arXiv subjects
Publications and source records attributed to Xiaolong Li.
We study the Robin eigenvalue problem for the Laplace-Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the second Robin eigenvalue on geodesic balls in manifolds whose sectional curvatures are bounded from above. Our second result asserts that geodesic balls in nonpositively curved space forms maximize the second Robin eigenvalue among bounded domains of the same volume.
Let $(M^n,g)$ be a complete simply connected $n$-dimensional Riemannian manifold with curvature bounds $\operatorname{Sect}_g\leq κ$ for $κ\leq 0$ and $\operatorname{Ric}_g\geq(n-1)Kg$ for $K\leq 0$. We prove that for any bounded domain $Ω\subset M^n$ with diameter $d$ and Lipschitz boundary, if $Ω^*$ is a geodesic ball in the simply connected space form with constant sectional curvature $κ$ enclosing the same volume as $Ω$, then $σ_1(Ω) \leq C σ_1(Ω^*)$, where $σ_1(Ω)$ and $ σ_1(Ω^*)$ denote the first nonzero Steklov eigenvalues of $Ω$ and $Ω^*$ respectively, and $C=C(n,κ, K, d)$ is an explicit constant. When $κ=K$, we have $C=1$ and recover the Brock-Weinstock inequality, asserting that geodesic balls uniquely maximize the first nonzero Steklov eigenvalue among domains of the same volume, in Euclidean space and the hyperbolic space.
In the past decade, there has been substantial progress at training increasingly deep neural networks. Recent advances within the teacher--student training paradigm have established that information about past training updates show promise as a source of guidance during subsequent training steps. Based on this notion, in this paper, we propose Long Short-Term Sample Distillation, a novel training policy that simultaneously leverages multiple phases of the previous training process to guide the later training updates to a neural network, while efficiently proceeding in just one single generation pass. With Long Short-Term Sample Distillation, the supervision signal for each sample is decomposed into two parts: a long-term signal and a short-term one. The long-term teacher draws on snapshots from several epochs ago in order to provide steadfast guidance and to guarantee teacher--student differences, while the short-term one yields more up-to-date cues with the goal of enabling higher-quality updates. Moreover, the teachers for each sample are unique, such that, overall, the model learns from a very diverse set of teachers. Comprehensive experimental results across a range of vision and NLP tasks demonstrate the effectiveness of this new training method.
Time-series forecasting is an important task in both academic and industry, which can be applied to solve many real forecasting problems like stock, water-supply, and sales predictions. In this paper, we study the case of retailers' sales forecasting on Tmall|the world's leading online B2C platform. By analyzing the data, we have two main observations, i.e., sales seasonality after we group different groups of retails and a Tweedie distribution after we transform the sales (target to forecast). Based on our observations, we design two mechanisms for sales forecasting, i.e., seasonality extraction and distribution transformation. First, we adopt Fourier decomposition to automatically extract the seasonalities for different categories of retailers, which can further be used as additional features for any established regression algorithms. Second, we propose to optimize the Tweedie loss of sales after logarithmic transformations. We apply these two mechanisms to classic regression models, i.e., neural network and Gradient Boosting Decision Tree, and the experimental results on Tmall dataset show that both mechanisms can significantly improve the forecasting results.
We present, GEM, the first heterogeneous graph neural network approach for detecting malicious accounts at Alipay, one of the world's leading mobile cashless payment platform. Our approach, inspired from a connected subgraph approach, adaptively learns discriminative embeddings from heterogeneous account-device graphs based on two fundamental weaknesses of attackers, i.e. device aggregation and activity aggregation. For the heterogeneous graph consists of various types of nodes, we propose an attention mechanism to learn the importance of different types of nodes, while using the sum operator for modeling the aggregation patterns of nodes in each type. Experiments show that our approaches consistently perform promising results compared with competitive methods over time.
Fraudulent claim detection is one of the greatest challenges the insurance industry faces. Alibaba's return-freight insurance, providing return-shipping postage compensations over product return on the e-commerce platform, receives thousands of potentially fraudulent claims every day. Such deliberate abuse of the insurance policy could lead to heavy financial losses. In order to detect and prevent fraudulent insurance claims, we developed a novel data-driven procedure to identify groups of organized fraudsters, one of the major contributions to financial losses, by learning network information. In this paper, we introduce a device-sharing network among claimants, followed by developing an automated solution for fraud detection based on graph learning algorithms, to separate fraudsters from regular customers and uncover groups of organized fraudsters. This solution applied at Alibaba achieves more than 80% precision while covering 44% more suspicious accounts compared with a previously deployed rule-based classifier after human expert investigations. Our approach can easily and effectively generalizes to other types of insurance.
Large-scale microfluidic microsystems with complex three-dimensional (3D) configurations are highly in demand by both fundamental research and industrial application, holding the potentials for fostering a wide range of innovative applications such as lab-on-a-chip and organ-on-a-chip as well as continuous-flow manufacturing of fine chemicals. However, freeform fabrication of such systems remains challenging for most of the current fabrication techniques in terms of fabrication resolution, flexibility, and achievable footprint size. Here, we report ultrashort pulse laser microfabrication of freeform microfluidic circuits with high aspect ratios and tunable diameters embedded in 3D printed glass objects. We achieve uniform microfluidic channel diameter by carefully distributing a string of extra access ports along the microfluidic channels for avoiding the over-etching in the thin microfluidic channels. After the chemical etching is completed, the extra access ports are sealed using carbon dioxide laser induced localized glass melting. We demonstrate a model hand of fused silica with a size of ~3 cm * 2.7 cm * 1.1 cm in which the whole blood vessel system is encapsulated.
We prove sharp lower bound estimates for the first nonzero eigenvalue of the weighted $p$-Lapacian operator with $1< p< \infty$ on a compact Bakry-Emery manifold $(M^n,g,f)$ satisfying $\Ric+\nabla^2 f \geq κ\, g$, provided that either $1<p \leq 2$ or $κ\leq 0$. Same conclusions hold when the manifold has nonempty boundary if we assume it is strictly convex and put Neumann boundary conditions on it. For $1<p \leq 2$, we provide a simple proof via the modulus of continuity estimates method. The proof for $κ\leq 0$ is based on a sharp gradient comparison theorem for the eigenfunction and a careful analysis of the underlying one-dimensional model equation. Our results generalize the work of Valtorta\cite{Valtorta12} and Naber-Valtorta\cite{NV14} for the $p$-Laplacian (namely $f=\text{const}$), and the work of Bakry-Qian\cite{BQ00} for the $f$-Laplacian (namely $p=2$).
Creating magnetic semiconductors that work at warm circumstance is still a great challenge in the physical sciences. Here, we report the discovery of ferromagnetism in the metal-free perylene diimide semiconductor, whose Curie temperature is higher than 400 Kelvin. A solvothermal approach is used to reduce and dissolve the rigid-backbone perylene diimide crystallites, and radical anion aggregates were fabricated by the subsequent self-assembly and oxidation process. Magnetic measurements exhibit the ferromagnetic ordering with the saturated magnetization of 0.48 $μ_{\rm B}$ per molecule and the appreciable magnetic anisotropy. X-ray magnetic circular dichroism spectra suggest the ferromagnetism stems from $π$ orbitals of radicals. Our findings unambitiously demonstrate the long-range ferromagnetic ordering can survive at room temperature in organic semiconductors, although which are intuitively regarded to be nonmagnetic.
With the explosive growth of e-commerce and the booming of e-payment, detecting online transaction fraud in real time has become increasingly important to Fintech business. To tackle this problem, we introduce the TitAnt, a transaction fraud detection system deployed in Ant Financial, one of the largest Fintech companies in the world. The system is able to predict online real-time transaction fraud in mere milliseconds. We present the problem definition, feature extraction, detection methods, implementation and deployment of the system, as well as empirical effectiveness. Extensive experiments have been conducted on large real-world transaction data to show the effectiveness and the efficiency of the proposed system.
A moving target may enter a radar coverage area unannounced and leave after an unspecified period, which implies that the target's entry time and departure time are unknown. In the absence of these time information, target detection and parameter estimation (DAPE) will be severely impacted. In this paper, we consider the coherent detection and parameters estimation problem for a radar moving target with unknown entry time and departure time (that is, the time when the target appears-in/leaves the radar detection field is unknown), involving across range cell (ARC) and Doppler spread (DS) effects within the observation period. A new algorithm, known as window Radon Fractional Fourier transform (WRFRFT) is proposed to detect and estimate the target's time parameters (i.e., entry time and departure time) and motion parameters (i.e., range, velocity and acceleration). The observation values of a maneuvering target are first intercepted and extracted by the window function and searching along the motion trajectory. Then these values are fractional Fourier transformed and well accumulated in the WRFRFT domain, where the DAPE of target could be accomplished thereafter. Experiments with simulated and real radar data sets prove its effectiveness.
In this paper we prove classification results for gradient shrinking Ricci solitons under two invariant conditions, namely nonnegative orthogonal bisectional curvature and weakly PIC1, without any curvature bound. New results on ancient solutions for the Ricci and Kähler-Ricci flow are also obtained. The main new feature is that no curvature upper bound is assumed.
We address the problem of data-driven image manipulation detection in the presence of an attacker with limited knowledge about the detector. Specifically, we assume that the attacker knows the architecture of the detector, the training data and the class of features V the detector can rely on. In order to get an advantage in his race of arms with the attacker, the analyst designs the detector by relying on a subset of features chosen at random in V. Given its ignorance about the exact feature set, the adversary attacks a version of the detector based on the entire feature set. In this way, the effectiveness of the attack diminishes since there is no guarantee that attacking a detector working in the full feature space will result in a successful attack against the reduced-feature detector. We theoretically prove that, thanks to random feature selection, the security of the detector increases significantly at the expense of a negligible loss of performance in the absence of attacks. We also provide an experimental validation of the proposed procedure by focusing on the detection of two specific kinds of image manipulations, namely adaptive histogram equalization and median filtering. The experiments confirm the gain in security at the expense of a negligible loss of performance in the absence of attacks.
It is well known that when the fused silica is irradiated with focused femtosecond laser beams, space selective chemical etching can be achieved. The etching rate depends sensitively on the polarization of the laser. Surprisingly, we observe that by chirping the Fourier-transform-limited femtosecond laser pulses to picosecond pulses, the polarization dependence of the etching rate disappears, whereas an efficient etching rate can still be maintained. Observation with a scanning electron microscope reveals that the chirped pulses can induce interconnected nanocracks in the irradiated areas which facilitates efficient introduction of the etchant into the microchannel. The reported technology is of great use for fabrication of three-dimensional (3D) microfluidic systems and glass-based 3D printing.
We present, GeniePath, a scalable approach for learning adaptive receptive fields of neural networks defined on permutation invariant graph data. In GeniePath, we propose an adaptive path layer consists of two complementary functions designed for breadth and depth exploration respectively, where the former learns the importance of different sized neighborhoods, while the latter extracts and filters signals aggregated from neighbors of different hops away. Our method works in both transductive and inductive settings, and extensive experiments compared with competitive methods show that our approaches yield state-of-the-art results on large graphs.
Product reviews, in the form of texts dominantly, significantly help consumers finalize their purchasing decisions. Thus, it is important for e-commerce companies to predict review helpfulness to present and recommend reviews in a more informative manner. In this work, we introduce a convolutional neural network model that is able to extract abstract features from multi-granularity representations. Inspired by the fact that different words contribute to the meaning of a sentence differently, we consider to learn word-level embedding-gates for all the representations. Furthermore, as it is common that some product domains/categories have rich user reviews, other domains not. To help domains with less sufficient data, we integrate our model into a cross-domain relationship learning framework for effectively transferring knowledge from other domains. Extensive experiments show that our model yields better performance than the existing methods.
Collaborative filtering, especially latent factor model, has been popularly used in personalized recommendation. Latent factor model aims to learn user and item latent factors from user-item historic behaviors. To apply it into real big data scenarios, efficiency becomes the first concern, including offline model training efficiency and online recommendation efficiency. In this paper, we propose a Distributed Collaborative Hashing (DCH) model which can significantly improve both efficiencies. Specifically, we first propose a distributed learning framework, following the state-of-the-art parameter server paradigm, to learn the offline collaborative model. Our model can be learnt efficiently by distributedly computing subgradients in minibatches on workers and updating model parameters on servers asynchronously. We then adopt hashing technique to speedup the online recommendation procedure. Recommendation can be quickly made through exploiting lookup hash tables. We conduct thorough experiments on two real large-scale datasets. The experimental results demonstrate that, comparing with the classic and state-of-the-art (distributed) latent factor models, DCH has comparable performance in terms of recommendation accuracy but has both fast convergence speed in offline model training procedure and realtime efficiency in online recommendation procedure. Furthermore, the encouraging performance of DCH is also shown for several real-world applications in Ant Financial.
This work is devoted to the study of parabolic frequency for solutions of the heat equation on Riemannian manifolds. We show that the parabolic frequency functional is almost increasing on compact manifolds with nonnegative sectional curvature, which generalizes a monotonicity result proved by C. Poon and by L. Ni. The proof is based on a generalization of R. Hamilton's matrix Harnack inequality for small time. As applications, we obtain a unique continuation result. Monotonicity of a new quantity under two-dimensional Ricci flow, closely related to the parabolic frequency functional, is derived as well.