (NMR) spectroscopy plays a prominent role in revealing the quantum paramagnetism in these compounds. However, interpretation of NMR data that is often masked by defects can be controversial. Here, we show that the most significant interaction strength for NMR, i.e. the hyperfine coupling (HFC) strength, can be reasonably reproduced by first-principles calculations for these proposed QSLs. Applying this method to a supercell containing Cu-Zn defects enables us to map out the variation and distribution of HFC at different nuclear sites. This predictive power is expected to bridge the missing link in the analysis of the low-temperature NMR data.

cond-mat.str-el↗

arXiv2019

Superconductivity, pair density wave, and Neel order in cuprates

We investigate in underdoped cuprates possible coexistence of the superconducting (SC) order at zero momentum and pair density wave (PDW) at momentum ${\bf Q}=(π, π)$ in the presence of a Neel order. By symmetry, the $d$-wave uniform singlet pairing $dS_0$ can coexist with the $d$-wave triplet PDW $dT_{\bf Q}$, and the $p$-wave singlet PDW $pS_{\bf Q}$ can coexist with the $p$-wave uniform triplet $pT_0$. At half filling, we find the novel $pS_{\bf Q}+pT_0$ state is energetically more favorable than the $dS_0+dT_{\bf Q}$ state. At finite doping, however, the $dS_0+dT_{\bf Q}$ state is more favorable. In both types of states, the variational triplet parameters, $dT_{\bf Q}$ and $pT_0$, are of secondary significance. Our results point to a fully symmetric $\mathrm{Z_2}$ quantum spin liquid with spinon Fermi surface in proximity to the Neel order at zero doping, and to intertwined $d$-wave triplet PDW fluctuations and spin moment fluctuations along with the dominant $d$-wave singlet SC at finite doping. The results are obtained by variational quantum Monte Carlo simulations.

cond-mat.supr-con↗

arXiv2019

Iterative Normalization: Beyond Standardization towards Efficient Whitening

Batch Normalization (BN) is ubiquitously employed for accelerating neural network training and improving the generalization capability by performing standardization within mini-batches. Decorrelated Batch Normalization (DBN) further boosts the above effectiveness by whitening. However, DBN relies heavily on either a large batch size, or eigen-decomposition that suffers from poor efficiency on GPUs. We propose Iterative Normalization (IterNorm), which employs Newton's iterations for much more efficient whitening, while simultaneously avoiding the eigen-decomposition. Furthermore, we develop a comprehensive study to show IterNorm has better trade-off between optimization and generalization, with theoretical and experimental support. To this end, we exclusively introduce Stochastic Normalization Disturbance (SND), which measures the inherent stochastic uncertainty of samples when applied to normalization operations. With the support of SND, we provide natural explanations to several phenomena from the perspective of optimization, e.g., why group-wise whitening of DBN generally outperforms full-whitening and why the accuracy of BN degenerates with reduced batch sizes. We demonstrate the consistently improved performance of IterNorm with extensive experiments on CIFAR-10 and ImageNet over BN and DBN.

cs.CV↗

arXiv2019

Formation of finite-time singularities for nonlinear elastodynamics with small initial disturbances

This article concerns the formation of finite-time singularities in solutions to quasilinear hyperbolic systems with small initial data. By constructing a special test function, we first present a simpler proof of the main result in Sideris' "Formation of singularities in three-dimensional compressible fluids": the global classical solution is non-existent for compressible Euler equation even for some small initial data. Then we apply this approach to nonlinear elastodynamics and magnetohydrodynamics, showing that the classical solutions to these equations can still blow up in finite time even if the initial data is small enough.

math.AP↗

arXiv2019

The square root rule for adaptive importance sampling

In adaptive importance sampling, and other contexts, we have $K>1$ unbiased and uncorrelated estimates $\hatμ_k$ of a common quantity $μ$. The optimal unbiased linear combination weights them inversely to their variances but those weights are unknown and hard to estimate. A simple deterministic square root rule based on a working model that $\mathrm{Var}(\hatμ_k)\propto k^{-1/2}$ gives an unbisaed estimate of $μ$ that is nearly optimal under a wide range of alternative variance patterns. We show that if $\mathrm{Var}(\hatμ_k)\propto k^{-y}$ for an unknown rate parameter $y\in [0,1]$ then the square root rule yields the optimal variance rate with a constant that is too large by at most $9/8$ for any $0\le y\le 1$ and any number $K$ of estimates. Numerical work shows that rule is similarly robust to some other patterns with mildly decreasing variance as $k$ increases.

math.ST↗

arXiv2019

AED-Net: An Abnormal Event Detection Network

It is challenging to detect the anomaly in crowded scenes for quite a long time. In this paper, a self-supervised framework, abnormal event detection network (AED-Net), which is composed of PCAnet and kernel principal component analysis (kPCA), is proposed to address this problem. Using surveillance video sequences of different scenes as raw data, PCAnet is trained to extract high-level semantics of crowd's situation. Next, kPCA,a one-class classifier, is trained to determine anomaly of the scene. In contrast to some prevailing deep learning methods,the framework is completely self-supervised because it utilizes only video sequences in a normal situation. Experiments of global and local abnormal event detection are carried out on UMN and UCSD datasets, and competitive results with higher EER and AUC compared to other state-of-the-art methods are observed. Furthermore, by adding local response normalization (LRN) layer, we propose an improvement to original AED-Net. And it is proved to perform better by promoting the framework's generalization capacity according to the experiments.

cs.CV↗

arXiv2019

Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model

We propose an exactly solvable quantum spin-1/2 model with time reversal invariance on a two dimensional brick-wall lattice, where each unit cell consists of three sites. We find that the ground states are algebraic quantum spin liquid states. The spinon excitations are gapless and the energy dispersion is linear around two Dirac points. The ground states are of three-fold topological degeneracy on a torus. Breaking the time reversal symmetry opens a bulk energy gap and the $Z_2$ vortices obey non-Abelian statistics.

cond-mat.str-el↗

arXiv2019

Uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space

There is a few results about the global stability of nontrivial solutions to quasilinear wave equations. In this paper we are concerned with the uniqueness and stability of traveling waves to the time-like extremal hypersurface in Minkowski space. Firstly, we can get the existence and uniqueness of traveling wave solutions to the time-like extremal hypersurface in R1+(n+1), which can be considered as the generalized Bernstein theorem in Minkowski space. Furthermore, we also get the stability of traveling wave solutions with speed of light to time-like extremal hypersurface in 1 + (2 + 1) dimensional Minkowski space.

math.AP↗

arXiv2019

Generalization Error Bounds with Probabilistic Guarantee for SGD in Nonconvex Optimization

The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in expectation. In this paper, we establish various generalization error bounds with probabilistic guarantee for the SGD. Specifically, for both general nonconvex loss functions and gradient dominant loss functions, we characterize the on-average stability of the iterates generated by SGD in terms of the on-average variance of the stochastic gradients. Such characterization leads to improved bounds for the generalization error for SGD. We then study the regularized risk minimization problem with strongly convex regularizers, and obtain improved generalization error bounds for proximal SGD. With strongly convex regularizers, we further establish the generalization error bounds for nonconvex loss functions under proximal SGD with high-probability guarantee, i.e., exponential concentration in probability.

stat.ML↗

arXiv2019

SGD Converges to Global Minimum in Deep Learning via Star-convex Path

Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a variety of deep neural networks. However, there is still a lack of understanding on how and why SGD can train these complex networks towards a global minimum. In this study, we establish the convergence of SGD to a global minimum for nonconvex optimization problems that are commonly encountered in neural network training. Our argument exploits the following two important properties: 1) the training loss can achieve zero value (approximately), which has been widely observed in deep learning; 2) SGD follows a star-convex path, which is verified by various experiments in this paper. In such a context, our analysis shows that SGD, although has long been considered as a randomized algorithm, converges in an intrinsically deterministic manner to a global minimum.

cs.LG↗

arXiv2018

Finite time blow up for a model of incompressible Navier-Stokes Equations

T. Tao constructed an averaged Navier-Stokes equations which obey an energy identity. Nevertheless, he proved that smooth solutions can blow up in finite time. This demonstrates that any proposed positive solution to the famous regularity problem for the three dimensional incompressible Navier-Stokes equations which does not use the finer structure of the nonlinearity cannot possibly be successful. In this paper, we propose a very simple model of the Navier Stokes equation which also obey the energy identity and establish a similar result of finite-time blow up . The drawback of our result is that we only work in space dimensions n>=5.

math.AP↗

arXiv2018

MR-GAN: Manifold Regularized Generative Adversarial Networks

Despite the growing interest in generative adversarial networks (GANs), training GANs remains a challenging problem, both from a theoretical and a practical standpoint. To address this challenge, in this paper, we propose a novel way to exploit the unique geometry of the real data, especially the manifold information. More specifically, we design a method to regularize GAN training by adding an additional regularization term referred to as manifold regularizer. The manifold regularizer forces the generator to respect the unique geometry of the real data manifold and generate high quality data. Furthermore, we theoretically prove that the addition of this regularization term in any class of GANs including DCGAN and Wasserstein GAN leads to improved performance in terms of generalization, existence of equilibrium, and stability. Preliminary experiments show that the proposed manifold regularization helps in avoiding mode collapse and leads to stable training.

cs.LG↗

arXiv2018

Readout Electronics for CEPC Semi-Digital Hadron Calorimeter Pre-prototype

CEPC (Circular Electron and Positron Collider) is a large experiment facility proposed by Chinese particle physics community. One of its running option is being the Higgs factory. Calorimeter is the main part of this experiment to measure the jet energy. Semi-digital hadron calorimeter (SDHCAL) is one of the options for the hadron measurement. GEM detector with its high position resolution and flexible configuration is one of the candidates for the active layer of the SDHCAL. The main purpose of this paper is to provide a feasible readout method for the GEM-based semi-digital hadron calorimeter. A small-scale prototype is designed and implemented, including front-end board (FEB) and data interface board (DIF). The prototype electronics has been tested. The equivalent RMS noise of all channels is below 0.35fC. The dynamic range is up to 500fC and the gain variation is less than 1%. The readout electronics is applied on a double-layer GEM detector with 1cm*1cm readout pad. Result indicates that the electronics works well with the detector. The detection efficiency of MIP is over 95% with 5fC threshold.

physics.ins-det↗

arXiv2018

When Will Gradient Methods Converge to Max-margin Classifier under ReLU Models?

We study the implicit bias of gradient descent methods in solving a binary classification problem over a linearly separable dataset. The classifier is described by a nonlinear ReLU model and the objective function adopts the exponential loss function. We first characterize the landscape of the loss function and show that there can exist spurious asymptotic local minima besides asymptotic global minima. We then show that gradient descent (GD) can converge to either a global or a local max-margin direction, or may diverge from the desired max-margin direction in a general context. For stochastic gradient descent (SGD), we show that it converges in expectation to either the global or the local max-margin direction if SGD converges. We further explore the implicit bias of these algorithms in learning a multi-neuron network under certain stationary conditions, and show that the learned classifier maximizes the margins of each sample pattern partition under the ReLU activation.

cs.LG↗

arXiv2018

Stochastic Variance-Reduced Cubic Regularization for Nonconvex Optimization

Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample complexity issue for finite-sum problems with a large data size. %Various inexact variants of CR have been proposed to improve the sample complexity. In this paper, we propose a stochastic variance-reduced cubic-regularization (SVRC) method under random sampling, and study its convergence guarantee as well as sample complexity. We show that the iteration complexity of SVRC for achieving a second-order stationary solution within $ε$ accuracy is $O(ε^{-3/2})$, which matches the state-of-art result on CR types of methods. Moreover, our proposed variance reduction scheme significantly reduces the per-iteration sample complexity. The resulting total Hessian sample complexity of our SVRC is ${\Oc}(N^{2/3} ε^{-3/2})$, which outperforms the state-of-art result by a factor of $O(N^{2/15})$. We also study our SVRC under random sampling without replacement scheme, which yields a lower per-iteration sample complexity, and hence justifies its practical applicability.

math.OC↗

arXiv2018

Toward Understanding the Impact of Staleness in Distributed Machine Learning

Many distributed machine learning (ML) systems adopt the non-synchronous execution in order to alleviate the network communication bottleneck, resulting in stale parameters that do not reflect the latest updates. Despite much development in large-scale ML, the effects of staleness on learning are inconclusive as it is challenging to directly monitor or control staleness in complex distributed environments. In this work, we study the convergence behaviors of a wide array of ML models and algorithms under delayed updates. Our extensive experiments reveal the rich diversity of the effects of staleness on the convergence of ML algorithms and offer insights into seemingly contradictory reports in the literature. The empirical findings also inspire a new convergence analysis of stochastic gradient descent in non-convex optimization under staleness, matching the best-known convergence rate of O(1/\sqrt{T}).

cs.LG↗

arXiv2018

KDSL: a Knowledge-Driven Supervised Learning Framework for Word Sense Disambiguation

We propose KDSL, a new word sense disambiguation (WSD) framework that utilizes knowledge to automatically generate sense-labeled data for supervised learning. First, from WordNet, we automatically construct a semantic knowledge base called DisDict, which provides refined feature words that highlight the differences among word senses, i.e., synsets. Second, we automatically generate new sense-labeled data by DisDict from unlabeled corpora. Third, these generated data, together with manually labeled data and unlabeled data, are fed to a neural framework conducting supervised and unsupervised learning jointly to model the semantic relations among synsets, feature words and their contexts. The experimental results show that KDSL outperforms several representative state-of-the-art methods on various major benchmarks. Interestingly, it performs relatively well even when manually labeled data is unavailable, thus provides a potential solution for similar tasks in a lack of manual annotations.

cs.CL↗

arXiv2018

Asynchronous decentralized accelerated stochastic gradient descent

In this work, we introduce an asynchronous decentralized accelerated stochastic gradient descent type of method for decentralized stochastic optimization, considering communication and synchronization are the major bottlenecks. We establish $\mathcal{O}(1/ε)$ (resp., $\mathcal{O}(1/\sqrtε)$) communication complexity and $\mathcal{O}(1/ε^2)$ (resp., $\mathcal{O}(1/ε)$) sampling complexity for solving general convex (resp., strongly convex) problems.

math.OC↗