arXiv subjects

Yunfei Yang

Publications and source records attributed to Yunfei Yang.

34 records · Page 2Linked to original sources

arXiv2022

Exponential Approximation of Band-limited Functions from Nonuniform Sampling by Regularization Methods

Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling. Whether such an exponential convergence can also be achieved for nonuniform sampling by regularization methods was unresolved. In this paper, we give an affirmative and constructive answer to this question. Specifically, we show that one can recover a band-limited function by Gaussian or hyper-Gaussian regularized nonuniform sampling series with an exponential convergence rate. Our analysis is based on the residue theorem in complex analysis, which is used to represent the truncated error by a contour integral. Several concrete examples of nonuniform sampling with exponential convergence will be presented.

eess.SP↗

arXiv2022

Approximation in shift-invariant spaces with deep ReLU neural networks

We study the expressive power of deep ReLU neural networks for approximating functions in dilated shift-invariant spaces, which are widely used in signal processing, image processing, communications and so on. Approximation error bounds are estimated with respect to the width and depth of neural networks. The network construction is based on the bit extraction and data-fitting capacity of deep neural networks. As applications of our main results, the approximation rates of classical function spaces such as Sobolev spaces and Besov spaces are obtained. We also give lower bounds of the $L^p (1\le p \le \infty)$ approximation error for Sobolev spaces, which show that our construction of neural network is asymptotically optimal up to a logarithmic factor.

cs.LG↗

arXiv2022

Learning Distributions by Generative Adversarial Networks: Approximation and Generalization

We study how well generative adversarial networks (GAN) learn probability distributions from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new oracle inequality that decomposes the estimation error of GAN into the discriminator and generator approximation errors, generalization error and optimization error. To estimate the discriminator approximation error, we establish error bounds on approximating Hölder functions by ReLU neural networks, with explicit upper bounds on the Lipschitz constant of the network or norm constraint on the weights. For generator approximation error, we show that neural network can approximately transform a low-dimensional source distribution to a high-dimensional target distribution and bound such approximation error by the width and depth of neural network. Combining the approximation results with generalization bounds of neural networks from statistical learning theory, we establish the convergence rates of GANs in various settings, when the error is measured by a collection of integral probability metrics defined through Hölder classes, including the Wasserstein distance as a special case. In particular, for distributions concentrated around a low-dimensional set, we show that the convergence rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension.

cs.LG↗

arXiv2022

An error analysis of generative adversarial networks for learning distributions

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined through Hölder classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structures or have Hölder densities, when the network architectures are chosen properly. In particular, for distributions concentrated around a low-dimensional set, we show that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into the generator and discriminator approximation error and the statistical error, which may be of independent interest.

cs.LG↗

arXiv2021

DBIA: Data-free Backdoor Injection Attack against Transformer Networks

Recently, transformer architecture has demonstrated its significance in both Natural Language Processing (NLP) and Computer Vision (CV) tasks. Though other network models are known to be vulnerable to the backdoor attack, which embeds triggers in the model and controls the model behavior when the triggers are presented, little is known whether such an attack is still valid on the transformer models and if so, whether it can be done in a more cost-efficient manner. In this paper, we propose DBIA, a novel data-free backdoor attack against the CV-oriented transformer networks, leveraging the inherent attention mechanism of transformers to generate triggers and injecting the backdoor using the poisoned surrogate dataset. We conducted extensive experiments based on three benchmark transformers, i.e., ViT, DeiT and Swin Transformer, on two mainstream image classification tasks, i.e., CIFAR10 and ImageNet. The evaluation results demonstrate that, consuming fewer resources, our approach can embed backdoors with a high success rate and a low impact on the performance of the victim transformers. Our code is available at https://anonymous.4open.science/r/DBIA-825D.

cs.CV↗

arXiv2021

Non-Asymptotic Error Bounds for Bidirectional GANs

We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural networks used in the model. To the best of our knowledge, this is the first theoretical guarantee for the bidirectional GAN learning approach. An appealing feature of our results is that they do not assume the reference and the data distributions to have the same dimensions or these distributions to have bounded support. These assumptions are commonly assumed in the existing convergence analysis of the unidirectional GANs but may not be satisfied in practice. Our results are also applicable to the Wasserstein bidirectional GAN if the target distribution is assumed to have a bounded support. To prove these results, we construct neural network functions that push forward an empirical distribution to another arbitrary empirical distribution on a possibly different-dimensional space. We also develop a novel decomposition of the integral probability metric for the error analysis of bidirectional GANs. These basic theoretical results are of independent interest and can be applied to other related learning problems.

cs.LG↗

arXiv2021

On the capacity of deep generative networks for approximating distributions

We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a high-dimensional target distribution, when the closeness are measured by Wasserstein distances and maximum mean discrepancy. Upper bounds of the approximation error are obtained in terms of the width and depth of neural network. Furthermore, it is shown that the approximation error in Wasserstein distance grows at most linearly on the ambient dimension and that the approximation order only depends on the intrinsic dimension of the target distribution. On the contrary, when $f$-divergences are used as metrics of distributions, the approximation property is different. We show that in order to approximate the target distribution in $f$-divergences, the dimension of the source distribution cannot be smaller than the intrinsic dimension of the target distribution.

cs.LG↗

arXiv2021

Error Analysis of Deep Ritz Methods for Elliptic Equations

Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on deep Ritz method (DRM) \cite{Weinan2017The} for second order elliptic equations with Drichilet, Neumann and Robin boundary condition, respectively. We establish the first nonasymptotic convergence rate in $H^1$ norm for DRM using deep networks with smooth activation functions including logistic and hyperbolic tangent functions. Our results show how to set the hyper-parameter of depth and width to achieve the desired convergence rate in terms of number of training samples.

math.NA↗

arXiv2020

2.5-kV AlGaN/GaN Schottky Barrier Diode on Silicon Substrate with Recessed-anode Structure

In this letter, we demonstrate high-performance lateral AlGaN/GaN Schottky barrier diodes (SBD) on Si substrate with a recessed-anode structure. The optimized rapid etch process provides results in improving etching quality with a 0.26-nm roughness of the anode recessed surface. By using the high work function metal Pt as the Schottky electrode, a low Von of 0.71 V is obtained with a high uniformity of 0.023 V for 40 devices. Supported by the flat anode recess surface and related field plate design, the SBD device with the anode-cathode spacing of 15 um show the Ron,sp of 1.53 mOhm.cm2 only, the breakdown voltage can reach 1592 V with a high power FOM (Figure-of-Merit) of 1656 MW/cm2. For the SBD device with the anode-cathode spacing of 30 um, the breakdown voltage can be as high as 2521 V and the power FOM is 1244 MW/cm2.

physics.app-ph↗

arXiv2020

Light-weight Calibrator: a Separable Component for Unsupervised Domain Adaptation

Existing domain adaptation methods aim at learning features that can be generalized among domains. These methods commonly require to update source classifier to adapt to the target domain and do not properly handle the trade off between the source domain and the target domain. In this work, instead of training a classifier to adapt to the target domain, we use a separable component called data calibrator to help the fixed source classifier recover discrimination power in the target domain, while preserving the source domain's performance. When the difference between two domains is small, the source classifier's representation is sufficient to perform well in the target domain and outperforms GAN-based methods in digits. Otherwise, the proposed method can leverage synthetic images generated by GANs to boost performance and achieve state-of-the-art performance in digits datasets and driving scene semantic segmentation. Our method empirically reveals that certain intriguing hints, which can be mitigated by adversarial attack to domain discriminators, are one of the sources for performance degradation under the domain shift.

cs.CV↗

arXiv2020

Estimating red noise in quasi-periodic signals with MCMC-based Bayesian

Multi-parameter Bayesian inferences based on Markov chain Monte Carlo (MCMC) samples have been widely used to estimate red noise in solar period-periodic signals. To MCMC, proper priors and sufficient iterations are prerequisites ensuring the accuracy of red noise estimation. We used MCMC-based Bayesian inferences to estimate 100 groups of red noise synthesized randomly for evaluating its accuracy. At the same time, the Brooks-Gelman algorithm was employed to precisely diagnose the convergence of the Markov chains generated by MCMC. The root-mean-square error of parameter inferences to the synthetic data is only 1.14. Furthermore, we applied the algorithm to analyze the oscillation modes in a sunspot and a flare. A 70 s period is detected in the sunspot umbra in addition to 3- and 5-minute periods, and a 40 s period is detected in the flare. The results prove that estimating red noise with MCMC-based Bayesian has more high accuracy in the case of proper priors and convergence. We also find that the number of iterations increases dramatically to achieve convergence as the number of parameters grows. Therefore, we strongly recommend that when estimating red noise with MCMC-based Bayesian, different initial values must be selected to ensure that the entire posterior distribution is covered.

astro-ph.SR↗

arXiv2018

Progressive Weight Pruning of Deep Neural Networks using ADMM

Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model compression or pruning. However, most of the previous work took heuristic approaches. This work proposes a progressive weight pruning approach based on ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed method reaches extremely high pruning rate by using partial prunings with moderate pruning rates. Therefore, it resolves the accuracy degradation and long convergence time problems when pursuing extremely high pruning ratios. It achieves up to 34 times pruning rate for ImageNet dataset and 167 times pruning rate for MNIST dataset, significantly higher than those reached by the literature work. Under the same number of epochs, the proposed method also achieves faster convergence and higher compression rates. The codes and pruned DNN models are released in the link bit.ly/2zxdlss

cs.LG↗

arXiv2018

High-frequency Oscillations in the Atmosphere above a Sunspot Umbra

We use high spatial and temporal resolution observations, simultaneously obtained with the New Vacuum Solar Telescope and Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory, to investigate the high-frequency oscillations above a sunspot umbra. A novel time--frequency analysis method, namely the synchrosqueezing transform (SST), is employed to represent their power spectra and to reconstruct the high-frequency signals at different solar atmospheric layers. A validation study with synthetic signals demonstrates that SST is capable to resolving weak signals even when their strength is comparable with the high-frequency noise. The power spectra, obtained from both SST and the Fourier transform, of the entire umbral region indicate that there are significant enhancements between 10 and 14 mHz (labeled as 12 mHz) at different atmospheric layers. Analyzing the spectrum of a photospheric region far away from the umbra demonstrates that this 12~mHz component exists only inside the umbra. The animation based on the reconstructed 12 mHz component in AIA 171 Å illustrates that an intermittently propagating wave first emerges near the footpoints of coronal fan structures, and then propagates outward along the structures. A time--distance diagram, coupled with a subsonic wave speed ($\sim$ 49 km s$^{-1}$), highlights the fact that these coronal perturbations are best described as upwardly propagating magnetoacoustic slow waves. Thus, we first reveal the high-frequency oscillations with a period around one minute in imaging observations at different height above an umbra, and these oscillations seem to be related to the umbral perturbations in the photosphere.

astro-ph.SR↗

arXiv2018

Midterm Periodicity Analysis of the Mount Wilson Magnetic Indices Using the Synchrosqueezing Transform

A novel time--frequency technique, called the synchrosqueezing transform (SST), is used to investigate the midterm periodic variations of magnetic fields on the solar surface. The Magnetic Plage Strength Index (MPSI) and the Mount Wilson Sunspot Index (MWSI), measured daily by the Mount Wilson Observatory between 1970 January 19 and 2012 January 22, are selected. The short-, mid, and longer-term periodicities are represented and decomposed by the SST with hardly any mode mixing. This demonstrates that the SST is a useful time--frequency analysis technique to characterize the periodic modes of helioseismic data. Apart from the fundamental modes of the annual periodicity, $\sim$27 day rotational cycle and $\sim$11 year solar cycle, the SST reveals several midterm periodicities in the two magnetic activity indices, specifically, $\sim$157 day (i.e., Rieger-type periodicity), and $\sim$1.3 and 1.7 years. The periodic modes, with 116.4 and 276.2 day periodicity in the MPSI, with 108.5 and 251.6 day periodicity in the MWSI, and the 157.7 day periodicity in the two indices, are in better accord with those significant periodicities derived from the Rossby waves theoretical model. This study suggests that the modes are caused by the Rossby waves. For the 1.30 and 1.71 year periodicity of the MPSI, and the 1.33 and 1.67 year periodicity of the MWSI, our analysis infers that they are related to those periodicity with the same timescale in the interior of the Sun and in the high atmospheric layers.

astro-ph.SR↗

arXiv2016

On the relationship between G-band bright point dynamics and their magnetic field strengths

G-band bright points (GBPs) are regarded as good manifestations of magnetic flux concentrations. We aim to investigate the relationship between the dynamic properties of GBPs and their longitudinal magnetic field strengths. High spatial and temporal resolution observations were recorded simultaneously with G-band filtergrams and Narrow-band Filter Imager (NFI) Stokes I and V images with Hinode /Solar Optical Telescope. The GBPs are identified and tracked in the G-band images automatically, and the corresponding longitudinal magnetic field strength of each GBP is extracted from the calibrated NFI magnetograms by a point-to-point method. After categorizing the GBPs into five groups by their longitudinal magnetic field strengths, we analyze the dynamics of GBPs of each group. The results suggest that with increasing longitudinal magnetic field strengths of GBPs correspond to a decrease in their horizontal velocities and motion ranges as well as by showing more complicated motion paths. This suggests that magnetic elements showing weaker magnetic field strengths prefer to move faster and farther along straighter paths, while stronger ones move more slowly in more erratic paths within a smaller region. The dynamic behaviors of GBPs with different longitudinal magnetic field strengths can be explained by that the stronger flux concentrations withstand the convective flows much better than weaker ones.

astro-ph.SR↗

arXiv2015

Investigation of Umbral Dots with the New Vacuum Solar Telescope

Umbral dots (UDs) are small isolated brightenings observed in sunspot umbrae. They are convective phenomena existing inside umbrae. UDs are usually divided into central UDs (CUDs) and peripheral UDs (PUDs) according to their positions inside an umbra. Our purpose is to investigate UD properties and analyze their relationships, and further to find whether or not the properties depend on umbral magnetic field strengths. Thus, we selected high-resolution TiO images of four active regions (ARs) taken under the best seeing conditions with the \textit{New Vacuum Solar Telescope} in the Fuxian Solar Observatory of the Yunnan Astronomical Observatory, China. The four ARs (NOAA 11598, 11801, 12158, and 12178) include six sunspots. A total of 1220 CUDs and 603 PUDs were identified. Meanwhile, the radial component of the vector magnetic field of the sunspots taken with the \textit{Helioseismic and Magnetic Imager} on-board the \textit{Solar Dynamics Observatory} was used to analyze relationships between UD properties and umbral magnetic field strengths. We find that diameters and lifetimes of UDs exhibit an increasing trend with the brightness, but velocities do not. Moreover, diameters, intensities, lifetimes and velocities depend on the surrounding magnetic field. A CUD diameter was found larger, the CUD brighter, its lifetime longer, and its motion slower in a weak umbral magnetic field environment than in a strong one.

astro-ph.SR↗