Searcharxiv⌕ Search

arXiv subjects

Ping Li

Publications and source records attributed to Ping Li.

At least 145 records · Page 8Linked to original sources
arXiv2023

A Beam-Segmenting Polar Format Algorithm Based on Double PCS for Video SAR Persistent Imaging

Video synthetic aperture radar (SAR) is attracting more attention in recent years due to its abilities of high resolution, high frame rate and advantages in continuous observation. Generally, the polar format algorithm (PFA) is an efficient algorithm for spotlight mode video SAR. However, in the process of PFA, the wavefront curvature error (WCE) limits the imaging scene size and the 2-D interpolation affects the efficiency. To solve the aforementioned problems, a beam-segmenting PFA based on principle of chirp scaling (PCS), called BS-PCS-PFA, is proposed for video SAR imaging, which has the capability of persistent imaging for different carrier frequencies video SAR. Firstly, an improved PCS applicable to video SAR PFA is proposed to replace the 2-D interpolation and the coarse image in the ground output coordinate system (GOCS) is obtained. As for the distortion or defocus existing in the coarse image, a novel sub-block imaging method based on beam-segmenting fast filtering is proposed to segment the image into multiple sub-beam data, whose distortion and defocus can be ignored when the equivalent size of sub-block is smaller than the distortion negligible region. Through processing the sub-beam data and mosaicking the refocused subimages, the full image in GOCS without distortion and defocus is obtained. Moreover, a three-step MoCo method is applied to the algorithm for the adaptability to the actual irregular trajectories. The proposed method can significantly expand the effective scene size of PFA, and the better operational efficiency makes it more suitable for video SAR imaging. The feasibility of the algorithm is verified by the experimental data.

cs.CV↗
arXiv2023

The spectral rigidity of Ricci soliton and Einstein-type manifolds

We are concerned in this article with a classical topic in spectral geometry dating back to McKean-Singer, Patodi and Tanno: whether or not the constancy of sectional curvature (resp. holomorphic sectional curvature) of a compact Riemannian manifold (resp. Kähler manifold) can be completely determined by the eigenvalues of its $p$-Laplacian for a \emph{single} integer $p$? We treat this question under two conditions: gradient shrinking Ricci soliton for Riemannian manifolds and cohomologically Einstein for Kähler manifolds. We show that, with some sporadic unknown cases, this is true for each $p$. Furthermore, we show that the condition of being isospectral can be relaxed to a suitable almost-isospectral version.

math.DG↗
arXiv2023

Does Conceptual Representation Require Embodiment? Insights From Large Language Models

To what extent can language alone give rise to complex concepts, or is embodied experience essential? Recent advancements in large language models (LLMs) offer fresh perspectives on this question. Although LLMs are trained on restricted modalities, they exhibit human-like performance in diverse psychological tasks. Our study compared representations of 4,442 lexical concepts between humans and ChatGPTs (GPT-3.5 and GPT-4) across multiple dimensions, including five key domains: emotion, salience, mental visualization, sensory, and motor experience. We identify two main findings: 1) Both models strongly align with human representations in non-sensorimotor domains but lag in sensory and motor areas, with GPT-4 outperforming GPT-3.5; 2) GPT-4's gains are associated with its additional visual learning, which also appears to benefit related dimensions like haptics and imageability. These results highlight the limitations of language in isolation, and that the integration of diverse modalities of inputs leads to a more human-like conceptual representation.

cs.CL↗
arXiv2023

Pair-wise Layer Attention with Spatial Masking for Video Prediction

Video prediction yields future frames by employing the historical frames and has exhibited its great potential in many applications, e.g., meteorological prediction, and autonomous driving. Previous works often decode the ultimate high-level semantic features to future frames without texture details, which deteriorates the prediction quality. Motivated by this, we develop a Pair-wise Layer Attention (PLA) module to enhance the layer-wise semantic dependency of the feature maps derived from the U-shape structure in Translator, by coupling low-level visual cues and high-level features. Hence, the texture details of predicted frames are enriched. Moreover, most existing methods capture the spatiotemporal dynamics by Translator, but fail to sufficiently utilize the spatial features of Encoder. This inspires us to design a Spatial Masking (SM) module to mask partial encoding features during pretraining, which adds the visibility of remaining feature pixels by Decoder. To this end, we present a Pair-wise Layer Attention with Spatial Masking (PLA-SM) framework for video prediction to capture the spatiotemporal dynamics, which reflect the motion trend. Extensive experiments and rigorous ablation studies on five benchmarks demonstrate the advantages of the proposed approach. The code is available at GitHub.

cs.CV↗
arXiv2023

Accretion of the relativistic Vlasov gas onto a Kerr black hole

We study the accretion of relativistic Vlasov gas onto a Kerr black hole, regarding the particles as distributed throughout all the space, other than just in the equatorial plane. We solve the relativistic Liouville equation in the full $3+1$ dimensional framework of Kerr geometry. For the flow that is stationary and axial symmetric, we prove that the distribution function is independent of the conjugate coordinates. For an explicit distribution that can approximate to Maxwell-Jüttner distribution, we further calculate the particle current density, the stress energy momentum tensor and the unit accretion rates of mass, energy and angular momentum. The analytic results at large distance are shown to be consistent with the limits of the numerical ones computed at finite distance. Especially, we show that the unit mass accretion rate agrees with the Schwarzschild result in the case of low temperature limit. Furthermore, we find from the numerical results that the three unit accretion rates vary with the angle in Kerr metric and the accretion of Vlasov gas would slow down the Kerr black hole. The closer to the equator, the faster it slows down the black hole.

gr-qc↗
arXiv2023

Sketching for Convex and Nonconvex Regularized Least Squares with Sharp Guarantees

Randomized algorithms are important for solving large-scale optimization problems. In this paper, we propose a fast sketching algorithm for least square problems regularized by convex or nonconvex regularization functions, Sketching for Regularized Optimization (SRO). Our SRO algorithm first generates a sketch of the original data matrix, then solves the sketched problem. Different from existing randomized algorithms, our algorithm handles general Frechet subdifferentiable regularization functions in an unified framework. We present general theoretical result for the approximation error between the optimization results of the original problem and the sketched problem for regularized least square problems which can be convex or nonconvex. For arbitrary convex regularizer, relative-error bound is proved for the approximation error. Importantly, minimax rates for sparse signal estimation by solving the sketched sparse convex or nonconvex learning problems are also obtained using our general theoretical result under mild conditions. To the best of our knowledge, our results are among the first to demonstrate minimax rates for convex or nonconvex sparse learning problem by sketching under a unified theoretical framework. We further propose an iterative sketching algorithm which reduces the approximation error exponentially by iteratively invoking the sketching algorithm. Experimental results demonstrate the effectiveness of the proposed SRO and Iterative SRO algorithms.

math.OC↗
arXiv2023

Multifield tunable valley splitting in two-dimensional MXene Cr$_2$COOH

Manipulation of the valley degree of freedom provides a novel paradigm in quantum information technology. Here, through first-principles calculations and model analysis, we demonstrate that monolayer Cr$_2$COOH MXene is a promising candidate material for valleytronics applications. We reveal that Cr$_2$COOH is a ferromagnetic semiconductor and harbors valley features. Due to the simultaneous breaking inversion symmetry and time-reversal symmetry, the valleys are polarized spontaneously. Moreover, the valley polarization is sizeable in both the valence and conduction bands, benefiting the observation of the anomalous valley Hall effect. More remarkably, the valley splitting can be effectively tuned by the magnetization direction, strain and ferroelectric substrate. More interestingly, the ferroelectric substrate Sc$_2$CO$_2$ can not only regulate the MAE, but also tune valley polarization state. Our findings offer a practical way for realizing highly tunable valleys by multiferroic couplings.

cond-mat.mtrl-sci↗
arXiv2023

Recovering Linear Causal Models with Latent Variables via Cholesky Factorization of Covariance Matrix

Discovering the causal relationship via recovering the directed acyclic graph (DAG) structure from the observed data is a well-known challenging combinatorial problem. When there are latent variables, the problem becomes even more difficult. In this paper, we first propose a DAG structure recovering algorithm, which is based on the Cholesky factorization of the covariance matrix of the observed data. The algorithm is fast and easy to implement and has theoretical grantees for exact recovery. On synthetic and real-world datasets, the algorithm is significantly faster than previous methods and achieves the state-of-the-art performance. Furthermore, under the equal error variances assumption, we incorporate an optimization procedure into the Cholesky factorization based algorithm to handle the DAG recovering problem with latent variables. Numerical simulations show that the modified "Cholesky + optimization" algorithm is able to recover the ground truth graph in most cases and outperforms existing algorithms.

stat.ML↗
arXiv2023

The Phase Transition Phenomenon of Shuffled Regression

We study the phase transition phenomenon inherent in the shuffled (permuted) regression problem, which has found numerous applications in databases, privacy, data analysis, etc. In this study, we aim to precisely identify the locations of the phase transition points by leveraging techniques from message passing (MP). In our analysis, we first transform the permutation recovery problem into a probabilistic graphical model. We then leverage the analytical tools rooted in the message passing (MP) algorithm and derive an equation to track the convergence of the MP algorithm. By linking this equation to the branching random walk process, we are able to characterize the impact of the signal-to-noise-ratio ($\snr$) on the permutation recovery. Depending on whether the signal is given or not, we separately investigate the oracle case and the non-oracle case. The bottleneck in identifying the phase transition regimes lies in deriving closed-form formulas for the corresponding critical points, but only in rare scenarios can one obtain such precise expressions. To tackle this technical challenge, this study proposes the Gaussian approximation method, which allows us to obtain the closed-form formulas in almost all scenarios. In the oracle case, our method can fairly accurately predict the phase transition $\snr$. In the non-oracle case, our algorithm can predict the maximum allowed number of permuted rows and uncover its dependency on the sample number.

stat.ML↗
arXiv2023

On the Overlooked Structure of Stochastic Gradients

Stochastic gradients closely relate to both optimization and generalization of deep neural networks (DNNs). Some works attempted to explain the success of stochastic optimization for deep learning by the arguably heavy-tail properties of gradient noise, while other works presented theoretical and empirical evidence against the heavy-tail hypothesis on gradient noise. Unfortunately, formal statistical tests for analyzing the structure and heavy tails of stochastic gradients in deep learning are still under-explored. In this paper, we mainly make two contributions. First, we conduct formal statistical tests on the distribution of stochastic gradients and gradient noise across both parameters and iterations. Our statistical tests reveal that dimension-wise gradients usually exhibit power-law heavy tails, while iteration-wise gradients and stochastic gradient noise caused by minibatch training usually do not exhibit power-law heavy tails. Second, we further discover that the covariance spectra of stochastic gradients have the power-law structures overlooked by previous studies and present its theoretical implications for training of DNNs. While previous studies believed that the anisotropic structure of stochastic gradients matters to deep learning, they did not expect the gradient covariance can have such an elegant mathematical structure. Our work challenges the existing belief and provides novel insights on the structure of stochastic gradients in deep learning.

cs.LG↗
arXiv2023

STANLEY: Stochastic Gradient Anisotropic Langevin Dynamics for Learning Energy-Based Models

We propose in this paper, STANLEY, a STochastic gradient ANisotropic LangEvin dYnamics, for sampling high dimensional data. With the growing efficacy and potential of Energy-Based modeling, also known as non-normalized probabilistic modeling, for modeling a generative process of different natures of high dimensional data observations, we present an end-to-end learning algorithm for Energy-Based models (EBM) with the purpose of improving the quality of the resulting sampled data points. While the unknown normalizing constant of EBMs makes the training procedure intractable, resorting to Markov Chain Monte Carlo (MCMC) is in general a viable option. Realizing what MCMC entails for the EBM training, we propose in this paper, a novel high dimensional sampling method, based on an anisotropic stepsize and a gradient-informed covariance matrix, embedded into a discretized Langevin diffusion. We motivate the necessity for an anisotropic update of the negative samples in the Markov Chain by the nonlinearity of the backbone of the EBM, here a Convolutional Neural Network. Our resulting method, namely STANLEY, is an optimization algorithm for training Energy-Based models via our newly introduced MCMC method. We provide a theoretical understanding of our sampling scheme by proving that the sampler leads to a geometrically uniformly ergodic Markov Chain. Several image generation experiments are provided in our paper to show the effectiveness of our method.

stat.ML↗
arXiv2023

Faster Algorithms for Generalized Mean Densest Subgraph Problem

The densest subgraph of a large graph usually refers to some subgraph with the highest average degree, which has been extended to the family of $p$-means dense subgraph objectives by~\citet{veldt2021generalized}. The $p$-mean densest subgraph problem seeks a subgraph with the highest average $p$-th-power degree, whereas the standard densest subgraph problem seeks a subgraph with a simple highest average degree. It was shown that the standard peeling algorithm can perform arbitrarily poorly on generalized objective when $p>1$ but uncertain when $0<p<1$. In this paper, we are the first to show that a standard peeling algorithm can still yield $2^{1/p}$-approximation for the case $0<p < 1$. (Veldt 2021) proposed a new generalized peeling algorithm (GENPEEL), which for $p \geq 1$ has an approximation guarantee ratio $(p+1)^{1/p}$, and time complexity $O(mn)$, where $m$ and $n$ denote the number of edges and nodes in graph respectively. In terms of algorithmic contributions, we propose a new and faster generalized peeling algorithm (called GENPEEL++ in this paper), which for $p \in [1, +\infty)$ has an approximation guarantee ratio $(2(p+1))^{1/p}$, and time complexity $O(m(\log n))$, where $m$ and $n$ denote the number of edges and nodes in graph, respectively. This approximation ratio converges to 1 as $p \rightarrow \infty$.

cs.DS↗
arXiv2023

Transversals in a collections of trees

Let $\mathcal{S}$ be a fixed family of graphs on vertex set $V$ and $\mathcal{G}$ be a collection of elements in $\mathcal{S}$. We investigated the transversal problem of finding the maximum value of $|\mathcal{G}|$ when $\mathcal{G}$ contains no rainbow elements in $\mathcal{S}$. Specifically, we determine the exact values when $\mathcal{S}$ is a family of stars or a family of trees of the same order $n$ with $n$ dividing $|V|$. Further, all the extremal cases for $\mathcal{G}$ are characterized.

math.CO↗
arXiv2023

On the Last-iterate Convergence in Time-varying Zero-sum Games: Extra Gradient Succeeds where Optimism Fails

Last-iterate convergence has received extensive study in two player zero-sum games starting from bilinear, convex-concave up to settings that satisfy the MVI condition. Typical methods that exhibit last-iterate convergence for the aforementioned games include extra-gradient (EG) and optimistic gradient descent ascent (OGDA). However, all the established last-iterate convergence results hold for the restrictive setting where the underlying repeated game does not change over time. Recently, a line of research has focused on regret analysis of OGDA in time-varying games, i.e., games where payoffs evolve with time; the last-iterate behavior of OGDA and EG in time-varying environments remains unclear though. In this paper, we study the last-iterate behavior of various algorithms in two types of unconstrained, time-varying, bilinear zero-sum games: periodic and convergent perturbed games. These models expand upon the usual repeated game formulation and incorporate external environmental factors, such as the seasonal effects on species competition and vanishing external noise. In periodic games, we prove that EG will converge while OGDA and momentum method will diverge. This is quite surprising, as to the best of our knowledge, it is the first result that indicates EG and OGDA have qualitatively different last-iterate behaviors and do not exhibit similar behavior. In convergent perturbed games, we prove all these algorithms converge as long as the game itself stabilizes with a faster rate than $1/t$.

cs.GT↗
arXiv2023

Optimal Estimator for Linear Regression with Shuffled Labels

This paper considers the task of linear regression with shuffled labels, i.e., $\mathbf Y = \mathbf Π\mathbf X \mathbf B + \mathbf W$, where $\mathbf Y \in \mathbb R^{n\times m}, \mathbf Pi \in \mathbb R^{n\times n}, \mathbf X\in \mathbb R^{n\times p}, \mathbf B \in \mathbb R^{p\times m}$, and $\mathbf W\in \mathbb R^{n\times m}$, respectively, represent the sensing results, (unknown or missing) corresponding information, sensing matrix, signal of interest, and additive sensing noise. Given the observation $\mathbf Y$ and sensing matrix $\mathbf X$, we propose a one-step estimator to reconstruct $(\mathbf Π, \mathbf B)$. From the computational perspective, our estimator's complexity is $O(n^3 + np^2m)$, which is no greater than the maximum complexity of a linear assignment algorithm (e.g., $O(n^3)$) and a least square algorithm (e.g., $O(np^2 m)$). From the statistical perspective, we divide the minimum $snr$ requirement into four regimes, e.g., unknown, hard, medium, and easy regimes; and present sufficient conditions for the correct permutation recovery under each regime: $(i)$ $snr \geq Ω(1)$ in the easy regime; $(ii)$ $snr \geq Ω(\log n)$ in the medium regime; and $(iii)$ $snr \geq Ω((\log n)^{c_0}\cdot n^{{c_1}/{srank(\mathbf B)}})$ in the hard regime ($c_0, c_1$ are some positive constants and $srank(\mathbf B)$ denotes the stable rank of $\mathbf B$). In the end, we also provide numerical experiments to confirm the above claims.

stat.ML↗
arXiv2023

Adversarial Attacks on Video Object Segmentation with Hard Region Discovery

Video object segmentation has been applied to various computer vision tasks, such as video editing, autonomous driving, and human-robot interaction. However, the methods based on deep neural networks are vulnerable to adversarial examples, which are the inputs attacked by almost human-imperceptible perturbations, and the adversary (i.e., attacker) will fool the segmentation model to make incorrect pixel-level predictions. This will rise the security issues in highly-demanding tasks because small perturbations to the input video will result in potential attack risks. Though adversarial examples have been extensively used for classification, it is rarely studied in video object segmentation. Existing related methods in computer vision either require prior knowledge of categories or cannot be directly applied due to the special design for certain tasks, failing to consider the pixel-wise region attack. Hence, this work develops an object-agnostic adversary that has adversarial impacts on VOS by first-frame attacking via hard region discovery. Particularly, the gradients from the segmentation model are exploited to discover the easily confused region, in which it is difficult to identify the pixel-wise objects from the background in a frame. This provides a hardness map that helps to generate perturbations with a stronger adversarial power for attacking the first frame. Empirical studies on three benchmarks indicate that our attacker significantly degrades the performance of several state-of-the-art video object segmentation models.

cs.CV↗
arXiv2023

Triple-View Knowledge Distillation for Semi-Supervised Semantic Segmentation

To alleviate the expensive human labeling, semi-supervised semantic segmentation employs a few labeled images and an abundant of unlabeled images to predict the pixel-level label map with the same size. Previous methods often adopt co-training using two convolutional networks with the same architecture but different initialization, which fails to capture the sufficiently diverse features. This motivates us to use tri-training and develop the triple-view encoder to utilize the encoders with different architectures to derive diverse features, and exploit the knowledge distillation skill to learn the complementary semantics among these encoders. Moreover, existing methods simply concatenate the features from both encoder and decoder, resulting in redundant features that require large memory cost. This inspires us to devise a dual-frequency decoder that selects those important features by projecting the features from the spatial domain to the frequency domain, where the dual-frequency channel attention mechanism is introduced to model the feature importance. Therefore, we propose a Triple-view Knowledge Distillation framework, termed TriKD, for semi-supervised semantic segmentation, including the triple-view encoder and the dual-frequency decoder. Extensive experiments were conducted on two benchmarks, \ie, Pascal VOC 2012 and Cityscapes, whose results verify the superiority of the proposed method with a good tradeoff between precision and inference speed.

cs.CV↗
arXiv2023

Word Embedding with Neural Probabilistic Prior

To improve word representation learning, we propose a probabilistic prior which can be seamlessly integrated with word embedding models. Different from previous methods, word embedding is taken as a probabilistic generative model, and it enables us to impose a prior regularizing word representation learning. The proposed prior not only enhances the representation of embedding vectors but also improves the model's robustness and stability. The structure of the proposed prior is simple and effective, and it can be easily implemented and flexibly plugged in most existing word embedding models. Extensive experiments show the proposed method improves word representation on various tasks.

cs.CL↗