arXiv subjects

Long Tian

Publications and source records attributed to Long Tian.

At least 37 records · Page 2Linked to original sources

arXiv2023

Hierarchical Vector Quantized Transformer for Multi-class Unsupervised Anomaly Detection

Unsupervised image Anomaly Detection (UAD) aims to learn robust and discriminative representations of normal samples. While separate solutions per class endow expensive computation and limited generalizability, this paper focuses on building a unified framework for multiple classes. Under such a challenging setting, popular reconstruction-based networks with continuous latent representation assumption always suffer from the "identical shortcut" issue, where both normal and abnormal samples can be well recovered and difficult to distinguish. To address this pivotal issue, we propose a hierarchical vector quantized prototype-oriented Transformer under a probabilistic framework. First, instead of learning the continuous representations, we preserve the typical normal patterns as discrete iconic prototypes, and confirm the importance of Vector Quantization in preventing the model from falling into the shortcut. The vector quantized iconic prototype is integrated into the Transformer for reconstruction, such that the abnormal data point is flipped to a normal data point.Second, we investigate an exquisite hierarchical framework to relieve the codebook collapse issue and replenish frail normal patterns. Third, a prototype-oriented optimal transport method is proposed to better regulate the prototypes and hierarchically evaluate the abnormal score. By evaluating on MVTec-AD and VisA datasets, our model surpasses the state-of-the-art alternatives and possesses good interpretability. The code is available at https://github.com/RuiyingLu/HVQ-Trans.

cs.CV↗

arXiv2023

Quantitative unique continuation property for solutions to a bi-Laplacian equation with a potential

In this paper, we focus on the quantitative unique continuation property of solutions to \begin{equation*} Δ^2u=Vu, \end{equation*} where $V\in W^{1,\infty}$. We show that the maximal vanishing order of the solutions is not large than \begin{equation} C\left(\|V\|^{\frac{1}{4}}_{L^{\infty}}+\|\nabla V\|_{L^{\infty}}+1\right). \end{equation} Our key argument is to lift the original equation to that with a positive potential, then decompose the resulted fourth-order equation into a special system of two second-order equations. Based on the special system, we define a variant frequency function with weights and derive its almost monotonicity to establishing some doubling inequalities with explicit dependence on the Sobolev norm of the potential function.

math.AP↗

arXiv2023

Prototypes-oriented Transductive Few-shot Learning with Conditional Transport

Transductive Few-Shot Learning (TFSL) has recently attracted increasing attention since it typically outperforms its inductive peer by leveraging statistics of query samples. However, previous TFSL methods usually encode uniform prior that all the classes within query samples are equally likely, which is biased in imbalanced TFSL and causes severe performance degradation. Given this pivotal issue, in this work, we propose a novel Conditional Transport (CT) based imbalanced TFSL model called {\textbf P}rototypes-oriented {\textbf U}nbiased {\textbf T}ransfer {\textbf M}odel (PUTM) to fully exploit unbiased statistics of imbalanced query samples, which employs forward and backward navigators as transport matrices to balance the prior of query samples per class between uniform and adaptive data-driven distributions. For efficiently transferring statistics learned by CT, we further derive a closed form solution to refine prototypes based on MAP given the learned navigators. The above two steps of discovering and transferring unbiased statistics follow an iterative manner, formulating our EM-based solver. Experimental results on four standard benchmarks including miniImageNet, tieredImageNet, CUB, and CIFAR-FS demonstrate superiority of our model in class-imbalanced generalization.

cs.CV↗

arXiv2023

Some Quantitative Properties of Solutions to the Buckling Type Equation

In this paper, we investigate the quantitative unique continuation, propagation of smallness and measure bounds of nodal sets of solutions to the Buckling type equation $\triangle^2u+λ\triangle u-k^2u=0$ in a bounded analytic domain $Ω\subseteq\mathbb{R}^n$ with the homogeneous boundary conditions $u=0$ and $\frac{\partial u}{\partialν}=0$ on $\partialΩ$, where $λ,\ k$ are nonnegative real constants, and $ν$ is the outer unit normal vector on $\partialΩ$. We obtain that, the upper bounds for the maximal vanishing order of $u$ and the $n-1$ dimensional Hausdorff measure of the nodal set of $u$ are both $C(\sqrtλ+\sqrt{k}+1)$, where $C$ is a positive constant only depending on $n$ and $Ω$. Moreover, we also give a quantitative result of the propagation of smallness of $u$.

math.AP↗

arXiv2023

Learning Prototype-oriented Set Representations for Meta-Learning

Learning from set-structured data is a fundamental problem that has recently attracted increasing attention, where a series of summary networks are introduced to deal with the set input. In fact, many meta-learning problems can be treated as set-input tasks. Most existing summary networks aim to design different architectures for the input set in order to enforce permutation invariance. However, scant attention has been paid to the common cases where different sets in a meta-distribution are closely related and share certain statistical properties. Viewing each set as a distribution over a set of global prototypes, this paper provides a novel prototype-oriented optimal transport (POT) framework to improve existing summary networks. To learn the distribution over the global prototypes, we minimize its regularized optimal transport distance to the set empirical distribution over data points, providing a natural unsupervised way to improve the summary network. Since our plug-and-play framework can be applied to many meta-learning problems, we further instantiate it to the cases of few-shot classification and implicit meta generative modeling. Extensive experiments demonstrate that our framework significantly improves the existing summary networks on learning more powerful summary statistics from sets and can be successfully integrated into metric-based few-shot classification and generative modeling applications, providing a promising tool for addressing set-input and meta-learning problems.

cs.LG↗

arXiv2022

Adaptive Distribution Calibration for Few-Shot Learning with Hierarchical Optimal Transport

Few-shot classification aims to learn a classifier to recognize unseen classes during training, where the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples. A recent solution to this problem is calibrating the distribution of these few sample classes by transferring statistics from the base classes with sufficient examples, where how to decide the transfer weights from base classes to novel classes is the key. However, principled approaches for learning the transfer weights have not been carefully studied. To this end, we propose a novel distribution calibration method by learning the adaptive weight matrix between novel samples and base classes, which is built upon a hierarchical Optimal Transport (H-OT) framework. By minimizing the high-level OT distance between novel samples and base classes, we can view the learned transport plan as the adaptive weight information for transferring the statistics of base classes. The learning of the cost function between a base class and novel class in the high-level OT leads to the introduction of the low-level OT, which considers the weights of all the data samples in the base class. Experimental results on standard benchmarks demonstrate that our proposed plug-and-play model outperforms competing approaches and owns desired cross-domain generalization ability, indicating the effectiveness of the learned adaptive weights.

cs.LG↗

arXiv2022

Deterministic and universal quantum squeezing gate in virtue of teleportation-like protocol

Squeezing transformation as an essential component, gives rise to the possibility to perform various tasks of quantum information processing. However, the reported squeezing gate with best performance so far is a conditional realization at the expense of low success probability, while the performance of the deterministic ones is currently circumscribed by the limited squeezing degree of the non-classical ancilla. To address this issue, we develop and demonstrate a new scheme of deterministic and universal quantum squeezing gate with the property of non-local operation attributed to the teleportation-like protocol. We demonstrate high fidelity squeezing operation, even when the level of target squeezing being up to 10 dB, where a squeezed state with non-classical noise reduction of 6.5 dB is directly observed. Moreover, we perform a high-fidelity complex operation including a Fourier transformation and a phase squeezing gate, exploring the potential of implementing the complex task of quantum information processing with the presented functional unit. Our method can be applied to distributed quantum processor, the creation of exotic non-classical states, and quantum error correction.

quant-ph↗

arXiv2020

Resource reduction for simultaneous generation of two types of continuous variable nonclassical states

We demonstrate experimentally the simultaneous generation and detection of two types of continuous variable nonclassical states from one type-0 phase-matching optical parametric amplification (OPA) and subsequent two ring filter cavities (RFCs). The output field of the OPA includes the baseband ω0 and sideband modes ω0+/-nωf subjects to the cavity resonance condition, which are separated by two cascaded RFCs. The first RFC resonates with half the pump wavelength ω0 and the transmitted baseband component is a squeezed state. The reflected fields of the first RFC, including the sideband modes ω0+/-ωf, are separated by the second RFC, construct Einstein-Podolsky-Rosen entangled state. All freedoms, including the filter cavities for sideband separation and relative phases for the measurements of these sidebands, are actively stabilized. The noise variance of squeezed states is 10.2 dB below the shot noise limit (SNL), the correlation variances of both quadrature amplitude-sum and quadrature phase-difference for the entanglement state are 10.0 dB below the corresponding SNL.

quant-ph↗

arXiv2020

In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe$_2$As$_2$

A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe$_2$As$_2$, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature $T_s$. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature $T_N$ ($<T_s$) and create in-plane resistivity anisotropy above $T_s$. Here we use neutron polarization analysis to show that such a strain on BaFe$_2$As$_2$ also induces a static or quasi-static out-of-plane ($c$-axis) AF order and its associated critical spin fluctuations near $T_N/T_s$. Therefore, uniaxial pressure necessary to detwin single crystals of BaFe$_2$As$_2$ actually rotates the easy axis of the collinear AF order near $T_N/T_s$, and such effect due to spin-orbit coupling must be taken into account to unveil the intrinsic electronic/magnetic properties of the system.

cond-mat.supr-con↗

arXiv2020

On a universal solution to the transport-of-intensity equation

Transport-of-intensity equation (TIE) is one of the most well-known approaches for phase retrieval and quantitative phase imaging. It directly recovers the quantitative phase distribution of an optical field by through-focus intensity measurements in a noninterferometic, deterministic manner. Nevertheless, the accuracy and validity of state-of-the-art TIE solvers depend on restrictive preknowledge or assumptions, including appropriate boundary conditions, a well-defined closed region, and quasi-uniform in-focus intensity distribution, which, however, cannot be strictly satisfied simultaneously under practical experimental conditions. In this Letter, we propose a universal solution to TIE with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily-shaped regions, and simplified implementation and computation. With the "maximum intensity assumption", we firstly simplified TIE as a standard Possion equation to get an initial guess of the solution. Then the initial solution is further refined iteratively by solving the same Possion equation, and thus, the instability associated with the division by zero/small intensity values and large intensity variations can be effectively bypassed. Simulations and experiments with arbitrary phase, arbitrary aperture shapes, and nonuniform intensity distributions verify the effectiveness and universality of the proposed method.

eess.IV↗

arXiv2020

Variational Hetero-Encoder Randomized GANs for Joint Image-Text Modeling

For bidirectional joint image-text modeling, we develop variational hetero-encoder (VHE) randomized generative adversarial network (GAN), a versatile deep generative model that integrates a probabilistic text decoder, probabilistic image encoder, and GAN into a coherent end-to-end multi-modality learning framework. VHE randomized GAN (VHE-GAN) encodes an image to decode its associated text, and feeds the variational posterior as the source of randomness into the GAN image generator. We plug three off-the-shelf modules, including a deep topic model, a ladder-structured image encoder, and StackGAN++, into VHE-GAN, which already achieves competitive performance. This further motivates the development of VHE-raster-scan-GAN that generates photo-realistic images in not only a multi-scale low-to-high-resolution manner, but also a hierarchical-semantic coarse-to-fine fashion. By capturing and relating hierarchical semantic and visual concepts with end-to-end training, VHE-raster-scan-GAN achieves state-of-the-art performance in a wide variety of image-text multi-modality learning and generation tasks.

cs.CV↗

arXiv2019

Strong local moment antiferromagnetic spin fluctuations in V-doped LiFeAs

We use neutron scattering to study vanadium (hole)-doped LiFe$_{1-x}$V$_x$As. In the undoped state, LiFeAs exhibits superconductivity at $T_c=18$ K and transverse incommensurate spin excitations similar to electron overdoped iron pnictides. Upon vanadium-doping to form LiFe$_{0.955}$V$_{0.045}$, the transverse incommensurate spin excitations in LiFeAs transform into longitudinally elongated in a similar fashion as that of potassium (hole) doped Ba$_{0.7}$K$_{0.3}$Fe$_2$As$_2$, but with dramatically enhanced magnetic scattering and elimination of superconductivity. This is different from the suppression of the overall magnetic excitations in hole doped BaFe$_2$As$_2$ and the enhancement of superconductivity near optimal hole doping. These results are consistent with density function theory plus dynamic mean field theory calculations, suggesting that vanadium-doping in LiFeAs may induce an enlarged effective magnetic moment $S_{eff}$ with a spin crossover ground state arising from the inter-orbital scattering of itinerant electrons.

cond-mat.supr-con↗

arXiv2019

Spin fluctuation anisotropy as a probe of orbital-selective hole-electron quasiparticle excitations in detwinned Ba(Fe1-xCox)2As2

We use inelastic neutron scattering to study spin excitation anisotropy in mechanically detwinned Ba(Fe1-xCox)2As2 with x = 0.048 and 0.054. Both samples exhibit a tetragonal-to-orthorhombic structural transition at Ts, a collinear static antiferromagnetic (AF) order at wave vector Q1 = QAF = (1, 0) below the Neel temperature TN, and superconductivity below Tc (Ts > TN > Tc). In the high temperature paramagnetic tetragonal phase (T > Ts), spin excitations centered at Q1 and Q2 = (0, 1) are gapless and have four-fold (C4) rotational symmetry. On cooling to below TN but above Tc, spin excitations become highly anisotropic, developing a gap at Q2 but still are gapless at Q1. Upon entering into the superconducting state, a neutron spin resonance appears at Q1 with no magnetic scattering at Q2. By comparing these results with those from angle resolved photoemission spectroscopy experiments, we conclude that the anisotropic shift of the dyz and dxz bands in detwinned Ba(Fe1-xCox)2As2 below Ts is associated with the spin excitation anisotropy, and the superconductivity-induced resonance arises from the electron-hole Fermi surface nesting of quasiparticles with the dyz orbital characters.

cond-mat.supr-con↗

arXiv2019

Multiplexed spin-wave-photon entanglement source using temporal-multimode memories and feedforward-controlled readout

The sources, which generate atom-photon quantum correlations or entanglement based on quantum memory, are basic blocks for building quantum repeaters (QRs). For achieving highly entanglement-generation rates in ensemble-based QRs, spatial-, temporal- and spectral-multimode memories are needed. The previous temporal-multimode memories are based on rephrasing mechanisms in inhomogeneous-broadened media. Here, by applying a train of multi-direction write pulses into a homogeneous-broadened atomic ensemble to induce Duan-Lukin-Cirac-Zoller-like Raman processes, we prepare up to 19 pairs of modes, namely, a spin-wave mode and a photonic time bin. Spin-wave-photon (i.e., atom-photon) entanglement is probabilistically produced in the mode pairs. As a proof-in-principle demonstration, we show that the multiplexed source using all the spin-wave modes and feed-forward-control readout increases spin-wave-photon entanglement generation rate by a factor of $\sim$18.3, compared to non-multiplexed source using the individual modes. The measured Bell parameter for the multiplexed source is $2.30\pm 0.02$ combined with a memory lifetime of $30μs$.

quant-ph↗

arXiv2019

Coexistence of ferromagnetic and stripe antiferromagnetic spin fluctuations in SrCo$_2$As$_2$

We use inelastic neutron scattering to study energy and wave vector dependence of spin fluctuations in SrCo$_2$As$_2$, derived from SrFe$_{2-x}$Co$_x$As$_2$ iron pnictide superconductors. Our data reveals the coexistence of antiferromagnetic (AF) and ferromagnetic (FM) spin fluctuations at wave vectors $\textbf{Q}_{\rm AF}$=(1,0) and $\textbf{Q}_{\rm FM}$=(0,0)/(2,0), respectively. By comparing neutron scattering results with those of dynamic mean field theory calculation and angle-resolved photoemission spectroscopy experiments, we conclude that both AF and FM spin fluctuations in SrCo$_2$As$_2$ are closely associated with a flat band of the $e_g$ orbitals near the Fermi level, different from the $t_{2g}$ orbitals in superconducting SrFe$_{2-x}$Co$_x$As$_2$. Therefore, Co-substitution in SrFe$_{2-x}$Co$_x$As$_2$ induces a $t_{2g}$ to $e_g$ orbital switching, and is responsible for FM spin fluctuations detrimental to the singlet pairing superconductivity.

cond-mat.str-el↗

arXiv2018

Uniqueness of critical points of solutions to the mean curvature equation with Neumann and Robin boundary conditions

In this paper, we investigate the critical points of solutions to the prescribed constant mean curvature equation with Neumann and Robin boundary conditions respectively in a bounded smooth convex domain $Ω$ of $\mathbb{R}^{n}(n\geq2)$. Firstly, we show the non-degeneracy and uniqueness of the critical points of solutions in a planar domain by using the local Chen & Huang's comparison technique and the geometric properties of approximate surfaces at the non-degenerate critical points. Secondly, we deduce the uniqueness and non-degeneracy of the critical points of solutions in a rotationally symmetric domain of $\mathbb{R}^{n}(n\geq3)$ by the projection of higher dimensional space onto two dimensional plane.

math.AP↗

arXiv2018

Critical points of solutions to a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions

In this paper, we mainly investigate the critical points associated to solutions $u$ of a quasilinear elliptic equation with nonhomogeneous Dirichlet boundary conditions in a connected domain $Ω$ in $\mathbb{R}^2$. Based on the fine analysis about the distribution of connected components of a super-level set $\{x\in Ω: u(x)>t\}$ for any $\mathop {\min}_{\partialΩ}u(x)<t<\mathop {\max}_{\partialΩ}u(x)$, we obtain the geometric structure of interior critical points of $u$. Precisely, when $Ω$ is simply connected, we develop a new method to prove $Σ_{i = 1}^k {m_i}+1=N$, where $m_1,\cdots,m_k$ are the respective multiplicities of interior critical points $x_1,\cdots,x_k$ of $u$ and $N$ is the number of global maximal points of $u$ on $\partialΩ$. When $Ω$ is an annular domain with the interior boundary $γ_I$ and the external boundary $γ_E$, where $u|_{γ_I}=H,~u|_{γ_E}=ψ(x)$ and $ψ(x)$ has $N$ local (global) maximal points on $γ_E$. For the case $ψ(x)\geq H$ or $ψ(x)\leq H$ or $\mathop {\min}\limits_{γ_E}ψ(x)<H<\mathop {\max}\limits_{γ_E}ψ(x)$, we show that $Σ_{i = 1}^k {m_i} \le N$ (either $Σ_{i = 1}^k {m_i}=N$ or $Σ_{i = 1}^k {m_i}+1=N$).

math.AP↗

arXiv2018

Measure Upper Bounds of Nodal Sets of Robin Eigenfunctions

In this paper, we obtain the upper bounds for the Hausdorff measures of nodal sets of eigenfunctions with the Robin boundary conditions, i.e., \begin{equation*} {\left\{\begin{array}{l} \triangle u+λu=0,\quad in\quad Ω,\\ u_ν+μu=0,\quad on\quad\partialΩ, \end{array} \right.} \end{equation*} where the domain $Ω\subseteq\mathbb{R}^n$, $u_ν$ means the derivative of $u$ along the outer normal direction of $\partialΩ$. We show that, if $Ω$ is bounded and analytic, and the corresponding eigenvalue $λ$ is large enough,then the measure upper bounds for the nodal sets of eigenfunctions are $C\sqrtλ$, where $C$ is a positive constant depending only on $n$ and $Ω$ but not on $μ$ We also show that, if $\partialΩ$ is $C^{\infty}$ smooth and $\partialΩ\setminusΓ$ is piecewise analytic, where $Γ\subseteq\partialΩ$ is a union of some $n-2$ dimensional submanifolds of $\partialΩ$, $μ>0$, and $λ$ is large enough, then the corresponding measure upper bounds for the nodal sets of $u$ are $C(\sqrtλ+μ^α+μ^{-cα})$ for some positive number $α$, where $c$ is a positive constant depending only on $n$, and $C$ is a positive constant depending on $n$, $Ω$, $Γ$ and $α$.

math.AP↗