arXiv subjects

Xiaojun Chen

Publications and source records attributed to Xiaojun Chen.

At least 73 records · Page 4Linked to original sources

arXiv2024

Tight Error Bounds for the Sign-Constrained Stiefel Manifold

The sign-constrained Stiefel manifold in $\mathbb{R}^{n\times r}$ is a segment of the Stiefel manifold with fixed signs (nonnegative or nonpositive) for some columns of the matrices. It includes the nonnegative Stiefel manifold as a special case. We present global and local error bounds that provide an inequality with easily computable residual functions and explicit coefficients to bound the distance from matrices in $\mathbb{R}^{n\times r}$ to the sign-constrained Stiefel manifold. Moreover, we show that the error bounds cannot be improved except for the multiplicative constants under some mild conditions, which explains why two square-root terms are necessary in the bounds when $1< r <n$ and why the $\ell_1$ norm can be used in the bounds when $r = n$ or $r = 1$ for the sign constraints and orthogonality, respectively. The error bounds are applied to derive exact penalty methods for minimizing a Lipschitz continuous function with orthogonality and sign constraints.

math.OC↗

arXiv2024

Open-SQL Framework: Enhancing Text-to-SQL on Open-source Large Language Models

Despite the success of large language models (LLMs) in Text-to-SQL tasks, open-source LLMs encounter challenges in contextual understanding and response coherence. To tackle these issues, we present \ours, a systematic methodology tailored for Text-to-SQL with open-source LLMs. Our contributions include a comprehensive evaluation of open-source LLMs in Text-to-SQL tasks, the \openprompt strategy for effective question representation, and novel strategies for supervised fine-tuning. We explore the benefits of Chain-of-Thought in step-by-step inference and propose the \openexample method for enhanced few-shot learning. Additionally, we introduce token-efficient techniques, such as \textbf{Variable-length Open DB Schema}, \textbf{Target Column Truncation}, and \textbf{Example Column Truncation}, addressing challenges in large-scale databases. Our findings emphasize the need for further investigation into the impact of supervised fine-tuning on contextual learning capabilities. Remarkably, our method significantly improved Llama2-7B from 2.54\% to 41.04\% and Code Llama-7B from 14.54\% to 48.24\% on the BIRD-Dev dataset. Notably, the performance of Code Llama-7B surpassed GPT-4 (46.35\%) on the BIRD-Dev dataset.

cs.CL↗

arXiv2024

A Quasi-Newton Subspace Trust Region Algorithm for nonmonotone variational inequalities in adversarial learning over box constraints

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In this paper, we propose a quasi-Newton subspace trust region (QNSTR) algorithm for the least squares problems defined by the smoothing approximation of nonsmooth equations. Based on the structure of the nonmonotone VI, we use an adaptive quasi-Newton formula to approximate the Hessian matrix and solve a low-dimensional strongly convex quadratic program with ellipse constraints in a subspace at each step of the QNSTR algorithm efficiently. We prove the global convergence of the QNSTR algorithm to an $ε$-first-order stationary point of the min-max optimization problem. Moreover, we present numerical results based on the QNSTR algorithm with different subspaces for a mixed generative adversarial networks in eye image segmentation using real data to show the efficiency and effectiveness of the QNSTR algorithm for solving large-scale min-max optimization problems.

math.OC↗

arXiv2024

Nonsmooth convex-concave saddle point problems with cardinality penalties

In this paper, we focus on a class of convexly constrained nonsmooth convex-concave saddle point problems with cardinality penalties. Although such nonsmooth nonconvex-nonconcave and discontinuous min-max problems may not have a saddle point, we show that they have a local saddle point and a global minimax point, and some local saddle points have the lower bound properties. We define a class of strong local saddle points based on the lower bound properties for stability of variable selection. Moreover, we give a framework to construct continuous relaxations of the discontinuous min-max problems based on the convolution, such that they have the same saddle points with the original problem. We also establish the relations between the continuous relaxation problems and the original problems regarding local saddle points, global minimax points, local minimax points and stationary points. Finally, we illustrate our results with distributionally robust sparse convex regression, sparse robust bond portfolio construction and sparse convex-concave logistic regression saddle point problems.

math.OC↗

arXiv2024

ROG$_{PL}$: Robust Open-Set Graph Learning via Region-Based Prototype Learning

Open-set graph learning is a practical task that aims to classify the known class nodes and to identify unknown class samples as unknowns. Conventional node classification methods usually perform unsatisfactorily in open-set scenarios due to the complex data they encounter, such as out-of-distribution (OOD) data and in-distribution (IND) noise. OOD data are samples that do not belong to any known classes. They are outliers if they occur in training (OOD noise), and open-set samples if they occur in testing. IND noise are training samples which are assigned incorrect labels. The existence of IND noise and OOD noise is prevalent, which usually cause the ambiguity problem, including the intra-class variety problem and the inter-class confusion problem. Thus, to explore robust open-set learning methods is necessary and difficult, and it becomes even more difficult for non-IID graph data.To this end, we propose a unified framework named ROG$_{PL}$ to achieve robust open-set learning on complex noisy graph data, by introducing prototype learning. In specific, ROG$_{PL}$ consists of two modules, i.e., denoising via label propagation and open-set prototype learning via regions. The first module corrects noisy labels through similarity-based label propagation and removes low-confidence samples, to solve the intra-class variety problem caused by noise. The second module learns open-set prototypes for each known class via non-overlapped regions and remains both interior and border prototypes to remedy the inter-class confusion problem.The two modules are iteratively updated under the constraints of classification loss and prototype diversity loss. To the best of our knowledge, the proposed ROG$_{PL}$ is the first robust open-set node classification method for graph data with complex noise.

cs.LG↗

arXiv2024

Unsupervised multiple choices question answering via universal corpus

Unsupervised question answering is a promising yet challenging task, which alleviates the burden of building large-scale annotated data in a new domain. It motivates us to study the unsupervised multiple-choice question answering (MCQA) problem. In this paper, we propose a novel framework designed to generate synthetic MCQA data barely based on contexts from the universal domain without relying on any form of manual annotation. Possible answers are extracted and used to produce related questions, then we leverage both named entities (NE) and knowledge graphs to discover plausible distractors to form complete synthetic samples. Experiments on multiple MCQA datasets demonstrate the effectiveness of our method.

cs.CL↗

arXiv2024

MoZIP: A Multilingual Benchmark to Evaluate Large Language Models in Intellectual Property

Large language models (LLMs) have demonstrated impressive performance in various natural language processing (NLP) tasks. However, there is limited understanding of how well LLMs perform in specific domains (e.g, the intellectual property (IP) domain). In this paper, we contribute a new benchmark, the first Multilingual-oriented quiZ on Intellectual Property (MoZIP), for the evaluation of LLMs in the IP domain. The MoZIP benchmark includes three challenging tasks: IP multiple-choice quiz (IPQuiz), IP question answering (IPQA), and patent matching (PatentMatch). In addition, we also develop a new IP-oriented multilingual large language model (called MoZi), which is a BLOOMZ-based model that has been supervised fine-tuned with multilingual IP-related text data. We evaluate our proposed MoZi model and four well-known LLMs (i.e., BLOOMZ, BELLE, ChatGLM and ChatGPT) on the MoZIP benchmark. Experimental results demonstrate that MoZi outperforms BLOOMZ, BELLE and ChatGLM by a noticeable margin, while it had lower scores compared with ChatGPT. Notably, the performance of current LLMs on the MoZIP benchmark has much room for improvement, and even the most powerful ChatGPT does not reach the passing level. Our source code, data, and models are available at \url{https://github.com/AI-for-Science/MoZi}.

cs.CL↗

arXiv2024

Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture

We show that the specialized quantum D-module of the equivariant quantum cohomology ring of the minimal resolution of an ADE singularity is isomorphic to the D-module of graded traces on the minimal nilpotent orbit in the Lie algebra of the same type. This generalizes a recent result of Shlykov [Hikita conjecture for the minimal nilpotent orbit, to appear in Proc. AMS, https://doi.org/10.1090/proc/15281] and hence verifies in this case the quantum version of Hikita's conjecture, proposed by Kamnitzer, McBreen and Proudfoot [The quantum Hikita conjecture, Advances in Mathematics 390 (2021) 107947]. We also show analogous isomorphisms for singularities of BCFG type.

math.RT↗

arXiv2024

Multi-level Cross-modal Alignment for Image Clustering

Recently, the cross-modal pretraining model has been employed to produce meaningful pseudo-labels to supervise the training of an image clustering model. However, numerous erroneous alignments in a cross-modal pre-training model could produce poor-quality pseudo-labels and degrade clustering performance. To solve the aforementioned issue, we propose a novel \textbf{Multi-level Cross-modal Alignment} method to improve the alignments in a cross-modal pretraining model for downstream tasks, by building a smaller but better semantic space and aligning the images and texts in three levels, i.e., instance-level, prototype-level, and semantic-level. Theoretical results show that our proposed method converges, and suggests effective means to reduce the expected clustering risk of our method. Experimental results on five benchmark datasets clearly show the superiority of our new method.

cs.CV↗

arXiv2023

MedShapeNet -- A Large-Scale Dataset of 3D Medical Shapes for Computer Vision

Prior to the deep learning era, shape was commonly used to describe the objects. Nowadays, state-of-the-art (SOTA) algorithms in medical imaging are predominantly diverging from computer vision, where voxel grids, meshes, point clouds, and implicit surface models are used. This is seen from numerous shape-related publications in premier vision conferences as well as the growing popularity of ShapeNet (about 51,300 models) and Princeton ModelNet (127,915 models). For the medical domain, we present a large collection of anatomical shapes (e.g., bones, organs, vessels) and 3D models of surgical instrument, called MedShapeNet, created to facilitate the translation of data-driven vision algorithms to medical applications and to adapt SOTA vision algorithms to medical problems. As a unique feature, we directly model the majority of shapes on the imaging data of real patients. As of today, MedShapeNet includes 23 dataset with more than 100,000 shapes that are paired with annotations (ground truth). Our data is freely accessible via a web interface and a Python application programming interface (API) and can be used for discriminative, reconstructive, and variational benchmarks as well as various applications in virtual, augmented, or mixed reality, and 3D printing. Exemplary, we present use cases in the fields of classification of brain tumors, facial and skull reconstructions, multi-class anatomy completion, education, and 3D printing. In future, we will extend the data and improve the interfaces. The project pages are: https://medshapenet.ikim.nrw/ and https://github.com/Jianningli/medshapenet-feedback

cs.CV↗

arXiv2023

Electronic properties of nickelate superconductor R3Ni2O7 with oxygen vacancies

The discovery of superconductivity in La3Ni2O7 has attracted significant research interest in the field of nickelate superconductors. Despite extensive studies on pristine La3Ni2O7, the impact of oxygen vacancies (VO), a common type of intrinsic defect in oxides, on electronic structures and superconductivity in La3Ni2O7 remains unclear. In this article, we identify the most energetically favorable location for VO formation as the oxygen atom connecting the NiO6 bilayer, resulting in a significant reduction in the lattice constant along the c-axis. Interestingly, the electronic structure undergoes notable changes, particularly for the Ni dz2 and Ni dx2-y2 orbitals. The Ni dz2 orbitals change from partially filled in the pristine La3Ni2O7 to completely filled in the presence of VO, leading to a considerable decrease of its proportion near the Fermi level. Conversely, the proportion of Ni dx2-y2 states increases due to the orbital localization and slight upward shift. Additionally, we observe a significant increase in the hopping of intra-bilayer Ni dz2 orbitals when the VO exists, but with an opposite sign, which differs greatly from the previous understanding. The inter-orbital hopping between Ni dz2 and Ni dx2-y2 orbitals also changes its sign in the presence of VO. Our results indicate that the formation of VO may be harmful to the superconductivity in La3Ni2O7, given the general assumption for the critical role of Ni dz2 in generating superconductivity. Furthermore, we suggest that Ce3Ni2O7, which shares similar electronic structures to La3Ni2O7 but has a larger lattice volume, may be a better candidate for nickelate superconductor due to its lower VO concentration.

cond-mat.mtrl-sci↗

arXiv2023

Phase-Specific Augmented Reality Guidance for Microscopic Cataract Surgery Using Long-Short Spatiotemporal Aggregation Transformer

Phacoemulsification cataract surgery (PCS) is a routine procedure conducted using a surgical microscope, heavily reliant on the skill of the ophthalmologist. While existing PCS guidance systems extract valuable information from surgical microscopic videos to enhance intraoperative proficiency, they suffer from non-phasespecific guidance, leading to redundant visual information. In this study, our major contribution is the development of a novel phase-specific augmented reality (AR) guidance system, which offers tailored AR information corresponding to the recognized surgical phase. Leveraging the inherent quasi-standardized nature of PCS procedures, we propose a two-stage surgical microscopic video recognition network. In the first stage, we implement a multi-task learning structure to segment the surgical limbus region and extract limbus region-focused spatial feature for each frame. In the second stage, we propose the long-short spatiotemporal aggregation transformer (LS-SAT) network to model local fine-grained and global temporal relationships, and combine the extracted spatial features to recognize the current surgical phase. Additionally, we collaborate closely with ophthalmologists to design AR visual cues by utilizing techniques such as limbus ellipse fitting and regional restricted normal cross-correlation rotation computation. We evaluated the network on publicly available and in-house datasets, with comparison results demonstrating its superior performance compared to related works. Ablation results further validated the effectiveness of the limbus region-focused spatial feature extractor and the combination of temporal features. Furthermore, the developed system was evaluated in a clinical setup, with results indicating remarkable accuracy and real-time performance. underscoring its potential for clinical applications.

cs.CV↗

arXiv2023

Apple Vision Pro for Healthcare: "The Ultimate Display"? -- Entering the Wonderland of Precision Medicine

At the Worldwide Developers Conference (WWDC) in June 2023, Apple introduced the Vision Pro. The Vision Pro is a Mixed Reality (MR) headset, more specifically it is a Virtual Reality (VR) device with an additional Video See-Through (VST) capability. The VST capability turns the Vision Pro also into an Augmented Reality (AR) device. The AR feature is enabled by streaming the real world via cameras to the (VR) screens in front of the user's eyes. This is of course not unique and similar to other devices, like the Varjo XR-3. Nevertheless, the Vision Pro has some interesting features, like an inside-out screen that can show the headset wearers' eyes to "outsiders" or a button on the top, called "Digital Crown", that allows you to seamlessly blend digital content with your physical space by turning it. In addition, it is untethered, except for the cable to the battery, which makes the headset more agile, compared to the Varjo XR-3. This could actually come closer to the "Ultimate Display", which Ivan Sutherland had already sketched in 1965. Not available to the public yet, like the Ultimate Display, we want to take a look into the crystal ball in this perspective to see if it can overcome some clinical challenges that - especially - AR still faces in the medical domain, but also go beyond and discuss if the Vision Pro could support clinicians in essential tasks to spend more time with their patients.

cs.AI↗

arXiv2023

$\mathcal{G}^2Pxy$: Generative Open-Set Node Classification on Graphs with Proxy Unknowns

Node classification is the task of predicting the labels of unlabeled nodes in a graph. State-of-the-art methods based on graph neural networks achieve excellent performance when all labels are available during training. But in real-life, models are often applied on data with new classes, which can lead to massive misclassification and thus significantly degrade performance. Hence, developing open-set classification methods is crucial to determine if a given sample belongs to a known class. Existing methods for open-set node classification generally use transductive learning with part or all of the features of real unseen class nodes to help with open-set classification. In this paper, we propose a novel generative open-set node classification method, i.e. $\mathcal{G}^2Pxy$, which follows a stricter inductive learning setting where no information about unknown classes is available during training and validation. Two kinds of proxy unknown nodes, inter-class unknown proxies and external unknown proxies are generated via mixup to efficiently anticipate the distribution of novel classes. Using the generated proxies, a closed-set classifier can be transformed into an open-set one, by augmenting it with an extra proxy classifier. Under the constraints of both cross entropy loss and complement entropy loss, $\mathcal{G}^2Pxy$ achieves superior effectiveness for unknown class detection and known class classification, which is validated by experiments on benchmark graph datasets. Moreover, $\mathcal{G}^2Pxy$ does not have specific requirement on the GNN architecture and shows good generalizations.

cs.LG↗

arXiv2023

Practical and General Backdoor Attacks against Vertical Federated Learning

Federated learning (FL), which aims to facilitate data collaboration across multiple organizations without exposing data privacy, encounters potential security risks. One serious threat is backdoor attacks, where an attacker injects a specific trigger into the training dataset to manipulate the model's prediction. Most existing FL backdoor attacks are based on horizontal federated learning (HFL), where the data owned by different parties have the same features. However, compared to HFL, backdoor attacks on vertical federated learning (VFL), where each party only holds a disjoint subset of features and the labels are only owned by one party, are rarely studied. The main challenge of this attack is to allow an attacker without access to the data labels, to perform an effective attack. To this end, we propose BadVFL, a novel and practical approach to inject backdoor triggers into victim models without label information. BadVFL mainly consists of two key steps. First, to address the challenge of attackers having no knowledge of labels, we introduce a SDD module that can trace data categories based on gradients. Second, we propose a SDP module that can improve the attack's effectiveness by enhancing the decision dependency between the trigger and attack target. Extensive experiments show that BadVFL supports diverse datasets and models, and achieves over 93% attack success rate with only 1% poisoning rate.

cs.CR↗

arXiv2023

Semantic-Enhanced Image Clustering

Image clustering is an important and open-challenging task in computer vision. Although many methods have been proposed to solve the image clustering task, they only explore images and uncover clusters according to the image features, thus being unable to distinguish visually similar but semantically different images. In this paper, we propose to investigate the task of image clustering with the help of a visual-language pre-training model. Different from the zero-shot setting, in which the class names are known, we only know the number of clusters in this setting. Therefore, how to map images to a proper semantic space and how to cluster images from both image and semantic spaces are two key problems. To solve the above problems, we propose a novel image clustering method guided by the visual-language pre-training model CLIP, named \textbf{Semantic-Enhanced Image Clustering (SIC)}. In this new method, we propose a method to map the given images to a proper semantic space first and efficient methods to generate pseudo-labels according to the relationships between images and semantics. Finally, we propose performing clustering with consistency learning in both image space and semantic space, in a self-supervised learning fashion. The theoretical result of convergence analysis shows that our proposed method can converge at a sublinear speed. Theoretical analysis of expectation risk also shows that we can reduce the expected risk by improving neighborhood consistency, increasing prediction confidence, or reducing neighborhood imbalance. Experimental results on five benchmark datasets clearly show the superiority of our new method.

cs.CV↗

arXiv2023

Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry

We study the ``twisted" Poincaré duality of smooth Poisson manifolds, and show that, if the modular vector field is diagonalizable, then there is a mixed complex associated to the Poisson complex, which, combining with the twisted Poincaré duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology. This generalizes the previous results obtained by Xu for unimodular Poisson manifolds. We also show that the Batalin-Vilkovisky algebra structure is preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras it is also preserved by Koszul duality.

math.DG↗

arXiv2022

Lifted Stationary Points of Sparse Optimization with Complementarity Constraints

We aim to compute lifted stationary points of a sparse optimization problem (P0) with complementarity constraints. We define a continuous relaxation problem (Rv) that has the same global minimizers and optimal value with problem (P0). Problem (Rv) is a mathematical program with complementarity constraints (MPCC) and a difference-of-convex (DC) objective function. We define MPCC lifted-stationarity of (Rv) and show that it is weaker than directional stationarity, but stronger than Clarke stationarity for local optimality. Moreover, we propose an approximation method to solve (Rv) and an augmented Lagrangian method to solve its subproblem, which relaxes the equality constraint in (Rv) with a tolerance. We prove the convergence of our algorithm to an MPCC lifted-stationary point of problem (Rv) and use a sparse optimization problem with vertical linear complementarity constraints to demonstrate the efficiency of our algorithm on finding sparse solutions in practice.

math.OC↗