arXiv subjects
Publications and source records attributed to Yuanyuan Xu.
We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an $n\times n$ random matrix with independent identically distributed complex entries as $n$ tends to infinity. All terms in the expansion are universal.
We study the challenging task of malware recognition on both known and novel unknown malware families, called malware open-set recognition (MOSR). Previous works usually assume the malware families are known to the classifier in a close-set scenario, i.e., testing families are the subset or at most identical to training families. However, novel unknown malware families frequently emerge in real-world applications, and as such, require to recognize malware instances in an open-set scenario, i.e., some unknown families are also included in the test-set, which has been rarely and non-thoroughly investigated in the cyber-security domain. One practical solution for MOSR may consider jointly classifying known and detecting unknown malware families by a single classifier (e.g., neural network) from the variance of the predicted probability distribution on known families. However, conventional well-trained classifiers usually tend to obtain overly high recognition probabilities in the outputs, especially when the instance feature distributions are similar to each other, e.g., unknown v.s. known malware families, and thus dramatically degrades the recognition on novel unknown malware families. In this paper, we propose a novel model that can conservatively synthesize malware instances to mimic unknown malware families and support a more robust training of the classifier. Moreover, we also build a new large-scale malware dataset, named MAL-100, to fill the gap of lacking large open-set malware benchmark dataset. Experimental results on two widely used malware datasets and our MAL-100 demonstrate the effectiveness of our model compared with other representative methods.
Malware open-set recognition (MOSR) aims at jointly classifying malware samples from known families and detect the ones from novel unknown families, respectively. Existing works mostly rely on a well-trained classifier considering the predicted probabilities of each known family with a threshold-based detection to achieve the MOSR. However, our observation reveals that the feature distributions of malware samples are extremely similar to each other even between known and unknown families. Thus the obtained classifier may produce overly high probabilities of testing unknown samples toward known families and degrade the model performance. In this paper, we propose the Multi-modal Dual-Embedding Networks, dubbed MDENet, to take advantage of comprehensive malware features (i.e., malware images and malware sentences) from different modalities to enhance the diversity of malware feature space, which is more representative and discriminative for down-stream recognition. Last, to further guarantee the open-set recognition, we dually embed the fused multi-modal representation into one primary space and an associated sub-space, i.e., discriminative and exclusive spaces, with contrastive sampling and rho-bounded enclosing sphere regularizations, which resort to classification and detection, respectively. Moreover, we also enrich our previously proposed large-scaled malware dataset MAL-100 with multi-modal characteristics and contribute an improved version dubbed MAL-100+. Experimental results on the widely used malware dataset Mailing and the proposed MAL-100+ demonstrate the effectiveness of our method.
We show that the fluctuations of the largest eigenvalue of any generalized Wigner matrix $H$ converge to the Tracy-Widom laws at a rate nearly $O(N^{-1/3})$, as the matrix dimension $N$ tends to infinity. We allow the variances of the entries of $H$ to have distinct values but of comparable sizes such that $\sum_{i} \mathbb{E}|h_{ij}|^2=1$. Our result improves the previous rate $O(N^{-2/9})$ by Bourgade [8] and the proof relies on the first long-time Green function comparison theorem near the edges without the second moment matching restriction.
We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process, asymptotically as the dimension tends to infinity. In the complex case these facts have already been established by Bender \cite{MR2594353} and in the real case by Akemann and Phillips \cite{MR3192169} even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this note is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating $\max\Re\mathrm{Spec}(X)$ for any large matrix $X$ with i.i.d. entries in the companion paper \cite{2206.04448}.
Pyrochlore iridates are thought to be a fertile ground for the realization of topologically non-trivial and strongly correlated states of matter. Here we provide a compelling evidence of interacting Weyl electrons in Nd$_2$Ir$_2$O$_7$ and quadratic band touching in Pr$_2$Ir$_2$O$_7$ by Raman scattering. We observe a magnetically-driven phase transition between the topological Weyl semimetal and a Luttinger semimetal with quadratic band touching in Nd$_2$Ir$_2$O$_7$. Our theoretical analysis of the Raman scattering from Weyl and Luttinger quasiparticles agrees with experimental observations, and enables a characterization of the material parameters while revealing interaction and disorder effects through a relatively short quasiparticle lifetime.
Quantum spin liquids (QSLs) are topologically ordered exotic states of matter that host fractionalized excitations. Kitaev proposed a particular route towards a QSL via strongly bond-dependent interactions on the hexagonal lattice. A number of candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions, which put these systems far from the QSL regime. Using time-domain terahertz spectroscopy (TDTS) we observed a broad magnetic continuum over a wide range of temperature and field in the honeycomb cobalt-based magnet, BaCo$_2$(AsO$_4$)$_2$, which has been proposed to be more ideal versions of a Kitaev QSL. Applying a small in-plane magnetic field of $\sim$ 0.5 T suppresses the magnetic order and at at even higher fields gives rise to a spin-polarized state. With 4T magnetic field oriented principally out-of-plane, a broad magnetic continuum was observed that could be consistent with a field induced QSL. Our results indicate BaCo$_2$(AsO$_4$)$_2$ to be a promising QSL candidate.
We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.
We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size $N$ converge to the Tracy--Widom laws at a rate $O(N^{-1/3+ω})$, as $N$ tends to infinity. For Wigner matrices this improves the previous rate $O(N^{-2/9+ω})$ obtained by Bourgade [5] for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős, Yau and Yin [19] to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein--Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles.
Multi-label zero-shot learning extends conventional single-label zero-shot learning to a more realistic scenario that aims at recognizing multiple unseen labels of classes for each input sample. Existing works usually exploit attention mechanism to generate the correlation among different labels. However, most of them are usually biased on several major classes while neglect most of the minor classes with the same importance in input samples, and may thus result in overly diffused attention maps that cannot sufficiently cover minor classes. We argue that disregarding the connection between major and minor classes, i.e., correspond to the global and local information, respectively, is the cause of the problem. In this paper, we propose a novel framework of unbiased multi-label zero-shot learning, by considering various class-specific regions to calibrate the training process of the classifier. Specifically, Pyramid Feature Attention (PFA) is proposed to build the correlation between global and local information of samples to balance the presence of each class. Meanwhile, for the generated semantic representations of input samples, we propose Semantic Attention (SA) to strengthen the element-wise correlation among these vectors, which can encourage the coordinated representation of them. Extensive experiments on the large-scale multi-label zero-shot benchmarks NUS-WIDE and Open-Image demonstrate that the proposed method surpasses other representative methods by significant margins.
Because of its wide application, critical nodes identification has become an important research topic at the micro level of network science. Influence maximization is one of the main problems in critical nodes mining and is usually handled with heuristics. In this paper, a deep graph learning framework IMGNN is proposed and the corresponding training sample generation scheme is designed. The framework takes centralities of nodes in a network as input and the probability that nodes in the optimal initial spreaders as output. By training on a large number of small synthetic networks, IMGNN is more efficient than human-based heuristics in minimizing the size of initial spreaders under the fixed infection scale. The experimental results on one synthetic and five real networks show that, compared with traditional non-iterative node ranking algorithms, IMGNN has the smallest proportion of initial spreaders under different infection probabilities when the final infection scale is fixed. And the reordered version of IMGNN outperforms all the latest critical nodes mining algorithms.
Magnetic materials with pyrochlore crystal structure form exotic magnetic states due to the high lattice frustration. In this work we follow the effects of coupling of the lattice and electronic and magnetic degrees of freedom in two Praseodymium-based pyrochlores Pr$_2$Zr$_2$O$_7$ and Pr$_2$Ir$_2$O$_7$. In both materials the presence of magnetic interactions does not lead to magnetically ordered low temperature states, however their electronic properties are different. A comparison of Raman phonon spectra of Pr$_2$Zr$_2$O$_7$ and Pr$_2$Ir$_2$O$_7$ allows us to identify magneto-elastic coupling in Pr$_2$Zr$_2$O$_7$ that elucidates its magnetic properties at intermediate temperatures, and allows us to characterize phonon-electron coupling in the semimetallic Pr$_2$Ir$_2$O$_7$. We also show that the effects of random disorder on the Raman phonon spectra is small.
We establish a quantitative version of the Tracy--Widom law for the largest eigenvalue of high dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix $X^*X$ converge to its Tracy--Widom limit at a rate nearly $N^{-1/3}$, where $X$ is an $M \times N$ random matrix whose entries are independent real or complex random variables, assuming that both $M$ and $N$ tend to infinity at a constant rate. This result improves the previous estimate $N^{-2/9}$ obtained by Wang [73]. Our proof relies on a Green function comparison method [27] using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble.
Pr$_2$Zr$_2$O$_7$ is a pyrochlore quantum spin-ice candidate. Using Raman scattering spectroscopy we probe crystal electric field excitations of Pr$^{3+}$, and demonstrate the importance of their interactions with the lattice. We identify a vibronic interaction with a phonon that leads to a splitting of a doublet crystal field excitation at around 55~meV. We also probe a splitting of the non-Kramers ground state doublet of Pr$^{3+}$ by observing a double line of the excitations to the first excited singlet state $E^0_g \rightarrow A_{1g}$. We show that the splitting has a strong temperature dependence, with the doublet structure most prominent between 50~K and 100~K, and the weight of one of the components strongly decreases on cooling. We suggest a static or dynamic deviation of Pr$^{3+}$ from the position in the ideal crystal structure can be the origin of the effect, with the deviation strongly decreasing at low temperatures.
We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic real bounded diagonal matrix. We prove a universal Central Limit Theorem for the linear eigenvalue statistics of $X_N$ for all mesoscopic scales both in the spectral bulk and at regular edges where the global eigenvalue density vanishes as a square root. The method relies on the characteristic function method in [47], local laws for the Green function of $X_N$ in [3, 46, 51] and analytic subordination properties of the free additive convolution [24, 41]. We also prove the analogous results for high-dimensional sample covariance matrices.
We consider random matrices of the form $H_N=A_N+U_N B_N U^*_N$, where $A_N$, $B_N$ are two $N$ by $N$ deterministic Hermitian matrices and $U_N$ is a Haar distributed random unitary matrix. We establish a universal Central Limit Theorem for the linear eigenvalue statistics of $H_N$ on all mesoscopic scales inside the regular bulk of the spectrum. The proof is based on studying the characteristic function of the linear eigenvalue statistics, and consists of two main steps: (1) generating Ward identities using the left-translation-invariance of the Haar measure, along with a local law for the resolvent of $H_N$ and analytic subordination properties of the free additive convolution, allow us to derive an explicit formula for the derivative of the characteristic function; (2) a local law for two-point product functions of resolvents is derived using a partial randomness decomposition of the Haar measure. We also prove the corresponding results for orthogonal conjugations.
We consider an $N$ by $N$ real or complex generalized Wigner matrix $H_N$, whose entries are independent centered random variables with uniformly bounded moments. We assume that the variance profile, $s_{ij}:=\mathbb{E} |H_{ij}|^2$, satisfies $\sum_{i=1}^Ns_{ij}=1$, for all $1 \leq j \leq N$ and $c^{-1} \leq N s_{ij} \leq c$ for all $ 1 \leq i,j \leq N$ with some constant $c \geq 1$. We establish Gaussian fluctuations for the linear eigenvalue statistics of $H_N$ on global scales, as well as on all mesoscopic scales up to the spectral edges, with the expectation and variance formulated in terms of the variance profile. We subsequently obtain the universal mesoscopic central limit theorems for the linear eigenvalue statistics inside the bulk and at the edges respectively.
Face detection and alignment in unconstrained environment is always deployed on edge devices which have limited memory storage and low computing power. This paper proposes a one-stage method named CenterFace to simultaneously predict facial box and landmark location with real-time speed and high accuracy. The proposed method also belongs to the anchor free category. This is achieved by: (a) learning face existing possibility by the semantic maps, (b) learning bounding box, offsets and five landmarks for each position that potentially contains a face. Specifically, the method can run in real-time on a single CPU core and 200 FPS using NVIDIA 2080TI for VGA-resolution images, and can simultaneously achieve superior accuracy (WIDER FACE Val/Test-Easy: 0.935/0.932, Medium: 0.924/0.921, Hard: 0.875/0.873 and FDDB discontinuous: 0.980, continuous: 0.732). A demo of CenterFace can be available at https://github.com/Star-Clouds/CenterFace.