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Jian Xiao

Publications and source records attributed to Jian Xiao.

At least 37 records · Page 2Linked to original sources

CAdam: Confidence-Based Optimization for Online Learning

Modern recommendation systems frequently employ online learning to dynamically update their models with freshly collected data. The most commonly used optimizer for updating neural networks in these contexts is the Adam optimizer, which integrates momentum ($m_t$) and adaptive learning rate ($v_t$). However, the volatile nature of online learning data, characterized by its frequent distribution shifts and presence of noise, poses significant challenges to Adam's standard optimization process: (1) Adam may use outdated momentum and the average of squared gradients, resulting in slower adaptation to distribution changes, and (2) Adam's performance is adversely affected by data noise. To mitigate these issues, we introduce CAdam, a confidence-based optimization strategy that assesses the consistency between the momentum and the gradient for each parameter dimension before deciding on updates. If momentum and gradient are in sync, CAdam proceeds with parameter updates according to Adam's original formulation; if not, it temporarily withholds updates and monitors potential shifts in data distribution in subsequent iterations. This method allows CAdam to distinguish between the true distributional shifts and mere noise, and to adapt more quickly to new data distributions. In various settings with distribution shift or noise, our experiments demonstrate that CAdam surpasses other well-known optimizers, including the original Adam. Furthermore, in large-scale A/B testing within a live recommendation system, CAdam significantly enhances model performance compared to Adam, leading to substantial increases in the system's gross merchandise volume (GMV).

cs.LG↗

Numerical characterization of the hard Lefschetz classes of dimension two, II: supercritical collections of free divisor classes

For $(n-2)$ free divisor classes on a smooth projective variety of dimension $n$, the product of these free divisor classes induces a Lefschetz type operator acting on the Néron-Severi space or the cohomology group of $(1,1)$ classes. We give a characterization of this kernel space, when the collection of these free divisor classes is supercritical. This resolves Shenfeld-van Handel's open problem in this setting. As consequences, we provide an algebro-geometric proof of the characterization of the extremals of the Alexandrov-Fenchel inequality for a supercritical collection of rational convex polytopes; we also give a characterization of the extremals of the Khovanskii-Teissier inequality given by the intersection numbers of two arbitrary free divisor classes.

math.AG↗

Channel Estimation for Pinching-Antenna Systems (PASS)

Pinching Antennas (PAs) represent a revolutionary flexible antenna technology that leverages dielectric waveguides and electromagnetic coupling to mitigate large-scale path loss. This letter is the first to explore channel estimation for Pinching-Antenna SyStems (PASS), addressing their uniquely ill-conditioned and underdetermined channel characteristics. In particular, two efficient deep learning-based channel estimators are proposed. 1) PAMoE: This estimator incorporates dynamic padding, feature embedding, fusion, and mixture of experts (MoE) modules, which effectively leverage the positional information of PAs and exploit expert diversity. 2) PAformer: This Transformer-style estimator employs the self-attention mechanism to predict channel coefficients in a per-antenna manner, which offers more flexibility to adaptively deal with dynamic numbers of PAs in practical deployment. Numerical results demonstrate that 1) the proposed deep learning-based channel estimators outperform conventional methods and exhibit excellent zero-shot learning capabilities, and 2) PAMoE delivers higher channel estimation accuracy via MoE specialization, while PAformer natively handles an arbitrary number of PAs, trading self-attention complexity for superior scalability.

cs.IT↗

Positivity in the shadow of Hodge index theorem

Taking a compact Kähler manifold as playground, we explore the powerfulness of Hodge index theorem. A main object is the Lorentzian classes on a compact Kähler manifold, behind which the characterization via Lorentzian polynomials over the Kähler cone and hence the validity of Hodge index theorem. Along the exploration, we discover several applications in complex geometry that may be unexpected before. (1) For a Lefschetz type operator given by the complete intersection of nef classes, we give a complete characterization of its kernel face against the pseudo-effective cone. (2) We provide a new approach to Teissier's proportionality problem from the validity of hard Lefschetz property. This perspective enables us to establish the extremals for the Brunn-Minkowski inequality on a strictly Lorentzian class, and thus also characterize the most extremal case for a log-concavity sequence given by the intersection numbers of two nef classes. These Lorentzian classes include the fundamental classes of smooth projective varieties or compact Kähler manifolds as typical examples, hence our result extends Boucksom-Favre-Jonsson's and Fu-Xiao's results in respective settings to broader contexts, e.g. certain algebraic cycle classes given by reducible subvarieties. (3) Furthermore, we also strengthen the proportionality characterization by comparing various quantitative deficits and establishing stability estimates. Two quantitative sharper stability estimates with close relation with complex Monge--Ampère equations and Newton-Okounkov bodies are also discussed.

math.AG↗

Aerial Reliable Collaborative Communications for Terrestrial Mobile Users via Evolutionary Multi-Objective Deep Reinforcement Learning

Unmanned aerial vehicles (UAVs) have emerged as the potential aerial base stations (BSs) to improve terrestrial communications. However, the limited onboard energy and antenna power of a UAV restrict its communication range and transmission capability. To address these limitations, this work employs collaborative beamforming through a UAV-enabled virtual antenna array to improve transmission performance from the UAV to terrestrial mobile users, under interference from non-associated BSs and dynamic channel conditions. Specifically, we introduce a memory-based random walk model to more accurately depict the mobility patterns of terrestrial mobile users. Following this, we formulate a multi-objective optimization problem (MOP) focused on maximizing the transmission rate while minimizing the flight energy consumption of the UAV swarm. Given the NP-hard nature of the formulated MOP and the highly dynamic environment, we transform this problem into a multi-objective Markov decision process and propose an improved evolutionary multi-objective reinforcement learning algorithm. Specifically, this algorithm introduces an evolutionary learning approach to obtain the approximate Pareto set for the formulated MOP. Moreover, the algorithm incorporates a long short-term memory network and hyper-sphere-based task selection method to discern the movement patterns of terrestrial mobile users and improve the diversity of the obtained Pareto set. Simulation results demonstrate that the proposed method effectively generates a diverse range of non-dominated policies and outperforms existing methods. Additional simulations demonstrate the scalability and robustness of the proposed CB-based method under different system parameters and various unexpected circumstances.

cs.NE↗

Task Scheduling in Geo-Distributed Computing: A Survey

Geo-distributed computing, a paradigm that assigns computational tasks to globally distributed nodes, has emerged as a promising approach in cloud computing, edge computing, cloud-edge computing and supercomputer computing (HPC). It enables low-latency services, ensures data locality, and handles large-scale applications. As global computing capacity and task demands increase rapidly, scheduling tasks for efficient execution in geo-distributed computing systems has become an increasingly critical research challenge. It arises from the inherent characteristics of geographic distribution, including heterogeneous network conditions, region-specific resource pricing, and varying computational capabilities across locations. Researchers have developed diverse task scheduling methods tailored to geo-distributed scenarios, aiming to achieve objectives such as performance enhancement, fairness assurance, and fault-tolerance improvement. This survey provides a comprehensive and systematic review of task scheduling techniques across four major distributed computing environments, with an in-depth analysis of these approaches based on their core scheduling objectives. Through our analysis, we identify key research challenges and outline promising directions for advancing task scheduling in geo-distributed computing.

cs.DC↗

Wideband Beamforming for RIS Assisted Near-Field Communications

A near-field wideband beamforming scheme is investigated for reconfigurable intelligent surface (RIS) assisted multiple-input multiple-output (MIMO) systems, in which a deep learning-based end-to-end (E2E) optimization framework is proposed to maximize the system spectral efficiency. To deal with the near-field double beam split effect, the base station is equipped with frequency-dependent hybrid precoding architecture by introducing sub-connected true time delay (TTD) units, while two specific RIS architectures, namely true time delay-based RIS (TTD-RIS) and virtual subarray-based RIS (SA-RIS), are exploited to realize the frequency-dependent passive beamforming at the RIS. Furthermore, the efficient E2E beamforming models without explicit channel state information are proposed, which jointly exploits the uplink channel training module and the downlink wideband beamforming module. In the proposed network architecture of the E2E models, the classical communication signal processing methods, i.e., polarized filtering and sparsity transform, are leveraged to develop a signal-guided beamforming network. Numerical results show that the proposed E2E models have superior beamforming performance and robustness to conventional beamforming benchmarks. Furthermore, the tradeoff between the beamforming gain and the hardware complexity is investigated for different frequency-dependent RIS architectures, in which the TTD-RIS can achieve better spectral efficiency than the SA-RIS while requiring additional energy consumption and hardware cost.

cs.IT↗

Text Proxy: Decomposing Retrieval from a 1-to-N Relationship into N 1-to-1 Relationships for Text-Video Retrieval

Text-video retrieval (TVR) has seen substantial advancements in recent years, fueled by the utilization of pre-trained models and large language models (LLMs). Despite these advancements, achieving accurate matching in TVR remains challenging due to inherent disparities between video and textual modalities and irregularities in data representation. In this paper, we propose Text-Video-ProxyNet (TV-ProxyNet), a novel framework designed to decompose the conventional 1-to-N relationship of TVR into N distinct 1-to-1 relationships. By replacing a single text query with a series of text proxies, TV-ProxyNet not only broadens the query scope but also achieves a more precise expansion. Each text proxy is crafted through a refined iterative process, controlled by mechanisms we term as the director and dash, which regulate the proxy's direction and distance relative to the original text query. This setup not only facilitates more precise semantic alignment but also effectively manages the disparities and noise inherent in multimodal data. Our experiments on three representative video-text retrieval benchmarks, MSRVTT, DiDeMo, and ActivityNet Captions, demonstrate the effectiveness of TV-ProxyNet. The results show an improvement of 2.0% to 3.3% in R@1 over the baseline. TV-ProxyNet achieved state-of-the-art performance on MSRVTT and ActivityNet Captions, and a 2.0% improvement on DiDeMo compared to existing methods, validating our approach's ability to enhance semantic mapping and reduce error propensity.

cs.CV↗

The inequalities of Chern classes and Riemann-Roch type inequalities

Motivated by Kollár-Matsusaka's Riemann-Roch type inequalities, applying effective very ampleness of adjoint bundles on Fujita conjecture and log-concavity given by Khovanskii-Teissier inequalities, we show that for any partition $λ$ of the positive integer $d$ there exists a universal bivariate polynomial $Q_λ(x, y)$ which has deg $Q \leq d$ and whose coefficients depend only on $n$, such that for any projective manifold $X$ of dimension $n$ and any ample line bundle $L$ on $X$, \begin{equation*} \left|c_λ(X)\cdot L^{n -d}\right|\leq \frac{Q_λ(L^{n}, K_X \cdot L^{n -1} )}{(L^{n})^{d-1}}, \end{equation*} where $K_X$ is the canonical bundle of $X$ and $c_λ(X)$ is the monomial Chern class given by the partition $λ$. As a special case, when $K_X$ or $-K_X$ is ample, this implies that there exists a constant $c_n$ depending only on $n$ such that for any monomial Chern classes of top degree, the Chern number ratios \begin{equation*} \left|\frac{c_λ(X)}{c_1 (X) ^{n}}\right|\leq c_n, \end{equation*} which recovers a recent result of Du-Sun. The main result also yields an asymptotic version of the sharper Riemann-Roch type inequality. Furthermore, using similar method we also obtain inequalities for Chern classes of the logarithmic tangent bundle.

math.AG↗

DA-Flow: Dual Attention Normalizing Flow for Skeleton-based Video Anomaly Detection

Cooperation between temporal convolutional networks (TCN) and graph convolutional networks (GCN) as a processing module has shown promising results in skeleton-based video anomaly detection (SVAD). However, to maintain a lightweight model with low computational and storage complexity, shallow GCN and TCN blocks are constrained by small receptive fields and a lack of cross-dimension interaction capture. To tackle this limitation, we propose a lightweight module called the Dual Attention Module (DAM) for capturing cross-dimension interaction relationships in spatio-temporal skeletal data. It employs the frame attention mechanism to identify the most significant frames and the skeleton attention mechanism to capture broader relationships across fixed partitions with minimal parameters and flops. Furthermore, the proposed Dual Attention Normalizing Flow (DA-Flow) integrates the DAM as a post-processing unit after GCN within the normalizing flow framework. Simulations show that the proposed model is robust against noise and negative samples. Experimental results show that DA-Flow reaches competitive or better performance than the existing state-of-the-art (SOTA) methods in terms of the micro AUC metric with the fewest number of parameters. Moreover, we found that even without training, simply using random projection without dimensionality reduction on skeleton data enables substantial anomaly detection capabilities.

cs.CV↗

Intersection theoretic inequalities via Lorentzian polynomials

We explore the applications of Lorentzian polynomials to the fields of algebraic geometry, analytic geometry and convex geometry. In particular, we establish a series of intersection theoretic inequalities, which we call rKT property, with respect to $m$-positive classes and Schur classes. We also study its convexity variants -- the geometric inequalities for $m$-convex functions on the sphere and convex bodies. Along the exploration, we prove that any finite subset on the closure of the cone generated by $m$-positive classes can be endowed with a polymatroid structure by a canonical numerical-dimension type function, extending our previous result for nef classes; and we prove Alexandrov-Fenchel inequalities for valuations of Schur type. We also establish various analogs of sumset estimates (Plünnecke-Ruzsa inequalities) from additive combinatorics in our contexts.

math.AG↗

Divide and Conquer in Video Anomaly Detection: A Comprehensive Review and New Approach

Video anomaly detection is a complex task, and the principle of "divide and conquer" is often regarded as an effective approach to tackling intricate issues. It's noteworthy that recent methods in video anomaly detection have revealed the application of the divide and conquer philosophy (albeit with distinct perspectives from traditional usage), yielding impressive outcomes. This paper systematically reviews these literatures from six dimensions, aiming to enhance the use of the divide and conquer strategy in video anomaly detection. Furthermore, based on the insights gained from this review, a novel approach is presented, which integrates human skeletal frameworks with video data analysis techniques. This method achieves state-of-the-art performance on the ShanghaiTech dataset, surpassing all existing advanced methods.

cs.CV↗

Human Kinematics-inspired Skeleton-based Video Anomaly Detection

Previous approaches to detecting human anomalies in videos have typically relied on implicit modeling by directly applying the model to video or skeleton data, potentially resulting in inaccurate modeling of motion information. In this paper, we conduct an exploratory study and introduce a new idea called HKVAD (Human Kinematic-inspired Video Anomaly Detection) for video anomaly detection, which involves the explicit use of human kinematic features to detect anomalies. To validate the effectiveness and potential of this perspective, we propose a pilot method that leverages the kinematic features of the skeleton pose, with a specific focus on the walking stride, skeleton displacement at feet level, and neck level. Following this, the method employs a normalizing flow model to estimate density and detect anomalies based on the estimated density. Based on the number of kinematic features used, we have devised three straightforward variant methods and conducted experiments on two highly challenging public datasets, ShanghaiTech and UBnormal. Our method achieves good results with minimal computational resources, validating its effectiveness and potential.

cs.CV↗

Hard Lefschetz theorems for free line bundles

We introduce a partial positivity notion for algebraic maps via the defect of semismallness. This positivity notion is modeled on $m$-positivity in the analytic setting and $m$-ampleness in the geometric setting. Using this positivity condition for algebraic maps, we establish Kähler packages, that is, Hard Lefschetz theorems and Hodge-Riemann bilinear relations, for the complete intersections of Chern classes of free line bundles.

math.AG↗

HLC2: a highly efficient cross-matching framework for large astronomical catalogues on heterogeneous computing environments

Cross-matching operation, which is to find corresponding data for the same celestial object or region from multiple catalogues,is indispensable to astronomical data analysis and research. Due to the large amount of astronomical catalogues generated by the ongoing and next-generation large-scale sky surveys, the time complexity of the cross-matching is increasing dramatically. Heterogeneous computing environments provide a theoretical possibility to accelerate the cross-matching, but the performance advantages of heterogeneous computing resources have not been fully utilized. To meet the challenge of cross-matching for substantial increasing amount of astronomical observation data, this paper proposes Heterogeneous-computing-enabled Large Catalogue Cross-matcher (HLC2), a high-performance cross-matching framework based on spherical position deviation on CPU-GPU heterogeneous computing platforms. It supports scalable and flexible cross-matching and can be directly applied to the fusion of large astronomical cataloguesfrom survey missions and astronomical data centres. A performance estimation model is proposed to locate the performance bottlenecks and guide the optimizations. A two-level partitioning strategy is designed to generate an optimized data placement according to the positions of celestial objects to increase throughput. To make HLC2 a more adaptive solution, the architecture-aware task splitting, thread parallelization, and concurrent scheduling strategies are designed and integrated. Moreover, a novel quad-direction strategy is proposed for the boundary problem to effectively balance performance and completeness. We have experimentally evaluated HLC2 using public released catalogue data. Experiments demonstrate that HLC2 scales well on different sizes of catalogues and the cross-matching speed is significantly improved compared to the state-of-the-art cross-matchers.

astro-ph.IM↗

Hard Lefschetz properties, complete intersections and numerical dimensions

We study the positivity of complete intersections of nef classes. We first give a sufficient and necessary characterization on the complete intersection classes which have hard Lefschetz property on a compact complex torus, equivalently, in the linear case. In turn, this provides us new kinds of cohomology classes which have Hodge-Riemann property or hard Lefschetz property on an arbitrary compact Kähler manifold. We also give a complete characterization on when the complete intersection classes are non-vanishing on an arbitrary compact Kähler manifold. Both characterizations are given by the numerical dimensions of various partial summations of the given nef classes. As an interesting byproduct, we show that the numerical dimension endows any finite set of nef classes with a loopless polymatroid structure.

math.AG↗

HEGrid: A High Efficient Multi-Channel Radio Astronomical Data Gridding Framework in Heterogeneous Computing Environments

The challenge to fully exploit the potential of existing and upcoming scientific instruments like large single-dish radio telescopes is to process the collected massive data effectively and efficiently. As a "quasi 2D stencil computation" with the "Moore neighborhood pattern," gridding is the most computationally intensive step in data reduction pipeline for radio astronomy studies, enabling astronomers to create correct sky images for further analysis. However, the existing gridding frameworks can either only run on multi-core CPU architecture or do not support high-concurrency, multi-channel data gridding. Their performance is then limited, and there are emerging needs for innovative gridding frameworks to process data from large single-dish radio telescopes like the Five-hundred-meter Aperture Spherical Telescope (FAST). To address those challenges, we developed a High Efficient Gridding framework, HEGrid, by overcoming the above limitations. Specifically, we propose and construct the gridding pipeline in heterogeneous computing environments and achieve multi-pipeline concurrency for high performance multi-channel processing. Furthermore, we propose pipeline-based co-optimization to alleviate the potential negative performance impact of possible intra- and inter-pipeline low computation and I/O utilization, including component share-based redundancy elimination, thread-level data reuse and overlapping I/O and computation. Our experiments are based on both simulated datasets and actual FAST observational datasets. The results show that HEGrid outperforms other state-of-the-art gridding frameworks by up to 5.5x and has robust hardware portability, including AMD Radeon Instinct GPU and NVIDIA GPU.

cs.DC↗

HCGrid: A Convolution-based Gridding Framework for RadioAstronomy in Hybrid Computing Environments

Gridding operation, which is to map non-uniform data samples onto a uniformly distributedgrid, is one of the key steps in radio astronomical data reduction process. One of the mainbottlenecks of gridding is the poor computing performance, and a typical solution for suchperformance issue is the implementation of multi-core CPU platforms. Although such amethod could usually achieve good results, in many cases, the performance of gridding is stillrestricted to an extent due to the limitations of CPU, since the main workload of gridding isa combination of a large number of single instruction, multi-data-stream operations, which ismore suitable for GPU, rather than CPU implementations. To meet the challenge of massivedata gridding for the modern large single-dish radio telescopes, e.g., the Five-hundred-meterAperture Spherical radio Telescope (FAST), inspired by existing multi-core CPU griddingalgorithms such as Cygrid, here we present an easy-to-install, high-performance, and open-source convolutional gridding framework, HCGrid,in CPU-GPU heterogeneous platforms. Itoptimises data search by employing multi-threading on CPU, and accelerates the convolutionprocess by utilising massive parallelisation of GPU. In order to make HCGrid a more adaptivesolution, we also propose the strategies of thread organisation and coarsening, as well as optimalparameter settings under various GPU architectures. A thorough analysis of computing timeand performance gain with several GPU parallel optimisation strategies show that it can leadto excellent performance in hybrid computing environments.

astro-ph.IM↗