arXiv subjects

Guodong Wang

Publications and source records attributed to Guodong Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Towards Training-free Anomaly Detection with Vision and Language Foundation Models

Anomaly detection is valuable for real-world applications, such as industrial quality inspection. However, most approaches focus on detecting local structural anomalies while neglecting compositional anomalies incorporating logical constraints. In this paper, we introduce LogSAD, a novel multi-modal framework that requires no training for both Logical and Structural Anomaly Detection. First, we propose a match-of-thought architecture that employs advanced large multi-modal models (i.e. GPT-4V) to generate matching proposals, formulating interests and compositional rules of thought for anomaly detection. Second, we elaborate on multi-granularity anomaly detection, consisting of patch tokens, sets of interests, and composition matching with vision and language foundation models. Subsequently, we present a calibration module to align anomaly scores from different detectors, followed by integration strategies for the final decision. Consequently, our approach addresses both logical and structural anomaly detection within a unified framework and achieves state-of-the-art results without the need for training, even when compared to supervised approaches, highlighting its robustness and effectiveness. Code is available at https://github.com/zhang0jhon/LogSAD.

cs.CV↗

arXiv2024

Align-DETR: Enhancing End-to-end Object Detection with Aligned Loss

DETR has set up a simple end-to-end pipeline for object detection by formulating this task as a set prediction problem, showing promising potential. Despite its notable advancements, this paper identifies two key forms of misalignment within the model: classification-regression misalignment and cross-layer target misalignment. Both issues impede DETR's convergence and degrade its overall performance. To tackle both issues simultaneously, we introduce a novel loss function, termed as Align Loss, designed to resolve the discrepancy between the two tasks. Align Loss guides the optimization of DETR through a joint quality metric, strengthening the connection between classification and regression. Furthermore, it incorporates an exponential down-weighting term to facilitate a smooth transition from positive to negative samples. Align-DETR also employs many-to-one matching for supervision of intermediate layers, akin to the design of H-DETR, which enhances robustness against instability. We conducted extensive experiments, yielding highly competitive results. Notably, our method achieves a 49.3% (+0.6) AP on the H-DETR baseline with the ResNet-50 backbone. It also sets a new state-of-the-art performance, reaching 50.5% AP in the 1x setting and 51.7% AP in the 2x setting, surpassing several strong competitors. Our code is available at https://github.com/FelixCaae/AlignDETR.

cs.CV↗

arXiv2024

New Constructions of Optimal Binary LCD Codes

Linear complementary dual (LCD) codes can provide an optimum linear coding solution for the two-user binary adder channel. LCD codes also can be used to against side-channel attacks and fault non-invasive attacks. Let $d_{LCD}(n, k)$ denote the maximum value of $d$ for which a binary $[n,k, d]$ LCD code exists. In \cite{BS21}, Bouyuklieva conjectured that $d_{LCD}(n+1, k)=d_{LCD}(n, k)$ or $d_{LCD}(n, k) + 1$ for any lenth $n$ and dimension $k \ge 2$. In this paper, we first prove Bouyuklieva's conjecture \cite{BS21} by constructing a binary $[n,k,d-1]$ LCD codes from a binary $[n+1,k,d]$ $LCD_{o,e}$ code, when $d \ge 3$ and $k \ge 2$. Then we provide a distance lower bound for binary LCD codes by expanded codes, and use this bound and some methods such as puncturing, shortening, expanding and extension, we construct some new binary LCD codes. Finally, we improve some previously known values of $d_{LCD}(n, k)$ of lengths $38 \le n \le 40$ and dimensions $9 \le k \le 15$. We also obtain some values of $d_{LCD}(n, k)$ with $41 \le n \le 50$ and $6 \le k \le n-6$.

cs.IT↗

arXiv2024

Desingularization of vortices for the incompressible Euler equation on a sphere

In this paper, we construct a family of global solutions to the incompressible Euler equation on a standard 2-sphere. These solutions are odd-symmetric with respect to the equatorial plane and rotate with a constant angular speed around the polar axis. More importantly, these solutions ``converges" to a pair of point vortices with equal strength and opposite signs. The construction is achieved by maximizing the energy-impulse functional relative to a family of suitable rearrangement classes and analyzing the asymptotic behavior of the maximizers. Based on their variational characterization, we also prove the stability of these rotating solutions with respect to odd-symmetric perturbations.

math.AP↗

arXiv2024

New constructions of DNA codes under multiple constraints and parallel searching algorithms

DNA codes have garnered significant interest due to their utilization in digital media storage, cryptography, and DNA computing. In this paper, we first extend the results of constructing reversible group codes \cite{Cengellenmis} and reversible composite group codes \cite{Korban5} to general even-order finite groups. By using these results, we give parallel searching algorithms to find some new DNA codes with better parameters. Secondly, by mapping codes over $\mathbb{F}_4$ to DNA codes, we establish a relationship between the $GC$-weight enumerator of DNA codes and the Hamming weight enumerator of their trace codes, which greatly improves the computational efficiency of searching for DNA codes. Based on this relationship, we propose an efficient algorithm for generating DNA codes with $50\%$ $GC$-content. Furthermore, we find that there is no direct connection between the $GC$-weight enumerator of a DNA code and the $GC$-weight enumerator of its dual code. Finally, we present algorithms for determining whether a DNA code is free from secondary structures or conflict-free, and some new DNA codes with better parameters under multiple constraints are obtained, which are listed in Tables 1 and 4.

cs.IT↗

arXiv2023

Observation of Flat Band and Van Hove Singularity in Non-superconducting Nitrogen-doped Lutetium Hydride

Hydrogen-rich materials offer a compelling avenue towards room temperature superconductivity, albeit under ultra-high pressure. However, the experimental investigation of the electronic band structure remains elusive, due to the inherent instability of most of the hydrogen-rich materials upon pressure release. Very recently, nitrogen-doped lutetium hydride was claimed to host room temperature superconductivity under near ambient pressure but was disproven by following works. Upon decompression, nitrogen doped lutetium hydride manifests a stable metallic phase with dark blue color. Moreover, high temperature superconductivity has been reported in lutetium hydrides Lu4H23 (~71 K) under around 200 GPa. These properties engender an unprecedented opportunity, allowing for the experimental investigation of the electronic band structure intrinsic to hydrogen-rich material. In this work, using angle resolved photoemission spectroscopy to investigate the non-superconducting nitrogen doped lutetium hydride, we observed significant flat band and Van Hove singularity marginally below the Fermi level. These salient features, identified as critical elements, proffer potential amplifiers for the realization of heightened superconductivity, as evidenced by prior research. Our results not only unveil a confluence of potent strong correlation effects and anisotropy within the Lu-H-N compound, but also provide a prospect for engineering high temperature superconductivity through the strategic manipulation of flat band and the VHS, effectively tailoring their alignment with the Fermi energy.

cond-mat.supr-con↗

arXiv2023

Unilaterally Aggregated Contrastive Learning with Hierarchical Augmentation for Anomaly Detection

Anomaly detection (AD), aiming to find samples that deviate from the training distribution, is essential in safety-critical applications. Though recent self-supervised learning based attempts achieve promising results by creating virtual outliers, their training objectives are less faithful to AD which requires a concentrated inlier distribution as well as a dispersive outlier distribution. In this paper, we propose Unilaterally Aggregated Contrastive Learning with Hierarchical Augmentation (UniCon-HA), taking into account both the requirements above. Specifically, we explicitly encourage the concentration of inliers and the dispersion of virtual outliers via supervised and unsupervised contrastive losses, respectively. Considering that standard contrastive data augmentation for generating positive views may induce outliers, we additionally introduce a soft mechanism to re-weight each augmented inlier according to its deviation from the inlier distribution, to ensure a purified concentration. Moreover, to prompt a higher concentration, inspired by curriculum learning, we adopt an easy-to-hard hierarchical augmentation strategy and perform contrastive aggregation at different depths of the network based on the strengths of data augmentation. Our method is evaluated under three AD settings including unlabeled one-class, unlabeled multi-class, and labeled multi-class, demonstrating its consistent superiority over other competitors.

cs.CV↗

arXiv2023

Stability of degree-2 Rossby-Haurwitz waves

Rossby-Haurwitz (RH) waves are important explicit solutions of the incompressible Euler equation on a two-dimensional rotating sphere. In this paper, we prove the orbital stability of degree-2 RH waves, which confirms a conjecture proposed by A. Constantin and P. Germain in [Arch. Ration. Mech. Anal. 245, 587-644, 2022]. The proofs are based on a variational approach, with the main challenge being to establish suitable variational characterizations for the solutions under consideration. In this process, the set of rearrangements of a fixed function plays a vital role. We also apply our approach to the stability analysis of degree-1 RH waves, Arnold-type flows, and zonal flows with monotone absolute vorticity.

math.AP↗

arXiv2023

Stability of two-dimensional steady Euler flows with concentrated vorticity

In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint that the vorticity is compactly supported in a finite number of disjoint regions of small diameter. We prove the nonlinear stability of these flows when the vorticity is concentrated in one small region, or in two small regions with opposite signs. The proof is achieved by showing that these flows constitute a compact and isolated set of local maximizers of the kinetic energy on an isovortical surface. The separation property of the stream function plays a crucial role in validating the isolatedness.

math.AP↗

arXiv2023

Stability of 2D steady Euler flows related to least energy solutions of the Lane-Emden equation

In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the orbital stability of these flows in terms of both the $L^s$ norm of the vorticity for any $s\in(1,+\infty)$ and the energy norm. As a consequence, nonlinear stability is obtained when the least energy solution is unique, which actually holds for a large class of domains and exponents. The proofs are based on a new variational characterization of least energy solutions in terms of the vorticity, a compactness argument, and proper use of conserved quantities of the Euler equation.

math.AP↗

arXiv2023

Stable plane Euler flows with concentrated and sign-changing vorticity

We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of point vortices with opposite signs. Compared with previous results, we do not need to assume the existence of an isolated local minimum point of the Kirchhoff-Routh function. Moreover, due to their variational nature, the solutions obtained are Lyapunov stable in $L^p$ norm of the vorticity. The proofs are achieved by maximizing the kinetic energy over an appropriate family of rearrangement classes of sign-changing functions and studying the limiting behavior of the maximizers.

math.AP↗

arXiv2022

Nonlinear stability of sinusoidal Euler flows on a flat two-torus

Sinusoidal flows are an important class of explicit stationary solutions of the two-dimensional incompressible Euler equations on a flat torus. For such flows, the steam functions are eigenfunctions of the negative Laplacian. In this paper, we prove that any sinusoidal flow related to some least eigenfunction is, up to phase translations, nonlinearly stable under $L^p$ norm of the vorticity for any $1<p<+\infty$, which improves a classical stability result by Arnold based on the energy-Casimir method. The key point of the proof is to distinguish least eigenstates with fixed amplitude from others by using isovortical property of the Euler equations.

math.AP↗

arXiv2022

An extension of Arnold's second stability theorem in a multiply-connected domain

We give a sufficient condition for the nonlinear stability of steady flows of a two-dimensional ideal fluid in a bounded multiply-connected domain, which generalizes a stability criterion proved by Arnold in the 1960s. The most important ingredient of the proof is to establish a variational characterization for the steady flow under consideration, which is achieved based on the energy-Casimir method proposed by Arnold, and the supporting functional method introduced by Wolansky and Ghil. Nonlinear stability then follows from a compactness argument related to the variational characterization and proper use of conserved quantities of the two-dimensional Euler equations.

math.AP↗

arXiv2022

Video Anomaly Detection by Solving Decoupled Spatio-Temporal Jigsaw Puzzles

Video Anomaly Detection (VAD) is an important topic in computer vision. Motivated by the recent advances in self-supervised learning, this paper addresses VAD by solving an intuitive yet challenging pretext task, i.e., spatio-temporal jigsaw puzzles, which is cast as a multi-label fine-grained classification problem. Our method exhibits several advantages over existing works: 1) the spatio-temporal jigsaw puzzles are decoupled in terms of spatial and temporal dimensions, responsible for capturing highly discriminative appearance and motion features, respectively; 2) full permutations are used to provide abundant jigsaw puzzles covering various difficulty levels, allowing the network to distinguish subtle spatio-temporal differences between normal and abnormal events; and 3) the pretext task is tackled in an end-to-end manner without relying on any pre-trained models. Our method outperforms state-of-the-art counterparts on three public benchmarks. Especially on ShanghaiTech Campus, the result is superior to reconstruction and prediction-based methods by a large margin.

cs.CV↗

arXiv2022

Asymptotic estimates for concentrated vortex pairs

In [Comm. Math. Phys. 324 (2013), 445--463], Burton-Lopes Filho-Nussenzveig Lopes studied the existence and stability of slowly traveling vortex pairs as maximizers of the kinetic energy penalized by the impulse relative to a prescribed rearrangement class. In this paper, we prove that after a suitable scaling transformation the maximization problem studied by Burton-Lopes Filho-Nussenzveig Lopes in fact gives rise to a family of concentrated vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. The key ingredient of the proof is to deduce a uniform bound for the size of the supports of the scaled maximizers.

math.AP↗

arXiv2022

On concentrated traveling vortex pairs with prescribed impulse

In this paper, we consider a constrained maximization problem related to planar vortex pairs with prescribed impulse. We prove existence, stability and asymptotic behavior for the maximizers, hence obtain a family of stable traveling vortex pairs approaching a pair of point vortices with equal magnitude and opposite signs. As a corollary, we get fine asymptotic estimates for Burton's vortex pairs with large impulse. For the non-concentrated case, we prove a form of stability for the Chaplygin-Lamb dipole.

math.AP↗

arXiv2022

Indirect-Instant Attention Optimization for Crowd Counting in Dense Scenes

One of appealing approaches to guiding learnable parameter optimization, such as feature maps, is global attention, which enlightens network intelligence at a fraction of the cost. However, its loss calculation process still falls short: 1)We can only produce one-dimensional 'pseudo labels' for attention, since the artificial threshold involved in the procedure is not robust; 2) The attention awaiting loss calculation is necessarily high-dimensional, and decreasing it by convolution will inevitably introduce additional learnable parameters, thus confusing the source of the loss. To this end, we devise a simple but efficient Indirect-Instant Attention Optimization (IIAO) module based on SoftMax-Attention , which transforms high-dimensional attention map into a one-dimensional feature map in the mathematical sense for loss calculation midway through the network, while automatically providing adaptive multi-scale fusion to feature pyramid module. The special transformation yields relatively coarse features and, originally, the predictive fallibility of regions varies by crowd density distribution, so we tailor the Regional Correlation Loss (RCLoss) to retrieve continuous error-prone regions and smooth spatial information . Extensive experiments have proven that our approach surpasses previous SOTA methods in many benchmark datasets.

cs.CV↗

arXiv2021

Learning Oriented Remote Sensing Object Detection via Naive Geometric Computing

Detecting oriented objects along with estimating their rotation information is one crucial step for analyzing remote sensing images. Despite that many methods proposed recently have achieved remarkable performance, most of them directly learn to predict object directions under the supervision of only one (e.g. the rotation angle) or a few (e.g. several coordinates) groundtruth values individually. Oriented object detection would be more accurate and robust if extra constraints, with respect to proposal and rotation information regression, are adopted for joint supervision during training. To this end, we innovatively propose a mechanism that simultaneously learns the regression of horizontal proposals, oriented proposals, and rotation angles of objects in a consistent manner, via naive geometric computing, as one additional steady constraint (see Figure 1). An oriented center prior guided label assignment strategy is proposed for further enhancing the quality of proposals, yielding better performance. Extensive experiments demonstrate the model equipped with our idea significantly outperforms the baseline by a large margin to achieve a new state-of-the-art result without any extra computational burden during inference. Our proposed idea is simple and intuitive that can be readily implemented. Source codes and trained models are involved in supplementary files.

cs.CV↗