arXiv subjects

Xiao Li

Publications and source records attributed to Xiao Li.

At least 343 records · Page 19Linked to original sources

arXiv2023

A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization

The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the symmetric NMF is not as easy as for its nonsymmetric counterpart, since the latter admits the splitting property that allows state-of-the-art alternating-type algorithms. To overcome this issue, we first split the decision variable and transform the symmetric NMF to a penalized nonsymmetric one, paving the way for designing efficient alternating-type algorithms. We then show that solving the penalized nonsymmetric reformulation returns a solution to the original symmetric NMF. Moreover, we design a family of alternating-type algorithms and show that they all admit strong convergence guarantee: the generated sequence of iterates is convergent and converges at least sublinearly to a critical point of the original symmetric NMF. Finally, we conduct experiments on both synthetic data and real image clustering to support our theoretical results and demonstrate the performance of the alternating-type algorithms.

cs.LG↗

arXiv2023

An Efficient Semi-Automated Scheme for Infrastructure LiDAR Annotation

Most existing perception systems rely on sensory data acquired from cameras, which perform poorly in low light and adverse weather conditions. To resolve this limitation, we have witnessed advanced LiDAR sensors become popular in perception tasks in autonomous driving applications. Nevertheless, their usage in traffic monitoring systems is less ubiquitous. We identify two significant obstacles in cost-effectively and efficiently developing such a LiDAR-based traffic monitoring system: (i) public LiDAR datasets are insufficient for supporting perception tasks in infrastructure systems, and (ii) 3D annotations on LiDAR point clouds are time-consuming and expensive. To fill this gap, we present an efficient semi-automated annotation tool that automatically annotates LiDAR sequences with tracking algorithms while offering a fully annotated infrastructure LiDAR dataset -- FLORIDA (Florida LiDAR-based Object Recognition and Intelligent Data Annotation) -- which will be made publicly available. Our advanced annotation tool seamlessly integrates multi-object tracking (MOT), single-object tracking (SOT), and suitable trajectory post-processing techniques. Specifically, we introduce a human-in-the-loop schema in which annotators recursively fix and refine annotations imperfectly predicted by our tool and incrementally add them to the training dataset to obtain better SOT and MOT models. By repeating the process, we significantly increase the overall annotation speed by three to four times and obtain better qualitative annotations than a state-of-the-art annotation tool. The human annotation experiments verify the effectiveness of our annotation tool. In addition, we provide detailed statistics and object detection evaluation results for our dataset in serving as a benchmark for perception tasks at traffic intersections.

cs.CV↗

arXiv2023

Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge

We study many-body localization (MBL) in the quasiperiodic $t_1$-$t_2$ model, focusing on the role of next-nearest-neighbor (NNN) hopping $t_2$, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction $U$. For weak interactions ($U\ll t_1$), this model is always nonthermal. For intermediate interactions ($U\sim t_1$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\gg t_1)$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.

cond-mat.dis-nn↗

arXiv2022

Incremental Methods for Weakly Convex Optimization

Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental proximal point, and incremental prox-linear methods -- for solving weakly convex optimization problems. Such a problem class covers many nonsmooth nonconvex instances that arise in engineering fields. We show that the three said incremental methods have an iteration complexity of $O(\varepsilon^{-4})$ for driving a natural stationarity measure to below $\varepsilon$. Moreover, we show that if the weakly convex function satisfies a sharpness condition, then all three incremental methods, when properly initialized and equipped with geometrically diminishing stepsizes, can achieve a local linear rate of convergence. Our work is the first to extend the convergence rate analysis of incremental methods from the nonsmooth convex regime to the weakly convex regime. Lastly, we conduct numerical experiments on the robust matrix sensing problem to illustrate the convergence performance of the three incremental methods.

math.OC↗

arXiv2022

Conditional HI mass functions and the HI-to-halo mass relation in the local Universe

We present a new HI mass estimator which relates the HI-to-stellar mass ratio to four galaxy properties: stellar surface mass density, color index $u-r$, stellar mass and concentration index, with the scatter of individual galaxies around the mean HI mass modeled with a Gaussian distribution. We calibrate the estimator using the xGASS sample, including both HI detection and non-detection, and constrain the model parameters through Bayesian inferences. Tests with mock catalogs demonstrate that our estimator provides unbiased HI masses for optical samples like the SDSS, thus suitable for statistical studies of HI gas contents in galaxies and dark matter halos. We apply our estimator to the SDSS spectroscopic sample to estimate the local HI mass function (HIMF), the conditional HI mass function (CHIMF) in galaxy groups and the HI-halo mass (HIHM) relation. Our HIMF agrees with the ALFALFA measurements at $M_{HI}\gtrsim 5\times 10^9M_{\odot}$, but with higher amplitude and a steeper slope at lower masses. We show that this discrepancy is caused primarily by the cosmic variance which is corrected for the SDSS sample but not for the ALFALFA. The CHIMFs for all halo masses can be described by a single Schechter function, and this is true for red, blue and satellite galaxies. For central galaxies the CHIMFs show a double-Gaussian profile, with the two components contributed by the red and blue galaxies, respectively. The total HI mass in a group increases monotonically with halo mass. The HI mass of central galaxies in galaxy groups increases rapidly with halo mass only at $M_h\lesssim10^{12}M_{\odot}$, while the mass dependence becomes much weaker at higher halo masses. The observed HI-halo mass relation is not reproduced by current hydrodynamic simulations and semi-analytic models of galaxy formation.

astro-ph.GA↗

arXiv2022

Recognizing Object by Components with Human Prior Knowledge Enhances Adversarial Robustness of Deep Neural Networks

Adversarial attacks can easily fool object recognition systems based on deep neural networks (DNNs). Although many defense methods have been proposed in recent years, most of them can still be adaptively evaded. One reason for the weak adversarial robustness may be that DNNs are only supervised by category labels and do not have part-based inductive bias like the recognition process of humans. Inspired by a well-known theory in cognitive psychology -- recognition-by-components, we propose a novel object recognition model ROCK (Recognizing Object by Components with human prior Knowledge). It first segments parts of objects from images, then scores part segmentation results with predefined human prior knowledge, and finally outputs prediction based on the scores. The first stage of ROCK corresponds to the process of decomposing objects into parts in human vision. The second stage corresponds to the decision process of the human brain. ROCK shows better robustness than classical recognition models across various attack settings. These results encourage researchers to rethink the rationality of currently widely-used DNN-based object recognition models and explore the potential of part-based models, once important but recently ignored, for improving robustness.

cs.CV↗

arXiv2022

DyRRen: A Dynamic Retriever-Reranker-Generator Model for Numerical Reasoning over Tabular and Textual Data

Numerical reasoning over hybrid data containing tables and long texts has recently received research attention from the AI community. To generate an executable reasoning program consisting of math and table operations to answer a question, state-of-the-art methods use a retriever-generator pipeline. However, their retrieval results are static, while different generation steps may rely on different sentences. To attend to the retrieved information that is relevant to each generation step, in this paper, we propose DyRRen, an extended retriever-reranker-generator framework where each generation step is enhanced by a dynamic reranking of retrieved sentences. It outperforms existing baselines on the FinQA dataset.

cs.CL↗

arXiv2022

Experimental demonstration of non-adjacent band topology connecting multiple nodal links

Nodal links are special configurations of band degeneracies in the momentum space, where nodal line branches encircle each other. In PT symmetric systems, nodal lines can be topologically characterized using the eigenvector frame rotations along an encircling loop and the linking structure can be described with non-Abelian frame charges interacting among adjacent bands. In this paper, we present a photonic multiple nodal links system, where non-adjacent band topology is proposed to characterize the hidden relation between nodal lines from non-adjacent band pairs. Through an orthogonal nodal chain, the nodal line from the lower two bands predicts the existence of nodal lines formed between the higher bands. We designed and fabricated a metamaterial, with which the multiple nodal links and non-adjacent band topology are experimentally demonstrated.

physics.optics↗

arXiv2022

Dynamic Treatment Regimes using Bayesian Additive Regression Trees for Censored Outcomes

To achieve the goal of providing the best possible care to each patient, physicians need to customize treatments for patients with the same diagnosis, especially when treating diseases that can progress further and require additional treatments, such as cancer. Making decisions at multiple stages as a disease progresses can be formalized as a dynamic treatment regime (DTR). Most of the existing optimization approaches for estimating dynamic treatment regimes including the popular method of Q-learning were developed in a frequentist context. Recently, a general Bayesian machine learning framework that facilitates using Bayesian regression modeling to optimize DTRs has been proposed. In this article, we adapt this approach to censored outcomes using Bayesian additive regression trees (BART) for each stage under the accelerated failure time modeling framework, along with simulation studies and a real data example that compare the proposed approach with Q-learning. We also develop an R wrapper function that utilizes a standard BART survival model to optimize DTRs for censored outcomes. The wrapper function can easily be extended to accommodate any type of Bayesian machine learning model.

stat.ME↗

arXiv2022

A Unified Convergence Theorem for Stochastic Optimization Methods

In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several representative conditions and is not tailored to any specific algorithm. As a direct application, we recover expected and almost sure convergence results of the stochastic gradient method (SGD) and random reshuffling (RR) under more general settings. Moreover, we establish new expected and almost sure convergence results for the stochastic proximal gradient method (prox-SGD) and stochastic model-based methods (SMM) for nonsmooth nonconvex optimization problems. These applications reveal that our unified theorem provides a plugin-type convergence analysis and strong convergence guarantees for a wide class of stochastic optimization methods.

math.OC↗

arXiv2022

Estimating Neural Reflectance Field from Radiance Field using Tree Structures

We present a new method for estimating the Neural Reflectance Field (NReF) of an object from a set of posed multi-view images under unknown lighting. NReF represents 3D geometry and appearance of objects in a disentangled manner, and are hard to be estimated from images only. Our method solves this problem by exploiting the Neural Radiance Field (NeRF) as a proxy representation, from which we perform further decomposition. A high-quality NeRF decomposition relies on good geometry information extraction as well as good prior terms to properly resolve ambiguities between different components. To extract high-quality geometry information from radiance fields, we re-design a new ray-casting based method for surface point extraction. To efficiently compute and apply prior terms, we convert different prior terms into different type of filter operations on the surface extracted from radiance field. We then employ two type of auxiliary data structures, namely Gaussian KD-tree and octree, to support fast querying of surface points and efficient computation of surface filters during training. Based on this, we design a multi-stage decomposition optimization pipeline for estimating neural reflectance field from neural radiance fields. Extensive experiments show our method outperforms other state-of-the-art methods on different data, and enable high-quality free-view relighting as well as material editing tasks.

cs.CV↗

arXiv2022

Are All Losses Created Equal: A Neural Collapse Perspective

While cross entropy (CE) is the most commonly used loss to train deep neural networks for classification tasks, many alternative losses have been developed to obtain better empirical performance. Among them, which one is the best to use is still a mystery, because there seem to be multiple factors affecting the answer, such as properties of the dataset, the choice of network architecture, and so on. This paper studies the choice of loss function by examining the last-layer features of deep networks, drawing inspiration from a recent line work showing that the global optimal solution of CE and mean-square-error (MSE) losses exhibits a Neural Collapse phenomenon. That is, for sufficiently large networks trained until convergence, (i) all features of the same class collapse to the corresponding class mean and (ii) the means associated with different classes are in a configuration where their pairwise distances are all equal and maximized. We extend such results and show through global solution and landscape analyses that a broad family of loss functions including commonly used label smoothing (LS) and focal loss (FL) exhibits Neural Collapse. Hence, all relevant losses(i.e., CE, LS, FL, MSE) produce equivalent features on training data. Based on the unconstrained feature model assumption, we provide either the global landscape analysis for LS loss or the local landscape analysis for FL loss and show that the (only!) global minimizers are neural collapse solutions, while all other critical points are strict saddles whose Hessian exhibit negative curvature directions either in the global scope for LS loss or in the local scope for FL loss near the optimal solution. The experiments further show that Neural Collapse features obtained from all relevant losses lead to largely identical performance on test data as well, provided that the network is sufficiently large and trained until convergence.

cs.LG↗

arXiv2022

Valley and spin splittings in a valley-layer-locked monolayer via atomic adsorption

To date, a number of valley materials have been discovered with the spin-valley or valley-layer couplings. It is highly desirable to realize the interplay of more electronic degrees of freedom in a valley material. Based on the first-principles calculations, we demonstrate the valley and spin degeneracy liftings in the band structure of a TiSiCO monolayer, with the help of the selective expression of the layer pseudospin via atomic adsorption. The introduction of the transition-metal adatoms provides an effective electric field and magnetic proximity effect, giving rise to the valley and spin splittings. These splittings can be further tuned by applying an external electric field. According to the modified band structure, various interlayer excitons with different combinations of spins and electric dipoles are selectively created, under the optical field of appropriate frequencies. The tunable spin and valley splittings in atom adsorbed TiSiCO monolayer offer opportunities for exploring the interactions between spin, valley and layer pseudospin, and designing advanced optoelectronic devices.

cond-mat.mtrl-sci↗

arXiv2022

Tunable valley and spin splittings in $\rm VSi_2N_4$ bilayer

The control and manipulation of the valley and spin degrees of freedom have received great interests in fundamental studies and advanced information technologies. Compared with magnetic means, it is highly desirable to realize more energy-efficient electric control of valley and spin. Using the first-principles calculations, we demonstrate tunable valley and spin degeneracy splittings in $\rm VSi_2N_4$ bilayers, with the aid of the layered structure and associated electric control. Depending on different interlayer magnetic couplings and stacking orders, the $\rm VSi_2N_4$ bilayers exhibit a variety of combinations of valley and spin degeneracies. Under the action of a vertical electric field, the degeneracy splittings become highly tunable for both the sign and magnitude. As a result, a series of anomalous Hall currents can be selectively realized with varied indices of valley and spin. These intriguing features offer a practical way for designing energy-efficient devices based on the couplings between multiple electronic degrees of freedom.

cond-mat.mtrl-sci↗

arXiv2022

AI for CSI Feedback Enhancement in 5G-Advanced

The 3rd Generation Partnership Project started the study of Release 18 in 2021. Artificial intelligence (AI)-native air interface is one of the key features of Release 18, where AI for channel state information (CSI) feedback enhancement is selected as the representative use case. This article provides an overview of AI for CSI feedback enhancement in 5G-Advanced. Several representative non-AI and AI-enabled CSI feedback frameworks are first introduced and compared. Then, the standardization of AI for CSI feedback enhancement in 5G-advanced is presented in detail. First, the scope of the AI for CSI feedback enhancement in 5G-Advanced is presented and discussed. Then, the main challenges and open problems in the standardization of AI for CSI feedback enhancement, especially focusing on performance evaluation and the design of new protocols for AI-enabled CSI feedback, are identified and discussed. This article provides a guideline for the standardization study of AI-based CSI feedback enhancement.

cs.IT↗

arXiv2022

SeanNet: Semantic Understanding Network for Localization Under Object Dynamics

We aim for domestic robots to perform long-term indoor service. Under the object-level scene dynamics induced by daily human activities, a robot needs to robustly localize itself in the environment subject to scene uncertainties. Previous works have addressed visual-based localization in static environments, yet the object-level scene dynamics challenge existing methods for the long-term deployment of the robot. This paper proposes a SEmantic understANding Network (SeanNet) architecture that enables an effective learning process with coupled visual and semantic inputs. With a dataset that contains object dynamics, we propose a cascaded contrastive learning scheme to train the SeanNet for learning a vector scene embedding. Subsequently, we can measure the similarity between the current observed scene and the target scene, whereby enables robust localization under object-level dynamics. In our experiments, we benchmark SeanNet against state-of-the-art image-encoding networks (baselines) on scene similarity measures. The SeanNet architecture with the proposed training method can achieve an 85.02\% accuracy which is higher than baselines. We further integrate the SeanNet and the other networks as the localizers into a visual navigation application. We demonstrate that SeanNet achieves higher success rates compared to the baselines.

cs.RO↗

arXiv2022

Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation

In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolson approximation and the Adams-Bashforth extrapolation for the temporal discretization, and by applying the Fourier spectral collocation to the spatial discretization. In addition, two stabilization terms in different forms are added for the sake of the numerical stability. We conduct a complete convergence analysis by using the higher-order consistency estimate for the numerical scheme, combined with the rough error estimate and the refined estimate. By regarding the numerical solution as a small perturbation of the exact solution, we are able to justify the discrete $\ell^\infty$ bound of the numerical solution, as a result of the rough error estimate. Subsequently, the refined error estimate is derived to obtain the optimal rate of convergence, following the established $\ell^\infty$ bound of the numerical solution. Moreover, the energy stability is also rigorously proved with respect to a modified energy. The proposed scheme can be viewed as the generalization of the second-order scheme presented in an earlier work, and the energy stability estimate has greatly improved the corresponding result therein.

math.NA↗

arXiv2022

Set-theoretic Localization for Mobile Robots with Infrastructure-based Sensing

In this paper, we introduce a set-theoretic approach for mobile robot localization with infrastructure-based sensing. The proposed method computes sets that over-bound the robot body and orientation under an assumption of known noise bounds on the sensor and robot motion model. We establish theoretical properties and computational approaches for this set-theoretic localization approach and illustrate its application to an automated valet parking example in simulations and to omnidirectional robot localization problems in real-world experiments. We demonstrate that the set-theoretic localization method can perform robustly against uncertainty set initialization and sensor noises compared to the FastSLAM.

cs.RO↗