arXiv subjects

Lei Xue

Publications and source records attributed to Lei Xue.

At least 37 records · Page 2Linked to original sources

arXiv2024

Dual Mixed Volume

We define and study the dual mixed volume rational function of a sequence of polytopes, a dual version of the mixed volume polynomial. This concept has direct relations to the adjoint polynomials and the canonical forms of polytopes. We show that dual mixed volume is additive under mixed subdivisions, and is related by a change of variables to the dual volume of the Cayley polytope. We study dual mixed volume of zonotopes, generalized permutohedra, and associahedra. The latter reproduces the planar $ϕ^3$-scalar amplitude at tree level.

math.CO↗

arXiv2024

Diversity-grounded Channel Prototypical Learning for Out-of-Distribution Intent Detection

In the realm of task-oriented dialogue systems, a robust intent detection mechanism must effectively handle malformed utterances encountered in real-world scenarios. This study presents a novel fine-tuning framework for large language models (LLMs) aimed at enhancing in-distribution (ID) intent classification and out-of-distribution (OOD) intent detection, which utilizes semantic matching with prototypes derived from ID class names. By harnessing the highly distinguishable representations of LLMs, we construct semantic prototypes for each ID class using a diversity-grounded prompt tuning approach. We rigorously test our framework in a challenging OOD context, where ID and OOD classes are semantically close yet distinct, referred to as \emph{near} OOD detection. For a thorough assessment, we benchmark our method against the prevalent fine-tuning approaches. The experimental findings reveal that our method demonstrates superior performance in both few-shot ID intent classification and near-OOD intent detection tasks.

cs.CL↗

arXiv2024

Compressed Sensing based Detection Schemes for Differential Spatial Modulation in Visible Light Communication Systems

Differential spatial modulation (DSM) exploits the time dimension to facilitate the differential modulation, which can perfectly avoid the challenge in acquiring of heavily entangled channel state information of visible light communication (VLC) system. However, it has huge search space and high complexity for large number of transmitters. In this paper, a novel vector correction (VC)-based orthogonal matching pursuit (OMP) detection algorithm is proposed to reduce the complexity, which exploits the sparsity and relativity of all transmitters, and then employs a novel correction criterion by correcting the index vectors of the error estimation for improving the demodulation performance. To overcome the local optimum dilemma in the atoms searching, an OMP-assisted genetic algorithm is also proposed to further improve the bit error rate (BER) performance of the VLC-DSM system. Simulation results demonstrate that the proposed schemes can significantly reduce the computational complexity at least by 62.5% while achieving an excellent BER performance as compared with traditional maximum likelihood based receiver.

eess.SP↗

arXiv2024

ARAP: Demystifying Anti Runtime Analysis Code in Android Apps

With the continuous growth in the usage of Android apps, ensuring their security has become critically important. An increasing number of malicious apps adopt anti-analysis techniques to evade security measures. Although some research has started to consider anti-runtime analysis (ARA), it is unfortunate that they have not systematically examined ARA techniques. Furthermore, the rapid evolution of ARA technology exacerbates the issue, leading to increasingly inaccurate analysis results. To effectively analyze Android apps, understanding their adopted ARA techniques is necessary. However, no systematic investigation has been conducted thus far. In this paper, we conduct the first systematic study of the ARA implementations in a wide range of 117,171 Android apps (including both malicious and benign ones) collected between 2016 and 2023. Additionally, we propose a specific investigation tool named ARAP to assist this study by leveraging both static and dynamic analysis. According to the evaluation results, ARAP not only effectively identifies the ARA implementations in Android apps but also reveals many important findings. For instance, almost all apps have implemented at least one category of ARA technology (99.6% for benign apps and 97.0% for malicious apps).

cs.CR↗

arXiv2024

Topology of Cut Complexes II

We continue the study of the $k$-cut complex $Δ_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jelić Milutinović, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2): 1630--1675 (2024)]. We give explicit formulas for the $f$- and $h$-polynomials of the cut complex $Δ_k(G_1+G_2) $ of the disjoint union of two graphs $G_1$ and $G_2$, and for the homology representation of $Δ_k(K_m+K_n)$. We also study the cut complex of the squared path and the grid graph. Our techniques include tools from combinatorial topology, discrete Morse theory and equivariant poset topology.

math.CO↗

arXiv2024

How Good Are LLMs at Out-of-Distribution Detection?

Out-of-distribution (OOD) detection plays a vital role in enhancing the reliability of machine learning (ML) models. The emergence of large language models (LLMs) has catalyzed a paradigm shift within the ML community, showcasing their exceptional capabilities across diverse natural language processing tasks. While existing research has probed OOD detection with relative small-scale Transformers like BERT, RoBERTa and GPT-2, the stark differences in scales, pre-training objectives, and inference paradigms call into question the applicability of these findings to LLMs. This paper embarks on a pioneering empirical investigation of OOD detection in the domain of LLMs, focusing on LLaMA series ranging from 7B to 65B in size. We thoroughly evaluate commonly-used OOD detectors, scrutinizing their performance in both zero-grad and fine-tuning scenarios. Notably, we alter previous discriminative in-distribution fine-tuning into generative fine-tuning, aligning the pre-training objective of LLMs with downstream tasks. Our findings unveil that a simple cosine distance OOD detector demonstrates superior efficacy, outperforming other OOD detectors. We provide an intriguing explanation for this phenomenon by highlighting the isotropic nature of the embedding spaces of LLMs, which distinctly contrasts with the anisotropic property observed in smaller BERT family models. The new insight enhances our understanding of how LLMs detect OOD data, thereby enhancing their adaptability and reliability in dynamic environments. We have released the source code at \url{https://github.com/Awenbocc/LLM-OOD} for other researchers to reproduce our results.

cs.CL↗

arXiv2024

Dual-Tap Optical-Digital Feedforward Equalization Enabling High-Speed Optical Transmission in IM/DD Systems

Intensity-modulation and direct-detection (IM/DD) transmission is widely adopted for high-speed optical transmission scenarios due to its cost-effectiveness and simplicity. However, as the data rate increases, the fiber chromatic dispersion (CD) would induce a serious power fading effect, and direct detection could generate inter-symbol interference (ISI). Moreover, the ISI becomes more severe with the increase of fiber length, thereby highly restricting the transmission distance of IM/DD systems. This paper proposes a dual-tap optical-digital feedforward equalization (DT-ODFE) scheme, which could effectively compensate for CD-induced power fading while maintaining low cost and simplicity. A theoretical channel response is formulated for IM/DD transmission, incorporating a dual-tap optical equalizer, and the theoretical analysis reveals that for an IM/DD transmission using 1371nm over 10km standard single-mode fiber (SSMF), frequency notch is removed from 33.7GHz to 46GHz. Simulation results show that the DT- ODFE achieves an SNR gain of 2.3dB over IM/DD systems with symbol-space feedforward equalizer (FFE) alone. As the fiber length increases to 15 km, DT- ODFE performs well, while FFE, decision-feedback equalizer (DFE) and Volterra nonlinear equalizers (VNLE) all fail to compensate for the power fading and the 7% hard-decision FEC limit is not satisfied. For 200 Gb/s/$λ$ PAM-4 over 15km SSMF, results show that the signal-to-noise ratio (SNR) of the proposed DT- ODFE with optimal coefficients satisfies the 7% hard-decision FEC limit, which uncovers the great potential of the DT- ODFE for high-speed IM/DD systems in LR/FR scenarios.

eess.SP↗

arXiv2024

Topology of Cut Complexes of Graphs

We define the $k$-cut complex of a graph $G$ with vertex set $V(G)$ to be the simplicial complex whose facets are the complements of sets of size $k$ in $V(G)$ inducing disconnected subgraphs of $G$. This generalizes the Alexander dual of a graph complex studied by Fröberg (1990), and Eagon and Reiner (1998). We describe the effect of various graph operations on the cut complex, and study its shellability, homotopy type and homology for various families of graphs, including trees, cycles, complete multipartite graphs, and the prism $K_n \times K_2$, using techniques from algebraic topology, discrete Morse theory and equivariant poset topology.

math.CO↗

arXiv2024

Total Cut Complexes of Graphs

Inspired by work of Fröberg (1990), and Eagon and Reiner (1998), we define the \emph{total $k$-cut complex} of a graph $G$ to be the simplicial complex whose facets are the complements of independent sets of size $k$ in $G$. We study the homotopy types and combinatorial properties of total cut complexes for various families of graphs, including chordal graphs, cycles, bipartite graphs, the prism $K_n \times K_2$, and grid graphs, using techniques from algebraic topology and discrete Morse theory.

math.CO↗

arXiv2023

Empirical Study on Transformer-based Techniques for Software Engineering

Many Transformer-based pre-trained models for code have been developed and applied to code-related tasks. In this paper, we review the existing literature, examine the suitability of model architectures for different tasks, and look at the generalization ability of models on different datasets, and their resource consumption. We examine three very representative pre-trained models for code: CodeBERT, CodeGPT, and CodeT5, and conduct experiments on the top-4 most targeted software engineering tasks that we found in our literature survey: Code Summarization, Bug Fixing, Bug Detection, and Code Search. In our study, we showcase the capability of decoder-only models (CodeGPT) for specific generation tasks under state-of-the-art evaluation metrics and contest the common belief that the encoder-decoder architecture is optimal for general-purpose coding tasks. Additionally, we found that the most frequently used models are not necessarily the most suitable for certain applications and the developers' needs are not adequately addressed by current research. As well, we found that the benchmark and frequent dataset for Bug Fixing and Code Summarization both fail to enable models to generalize onto other datasets for the same task (the frequent dataset refers to the dataset with the highest frequency used in literature other than the benchmark). We use statistical testing to support our conclusions from experiments. Finally, CodeBERT is highly efficient for understanding tasks, whereas CodeT5's efficiency for generation tasks is in doubt, as the highest resource consumption does not guarantee a consistent better performance on different metrics. We also discuss the numerous practical issues in advancing future research on transformer-based models for code-related tasks.

cs.SE↗

arXiv2023

Co-Design for Spectral Coexistence between RIS-aided MIMO Radar and MIMO Communication Systems

Reconfigurable intelligent surface (RIS) refers to a signal reflection surface containing a large number of low-cost passive reflecting elements. RIS can improve the performance of radar and communication systems by dynamically modulating the wireless channels. In this paper, we consider the co-design for improving the co-existence between multiple-input-multiple-output (MIMO) radar and MIMO communication system with the aid of RIS.The design purpose is to improve the radar detection performance and guarantee the communication capability. Due to the unimodular constraint on the RIS coefficients and the constant-envelope constraint on the radar transmit waveforms, the associated optimization problem is non-convex.To tackle this problem, we develop a cyclic method based on minorization-maximization, semi-definite programming, and alternating direction method of multipliers. Numerical examples verify the effectiveness of the proposed algorithm.

eess.SP↗

arXiv2023

Multi-Spectrally Constrained Low-PAPR Waveform Optimization for MIMO Radar Space-Time Adaptive Processing

This paper focuses on the joint design of transmit waveforms and receive filters for airborne multiple-input-multiple-output (MIMO) radar systems in spectrally crowded environments. The purpose is to maximize the output signal-to-interference-plus-noise-ratio (SINR) in the presence of signal-dependent clutter. To improve the practicability of the radar waveforms, both a multi-spectral constraint and a peak-to-average-power ratio (PAPR) constraint are imposed. A cyclic method is derived to iteratively optimize the transmit waveforms and receive filters. In particular, to tackle the encountered non-convex constrained fractional programming in designing the waveforms (for fixed filters), we resort to the Dinkelbach's transform, minorization-maximization (MM), and leverage the alternating direction method of multipliers (ADMM). We highlight that the proposed algorithm can iterate from an infeasible initial point and the waveforms at convergence not only satisfy the stringent constraints, but also attain superior performance.

eess.SP↗

arXiv2022

A Lower Bound Theorem for strongly regular CW spheres with up to $2d+1$ vertices

In 1967, Grünmbaum conjectured that any $d$-dimensional polytope with $d+s\leq 2d$ vertices has at least \[ϕ_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }-{d+1-s \choose k+1 } \] $k$-faces. This conjecture along with the characterization of equality cases was recently proved by the author. In this paper, several extensions of this result are established. Specifically, it is proved that lattices with the diamond property (for example, abstract polytopes) and $d+s\leq 2d$ atoms have at least $ϕ_k(d+s,d)$ elements of rank $k+1$. Furthermore, in the case of face lattices of strongly regular CW complexes representing normal pseudomanifolds with up to $2d$ vertices, a characterization of equality cases is given. Finally, sharp lower bounds on the number of $k$-faces of strongly regular CW complexes representing normal pseudomanifolds with $2d+1$ vertices are obtained. These bounds are given by the face numbers of certain polytopes with $2d+1$ vertices.

math.CO↗

arXiv2022

Numerical investigation of the scale effects of rock bridges

The concept of joint persistence has been widely used to study the mechanics and failure processes of rock masses benefitting from the simplicity of statistical linear weighing of the discontinuity. Nevertheless, this term neglects the scale effects of rock bridges, meaning that the same joint persistence may refer to different numbers and spacings of rock bridges, leading to erroneous equivalent rock mass responses. To fill in this gap, an intact rock bridge was dispersed as multi rock bridges while maintaining a constant joint persistence, subjected to direct shear by conducting numerical simulations employing Universal Distinct Element Code (UDEC). In this way, scale effects of rock bridges were investigated from the perspective of load-displacement curves, stress and displacement fields, crack propagations and AE characterizations. Results revealed that the shear resistance and the area and value of stress-concentration decreased with increasing dispersion. Furthermore, uneven distribution of displacement fields in an arc manner moving and degrading away from the load was first observed, indicating the sequential failure of multi rock bridges. It was also found that the propagation of wing cracks was insensitive to scale, while the asperity of macro shear fracture mainly formed by secondary cracks decreased with increasing dispersion. In addition, increasing dispersion of rock bridges would overlap the failure precursors identified by intense AE activities. Based on the abovementioned results, we evaluated existing methods to characterize the joint persistence, and a threshold was observed to possibly define a rock bridge.

physics.geo-ph↗

arXiv2022

Tree-based Search Graph for Approximate Nearest Neighbor Search

Nearest neighbor search supports important applications in many domains, such as database, machine learning, computer vision. Since the computational cost for accurate search is too high, the community turned to the research of approximate nearest neighbor search (ANNS). Among them, graph-based algorithm is one of the most important branches. Research by Fu et al. shows that the algorithms based on Monotonic Search Network (MSNET), such as NSG and NSSG, have achieved the state-of-the-art search performance in efficiency. The MSNET is dedicated to achieving monotonic search with minimal out-degree of nodes to pursue high efficiency. However, the current MSNET designs did not optimize the probability of the monotonic search, and the lower bound of the probability is only 50%. If they fail in monotonic search stage, they have to suffer tremendous backtracking cost to achieve the required accuracy. This will cause performance problems in search efficiency. To address this problem, we propose (r,p)-MSNET, which achieves guaranteed probability on monotonic search. Due to the high building complexity of a strict (r,p)-MSNET, we propose TBSG, which is an approximation with low complexity. Experiment conducted on four million-scaled datasets show that TBSG outperforms existing state-of-the-art graph-based algorithms in search efficiency. Our code has been released on Github.

cs.IR↗

arXiv2021

Evaluation on characterization of acoustic emission of brittle rocks from the experiment to numerical simulation

Acoustic emission (AE) characterization is an effective technique to indirectly capture the progressive failure process of the brittle rock. In previous studies, both the experiment and numerical simulation were adopted to investigate AE characteristics of the brittle rock. However, as the most popular numerical model, the moment tensor model (MTM) did not reproduce the monitoring and analyzing manner of AE signals from the physical experiment. Consequently, its result could not be constrained by the experimental result. It is thus necessary to evaluate the consistency and compatibility between the experiment and MTM. To fulfill this, we developed a particle-velocity-based model (PVBM) which enabled directly monitor and analyze the particle velocity in the numerical model and had good robustness. The PVBM imitated the actual experiment and could fill in gaps between the experiment and MTM. AE experiments of Marine shale under uniaxial compression were carried out, of which results were simulated by MTM. In general, the variation trend of the experimental result could be presented by MTM. Nevertheless, magnitudes of AE parameters by MTM presented notable differences with more than several orders compared with those by the experiment. We sequentially used PVBM as a proxy to analyze these discrepancies quantitatively and make a systematical evaluation on AE characterization of brittle rocks from the experiment to numerical simulation, considering the influence of wave reflection, energy geometrical diffusion, viscous attenuation, particle size as well as progressive deterioration of rock material. It was suggested that only the combination of MTM and PVBM could reasonably and accurately acquire AE characteristics of the actual AE experiment of brittle rocks by making full use of their respective advantages.

physics.geo-ph↗

arXiv2020

Non-Eulerian Dehn-Sommerville relations

The classical Dehn--Sommerville relations assert that the $h$-vector of an Eulerian simplicial complex is symmetric. We establish three generalizations of the Dehn--Sommerville relations: one for the $h$-vectors of pure simplicial complexes, another one for the flag $h$-vectors of balanced simplicial complexes and graded posets, and yet another one for the toric $h$-vectors of graded posets with restricted singularities. In all of these cases, we express any failure of symmetry in terms of "errors coming from the links." For simplicial complexes, this further extends Klee's semi-Eulerian relations.

math.CO↗

arXiv2020

A Proof of Grünbaum's Lower Bound Conjecture for general polytopes

In 1967, Grünbaum conjectured that any $d$-dimensional polytope with $d+s\leq 2d$ vertices has at least \[ϕ_k(d+s,d) = {d+1 \choose k+1 }+{d \choose k+1 }-{d+1-s \choose k+1 } \] $k$-faces. We prove this conjecture and also characterize the cases in which equality holds.

math.CO↗