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With the continuous popularity of deep learning and representation learning, fast vector search becomes a vital task in various ranking/retrieval based applications, say recommendation, ads ranking and question answering. Neural network based ranking is widely adopted due to its powerful capacity in modeling complex relationships, such as between users and items, questions and answers. However, it is usually exploited in offline or re-ranking manners for it is time-consuming in computations. Online neural network ranking--so called fast neural ranking--is considered challenging because neural network measures are usually non-convex and asymmetric. Traditional Approximate Nearest Neighbor (ANN) search which usually focuses on metric ranking measures, is not applicable to these advanced measures. In this paper, we introduce a novel graph searching framework to accelerate the searching in the fast neural ranking problem. The proposed graph searching algorithm is bi-level: we first construct a probable candidate set; then we only evaluate the neural network measure over the probable candidate set instead of evaluating the neural network over all neighbors. Specifically, we propose a gradient-based algorithm that approximates the rank of the neural network matching score to construct the probable candidate set; and we present an angle-based heuristic procedure to adaptively identify the proper size of the probable candidate set. Empirical results on public data confirm the effectiveness of our proposed algorithms.

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.

In response to the rapidly evolving nature of adversarial attacks against visual classifiers on a monthly basis, numerous defenses have been proposed to generalize against as many known attacks as possible. However, designing a defense method that generalizes to all types of attacks is not realistic because the environment in which defense systems operate is dynamic and comprises various unique attacks that emerge as time goes on. A well-matched approach to the dynamic environment lies in a defense system that continuously collects adversarial data online to quickly improve itself. Therefore, we put forward a practical defense deployment against a challenging threat model and propose, for the first time, the Continual Adversarial Defense (CAD) framework that adapts to attack sequences under four principles: (1) continual adaptation to new attacks without catastrophic forgetting, (2) few-shot adaptation, (3) memory-efficient adaptation, and (4) high accuracy on both clean and adversarial data. We explore and integrate cutting-edge continual learning, few-shot learning, and ensemble learning techniques to qualify the principles. Extensive experiments validate the effectiveness of our approach against multiple stages of modern adversarial attacks and demonstrate significant improvements over numerous baseline methods. In particular, CAD is capable of quickly adapting with minimal budget and a low cost of defense failure while maintaining good performance against previous attacks. Our research sheds light on a brand-new paradigm for continual defense adaptation against dynamic and evolving attacks.

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. K\"{a}hler 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 K\"{a}hler 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., Comment: 21 pages. arXiv admin note: text overlap with arXiv:1804.00517

Nonline of sight (NLOS) ultraviolet (UV) scattering communication can serve as a good candidate for outdoor optical wireless communication (OWC) in the cases of non-perfect transmitter-receiver alignment and radio silence. We design and demonstrate a NLOS UV scattering communication network system in this paper, where a beacon-enabled time division multiple access (TDMA) scheme is adopted. In our system, LED and PMT are employed for transmitter and receiver devices, repectivey. Furthermore, we design algorithms for beacon transmission, beacon reception, time compensation, and time slot transition for hardware realization in field-programmable gate array (FPGA) board based on master-slave structure, where master node periodically transmits beacon signals to slave nodes. Experimental results are provided to evaluate the time synchronization error and specify the system key parameters for real-time implementation. We perform field tests for real-time communication network with the transmission range over 110 multiplied by 90 square meters, where the system throughput reaches 800kbps.

Federated Learning (FL) faces two major issues: privacy leakage and poisoning attacks, which may seriously undermine the reliability and security of the system. Overcoming them simultaneously poses a great challenge. This is because privacy protection policies prohibit access to users' local gradients to avoid privacy leakage, while Byzantine-robust methods necessitate access to these gradients to defend against poisoning attacks. To address these problems, we propose a novel privacy-preserving Byzantine-robust FL framework PROFL. PROFL is based on the two-trapdoor additional homomorphic encryption algorithm and blinding techniques to ensure the data privacy of the entire FL process. During the defense process, PROFL first utilize secure Multi-Krum algorithm to remove malicious gradients at the user level. Then, according to the Pauta criterion, we innovatively propose a statistic-based privacy-preserving defense algorithm to eliminate outlier interference at the feature level and resist impersonation poisoning attacks with stronger concealment. Detailed theoretical analysis proves the security and efficiency of the proposed method. We conducted extensive experiments on two benchmark datasets, and PROFL improved accuracy by 39% to 75% across different attack settings compared to similar privacy-preserving robust methods, demonstrating its significant advantage in robustness.

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.

Open-system density matrix methods typically employ incoherent population injection to investigate the postionization dynamics in strong laser fields. The presence of coherence injection has long been a subject of debate. In this context, we introduce a coherence injection model based on the adiabatic strong-field approximation (ASFA). This model effectively predicts ionic coherence resulting from directional tunnel ionization. With increasing field strength, the degree of coherence predicted by the ASFA model gradually deviates from that of the SFA model but remains much milder compared to the results of the simple and partial-wave expansion models. The impact of coherence injection on the postionization molecular dynamics is explored in O$_2$ and N$_2$. We find that the ionization-induced vibrational coherence strongly enhances the population inversion of $X^2 \Sigma _g^+ -B^2 \Sigma _u^+ $ in N$_2^+$ and the dissociation probability of O$_2^+$. Conversely, the ionization-induced vibronic coherences have inhibitory effects on the related transitions. These findings reveal the significance of including the vibronic-state-resolved coherence injection in simulating molecular dynamics following strong-field ionization., Comment: 12 pages, 7 figures

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-J\"{u}ttner 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., Comment: 28 pages, 11 figures, accepted for publication in Physical Review D

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. We introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, and scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: 1) the synthesis of LES simulated instantaneous flow sequences from URANS inputs; 2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; 3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation., Comment: 37 pages, 31 figures

With the rapid development of Artificial Intelligent Internet of Things (AIoT), the image data from AIoT devices has been witnessing the explosive increasing. In this paper, a novel deep image semantic communication model is proposed for the efficient image communication in AIoT. Particularly, at the transmitter side, a high-precision image semantic segmentation algorithm is proposed to extract the semantic information of the image to achieve significant compression of the image data. At the receiver side, a semantic image restoration algorithm based on Generative Adversarial Network (GAN) is proposed to convert the semantic image to a real scene image with detailed information. Simulation results demonstrate that the proposed image semantic communication model can improve the image compression ratio and recovery accuracy by 71.93% and 25.07% on average in comparison with WebP and CycleGAN, respectively. More importantly, our demo experiment shows that the proposed model reduces the total delay by 95.26% in the image communication, when comparing with the original image transmission.

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.

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.

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., Comment: 8 pages, 7 figures, Accepted Physical Review B (2023). arXiv admin note: text overlap with arXiv:2305.13670

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.

Let $G$ be a graph and $S\subseteq V(G)$ with $|S|\geq 2$. Then the trees $T_1, T_2, \cdots, T_\ell$ in $G$ are \emph{internally disjoint Steiner trees} connecting $S$ (or $S$-Steiner trees) if $E(T_i) \cap E(T_j )=\emptyset$ and $V(T_i)\cap V(T_j)=S$ for every pair of distinct integers $i,j$, $1 \leq i, j \leq \ell$. Similarly, if we only have the condition $E(T_i) \cap E(T_j )=\emptyset$ but without the condition $V(T_i)\cap V(T_j)=S$, then they are \emph{edge-disjoint Steiner trees}. The \emph{generalized $k$-connectivity}, denoted by $\kappa_k(G)$, of a graph $G$, is defined as $\kappa_k(G)=\min\{\kappa_G(S)|S \subseteq V(G) \ \textrm{and} \ |S|=k \}$, where $\kappa_G(S)$ is the maximum number of internally disjoint $S$-Steiner trees. The \emph{generalized local edge-connectivity} $\lambda_{G}(S)$ is the maximum number of edge-disjoint Steiner trees connecting $S$ in $G$. The {\it generalized $k$-edge-connectivity} $\lambda_k(G)$ of $G$ is defined as $\lambda_k(G)=\min\{\lambda_{G}(S)\,|\,S\subseteq V(G) \ and \ |S|=k\}$. These measures are generalizations of the concepts of connectivity and edge-connectivity, and they and can be used as measures of vulnerability of networks. It is, in general, difficult to compute these generalized connectivities. However, there are precise results for some special classes of graphs. In this paper, we obtain the exact value of $\lambda_{k}(S(n,\ell))$ for $3\leq k\leq \ell^n$, and the exact value of $\kappa_{k}(S(n,\ell))$ for $3\leq k\leq \ell$, where $S(n, \ell)$ is the Sierpi\'{n}ski graphs with order $\ell^n$. As a direct consequence, these graphs provide additional interesting examples when $\lambda_{k}(S(n,\ell))=\kappa_{k}(S(n,\ell))$. We also study the some network properties of Sierpi\'{n}ski graphs., Comment: Steiner Tree; Generalized Connectivity; Sierpi\'{n}ski Graph

Recently developed deep neural models like NetGAN, CELL, and Variational Graph Autoencoders have made progress but face limitations in replicating key graph statistics on generating large graphs. Diffusion-based methods have emerged as promising alternatives, however, most of them present challenges in computational efficiency and generative performance. EDGE is effective at modeling large networks, but its current denoising approach can be inefficient, often leading to wasted computational resources and potential mismatches in its generation process. In this paper, we propose enhancements to the EDGE model to address these issues. Specifically, we introduce a degree-specific noise schedule that optimizes the number of active nodes at each timestep, significantly reducing memory consumption. Additionally, we present an improved sampling scheme that fine-tunes the generative process, allowing for better control over the similarity between the synthesized and the true network. Our experimental results demonstrate that the proposed modifications not only improve the efficiency but also enhance the accuracy of the generated graphs, offering a robust and scalable solution for graph generation tasks.

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., Comment: arXiv admin note: text overlap with arXiv:1207.5938 by other authors