arXiv subjects

Yufeng Zhang

Publications and source records attributed to Yufeng Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2023

Birkhoff Center and Statistical Behavior of Competitive Dynamical Systems

We investigate the location and structure of the Birkhoff center for competitive dynamical systems, and give a comprehensive description of recurrence and statistical behavior of orbits. An order-structure dichotomy is established for any connected component of the Birkhoff center, that is, either it is unordered, or it consists of strongly ordered equilibria. Moreover, there is a canonically defined countable disjoint family $\mathcal{F}$ of invariant $(n-1)$-cells such that each unordered connected component of the Birkhoff center lies on one of these cells. We further show that any connected component of the supports of invariant measures either consists of strongly ordered equilibria, or lies on one element of $\mathcal{F}$. In particular, any $3$-dimensional competitive flow has topological entropy $0$.

math.DS↗

arXiv2023

The $\bar{\partial}$-dressing Method for Two (2+1)-dimensional Equations and Combinatorics

The soliton solutions of two different (2+1)-dimensional equations with the third order and second order spatial spectral problems are studied by the $\bar{\partial}$-dressing method. The 3-reduced and 5-reduced equations of CKP equation are obtained for the first time by the binary Bell polynomial approach. The $\bar{\partial}$-dressing method is a very important method to explore the solution of a nonlinear soliton equation without analytical regions. Two different types of equations, the (2+1)-dimensional Kaup-Kuperschmidt equation named CKP equation and a generalized (2+1)-dimensional nonlinear wave equation, are studied by analyzing the eigenfunctions and Green's functions of their Lax representations as well as the inverse spectral transformations, then the new $\bar{\partial}$ problems are deduced to construct soliton solutions by choosing proper spectral transformations. Furthermore, once the time evolutions of the spectral data are determined, we will be able to completely obtain the solutions formally of the CKP equation and the generalized (2+1)-dimensional nonlinear wave equation. The reduced problem of the (2+1)-dimensional Kaup-Kuperschmidt is discussed. The main method is binary Bell polynomials related about the $\mathcal{Y}$-constraints and $P$-conditions which turns out to be an effective tool to represent the bilinear form. On the basis of this method, the bilinear form is determined under the scaling transformation. Starting from the bilinear representation, the CKP equation is reduced to Kaup-Kuperschmidt~equation and bidirectional Kaup-Kuperschmidt equation under the reduction of $t_3$ and $t_5$, respectively.

nlin.SI↗

arXiv2023

Conservation law and Lie symmetry analysis of the (1+1) dimensional dispersive long-wave equation

In this paper, we mainly study the integrability of 1+1 dimensional dispersive long-wave equation. Firstly, the Lie symmetry analysis of the equation is carried out in the first part. And the optimal system of the equation is obtained according to the symmetry, and the invariant solution and the reduced form of the target equation are solved according to the results. Secondly, we use different methods to solve the conservation law of the target equation. To begin with, we give the adjoint determination equation and adjoint symmetry of the 1+1 dimensional dispersive long-wave equation, and use the adjoint symmetry as the equation multiplier to find several conservation laws. Then we get a Lie bracket by using the relationship between the symmetry of the equation and the adjoint symmetry. Next its strict self-adjoint property is verified, and its conservation laws are solved by Ibragimov's method. Finally, the conservation laws of the target equation are solved by Noether's theorem. Thirdly we calculate some exact solutions of the target equation by three different methods. In the end of the paper, the Hamiltonian structure of the target equation, the generalized pre-symplectic that maps symmetries into adjoint-symmetries and some of its soliton solutions are calculated. In conclusion, we use the direct construction of conservation law method, Ibragimov's method and so on to solve some new conservation laws of 1+1 dimensional dispersive long-wave equation, use the relationship between symmetry and adjoint symmetry to construct the corresponding Lie brackets, and obtain some linear soliton solutions according to the conservation law of the equation.

math-ph↗

arXiv2023

What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization

In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a $\mathcal{O}(1/T)$ regret bound for perfectly pretrained ICL, where $T$ is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.

stat.ML↗

arXiv2023

Answering Subjective Induction Questions on Products by Summarizing Multi-sources Multi-viewpoints Knowledge

This paper proposes a new task in the field of Answering Subjective Induction Question on Products (SUBJPQA). The answer to this kind of question is non-unique, but can be interpreted from many perspectives. For example, the answer to 'whether the phone is heavy' has a variety of different viewpoints. A satisfied answer should be able to summarize these subjective opinions from multiple sources and provide objective knowledge, such as the weight of a phone. That is quite different from the traditional QA task, in which the answer to a factoid question is unique and can be found from a single data source. To address this new task, we propose a three-steps method. We first retrieve all answer-related clues from multiple knowledge sources on facts and opinions. The implicit commonsense facts are also collected to supplement the necessary but missing contexts. We then capture their relevance with the questions by interactive attention. Next, we design a reinforcement-based summarizer to aggregate all these knowledgeable clues. Based on a template-controlled decoder, we can output a comprehensive and multi-perspective answer. Due to the lack of a relevant evaluated benchmark set for the new task, we construct a large-scale dataset, named SupQA, consisting of 48,352 samples across 15 product domains. Evaluation results show the effectiveness of our approach.

cs.CL↗

arXiv2023

Fully parallel optical matrix-matrix multiplication

In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after another, but the computing method is still the optical vector-matrix multiplication method that was decades ago. Here, we propose a novel optical computing paradigm that can parallelly implement matrix-matrix multiplication operation, which can directly replace existing vector-matrix multiplication, greatly improving computational efficiency. This preprint presents theoretical analysis, and we will supplement experimental results and conclusions in the future.

physics.optics↗

arXiv2023

The effect of substrate temperature on cadmium telluride films in high temperature vapor deposition process

Physical vapor high-temperature deposition of CdTe thin films is one of the main methods for preparing high-efficiency CdTe solar cells, but high-temperature deposition also has an impact on the internal structure of the film. The difference in thermal expansion coefficients between the substrate and CdTe leads to the generation of internal stress in the CdTe thin film during the cooling process. In this work, we prepared thin films with different substrate temperatures using a homemade GVD device, and observed by SEM that the crystallization quality of the film gradually improved with the increase of substrate temperature, but accompanied by the shift of XRD peak position. We calculated the internal stress situation of the film by the shift amount, and the possible causes of stress generation were speculated by the results of TEM and SAED to be the combined effects of the different thermal expansion coefficients between the substrate and the film and the stacking fault defects inside the film.

cond-mat.mtrl-sci↗

arXiv2023

Robust and Efficient Fault Diagnosis of mm-Wave Active Phased Arrays using Baseband Signal

One key communication block in 5G and 6G radios is the active phased array (APA). To ensure reliable operation, efficient and timely fault diagnosis of APAs on-site is crucial. To date, fault diagnosis has relied on measurement of frequency domain radiation patterns using costly equipment and multiple strictly controlled measurement probes, which are time-consuming, complex, and therefore infeasible for on-site deployment. This paper proposes a novel method exploiting a Deep Neural Network (DNN) tailored to extract the features hidden in the baseband in-phase and quadrature signals for classifying the different faults. It requires only a single probe in one measurement point for fast and accurate diagnosis of the faulty elements and components in APAs. Validation of the proposed method is done using a commercial 28 GHz APA. Accuracies of 99% and 80% have been demonstrated for single- and multi-element failure detection, respectively. Three different test scenarios are investigated: on-off antenna elements, phase variations, and magnitude attenuation variations. In a low signal to noise ratio of 4 dB, stable fault detection accuracy above 90% is maintained. This is all achieved with a detection time of milliseconds (e.g 6~ms), showing a high potential for on-site deployment.

eess.SP↗

arXiv2023

Scene Graph Lossless Compression with Adaptive Prediction for Objects and Relations

The scene graph is a new data structure describing objects and their pairwise relationship within image scenes. As the size of scene graph in vision applications grows, how to losslessly and efficiently store such data on disks or transmit over the network becomes an inevitable problem. However, the compression of scene graph is seldom studied before because of the complicated data structures and distributions. Existing solutions usually involve general-purpose compressors or graph structure compression methods, which is weak at reducing redundancy for scene graph data. This paper introduces a new lossless compression framework with adaptive predictors for joint compression of objects and relations in scene graph data. The proposed framework consists of a unified prior extractor and specialized element predictors to adapt for different data elements. Furthermore, to exploit the context information within and between graph elements, Graph Context Convolution is proposed to support different graph context modeling schemes for different graph elements. Finally, a learned distribution model is devised to predict numerical data under complicated conditional constraints. Experiments conducted on labeled or generated scene graphs proves the effectiveness of the proposed framework in scene graph lossless compression task.

cs.MM↗

arXiv2023

Significant enhancement of critical current density in H+-intercalated FeSe single crystal

Superconducting transition temperature (Tc) and critical current density (Jc) are two key factors that are not only crucial for probing high-temperature superconducting mechanisms, but also for practical applications. The simple crystal structure of FeSe is very favorable for the fabrication of thin films and wires, but its application is limited by the relatively low Tc and small Jc. A previous study has found that the Tc of FeSe can be significantly enhanced over 40 K by using the protonation method. Here, we present a systematic study of Jc and vortex properties of H+-intercalated FeSe (Hx-FeSe) single crystals. The value of Jc for Hx-FeSe single crystal is significantly enhanced, exceeding 1.3*10^6 A/cm2 at 4 K, which is more than two orders of magnitude larger than 1.1*10^4 A/cm2 of pristine FeSe. The vortex pinning mechanism of Hx-FeSe is found to be surface pinning, which is different from the dominant strong point-like pinning in pristine FeSe. Moreover, the systematic study of the vortex phase transition and the underlying mechanism provides a wealth of information for the vortex phase diagram of Hx-FeSe single crystal. Our results confirm that the introduction of H+ intercalations into FeSe not only enhances the Tc, but also significantly increases the value of Jc, which is favorable for practical applications.

cond-mat.supr-con↗

arXiv2023

Kullback-Leibler Divergence-Based Out-of-Distribution Detection with Flow-Based Generative Models

Recent research has revealed that deep generative models including flow-based models and Variational Autoencoders may assign higher likelihoods to out-of-distribution (OOD) data than in-distribution (ID) data. However, we cannot sample OOD data from the model. This counterintuitive phenomenon has not been satisfactorily explained and brings obstacles to OOD detection with flow-based models. In this paper, we prove theorems to investigate the Kullback-Leibler divergence in flow-based model and give two explanations for the above phenomenon. Based on our theoretical analysis, we propose a new method \PADmethod\ to leverage KL divergence and local pixel dependence of representations to perform anomaly detection. Experimental results on prevalent benchmarks demonstrate the effectiveness and robustness of our method. For group anomaly detection, our method achieves 98.1\% AUROC on average with a small batch size of 5. On the contrary, the baseline typicality test-based method only achieves 64.6\% AUROC on average due to its failure on challenging problems. Our method also outperforms the state-of-the-art method by 9.1\% AUROC. For point-wise anomaly detection, our method achieves 90.7\% AUROC on average and outperforms the baseline by 5.2\% AUROC. Besides, our method has the least notable failures and is the most robust one.

cs.LG↗

arXiv2023

On the Properties of Kullback-Leibler Divergence Between Multivariate Gaussian Distributions

Kullback-Leibler (KL) divergence is one of the most important divergence measures between probability distributions. In this paper, we prove several properties of KL divergence between multivariate Gaussian distributions. First, for any two $n$-dimensional Gaussian distributions $\mathcal{N}_1$ and $\mathcal{N}_2$, we give the supremum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ when $KL(\mathcal{N}_2||\mathcal{N}_1)\leq \varepsilon\ (\varepsilon>0)$. For small $\varepsilon$, we show that the supremum is $\varepsilon + 2\varepsilon^{1.5} + O(\varepsilon^2)$. This quantifies the approximate symmetry of small KL divergence between Gaussians. We also find the infimum of $KL(\mathcal{N}_1||\mathcal{N}_2)$ when $KL(\mathcal{N}_2||\mathcal{N}_1)\geq M\ (M>0)$. We give the conditions when the supremum and infimum can be attained. Second, for any three $n$-dimensional Gaussians $\mathcal{N}_1$, $\mathcal{N}_2$, and $\mathcal{N}_3$, we find an upper bound of $KL(\mathcal{N}_1||\mathcal{N}_3)$ if $KL(\mathcal{N}_1||\mathcal{N}_2)\leq \varepsilon_1$ and $KL(\mathcal{N}_2||\mathcal{N}_3)\leq \varepsilon_2$ for $\varepsilon_1,\varepsilon_2\ge 0$. For small $\varepsilon_1$ and $\varepsilon_2$, we show the upper bound is $3\varepsilon_1+3\varepsilon_2+2\sqrt{\varepsilon_1\varepsilon_2}+o(\varepsilon_1)+o(\varepsilon_2)$. This reveals that KL divergence between Gaussians follows a relaxed triangle inequality. Importantly, all the bounds in the theorems presented in this paper are independent of the dimension $n$. Finally, We discuss the applications of our theorems in explaining counterintuitive phenomenon of flow-based model, deriving deep anomaly detection algorithm, and extending one-step robustness guarantee to multiple steps in safe reinforcement learning.

cs.IT↗

arXiv2022

Image-Text Retrieval with Binary and Continuous Label Supervision

Most image-text retrieval work adopts binary labels indicating whether a pair of image and text matches or not. Such a binary indicator covers only a limited subset of image-text semantic relations, which is insufficient to represent relevance degrees between images and texts described by continuous labels such as image captions. The visual-semantic embedding space obtained by learning binary labels is incoherent and cannot fully characterize the relevance degrees. In addition to the use of binary labels, this paper further incorporates continuous pseudo labels (generally approximated by text similarity between captions) to indicate the relevance degrees. To learn a coherent embedding space, we propose an image-text retrieval framework with Binary and Continuous Label Supervision (BCLS), where binary labels are used to guide the retrieval model to learn limited binary correlations, and continuous labels are complementary to the learning of image-text semantic relations. For the learning of binary labels, we improve the common Triplet ranking loss with Soft Negative mining (Triplet-SN) to improve convergence. For the learning of continuous labels, we design Kendall ranking loss inspired by Kendall rank correlation coefficient (Kendall), which improves the correlation between the similarity scores predicted by the retrieval model and the continuous labels. To mitigate the noise introduced by the continuous pseudo labels, we further design Sliding Window sampling and Hard Sample mining strategy (SW-HS) to alleviate the impact of noise and reduce the complexity of our framework to the same order of magnitude as the triplet ranking loss. Extensive experiments on two image-text retrieval benchmarks demonstrate that our method can improve the performance of state-of-the-art image-text retrieval models.

cs.CV↗

arXiv2022

Disconnected Emerging Knowledge Graph Oriented Inductive Link Prediction

Inductive link prediction (ILP) is to predict links for unseen entities in emerging knowledge graphs (KGs), considering the evolving nature of KGs. A more challenging scenario is that emerging KGs consist of only unseen entities, called as disconnected emerging KGs (DEKGs). Existing studies for DEKGs only focus on predicting enclosing links, i.e., predicting links inside the emerging KG. The bridging links, which carry the evolutionary information from the original KG to DEKG, have not been investigated by previous work so far. To fill in the gap, we propose a novel model entitled DEKG-ILP (Disconnected Emerging Knowledge Graph Oriented Inductive Link Prediction) that consists of the following two components. (1) The module CLRM (Contrastive Learning-based Relation-specific Feature Modeling) is developed to extract global relation-based semantic features that are shared between original KGs and DEKGs with a novel sampling strategy. (2) The module GSM (GNN-based Subgraph Modeling) is proposed to extract the local subgraph topological information around each link in KGs. The extensive experiments conducted on several benchmark datasets demonstrate that DEKG-ILP has obvious performance improvements compared with state-of-the-art methods for both enclosing and bridging link prediction. The source code is available online.

cs.LG↗

arXiv2022

Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones

We investigate the global dynamics from a measure-theoretic perspective for smooth flows with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently, almost all) orbits will be pseudo-ordered or convergent to equilibria. This reduces to Hirsch's prevalent convergence Theorem if the rank k=1; and implies an almost-sure Poincare-Bendixson Theorem for the case k=2. These results are then applied to obtain an almost sure Poincare-Bendixson theorem for high-dimensional differential equations.

math.DS↗

arXiv2022

Shaping Individualized Impedance Landscapes for Gait Training via Reinforcement Learning

Assist-as-needed (AAN) control aims at promoting therapeutic outcomes in robot-assisted rehabilitation by encouraging patients' active participation. Impedance control is used by most AAN controllers to create a compliant force field around a target motion to ensure tracking accuracy while allowing moderate kinematic errors. However, since the parameters governing the shape of the force field are often tuned manually or adapted online based on simplistic assumptions about subjects' learning abilities, the effectiveness of conventional AAN controllers may be limited. In this work, we propose a novel adaptive AAN controller that is capable of autonomously reshaping the force field in a phase-dependent manner according to each individual's motor abilities and task requirements. The proposed controller consists of a modified Policy Improvement with Path Integral algorithm, a model-free, sampling-based reinforcement learning method that learns a subject-specific impedance landscape in real-time, and a hierarchical policy parameter evaluation structure that embeds the AAN paradigm by specifying performance-driven learning goals. The adaptability of the proposed control strategy to subjects' motor responses and its ability to promote short-term motor adaptations are experimentally validated through treadmill training sessions with able-bodied subjects who learned altered gait patterns with the assistance of a powered ankle-foot orthosis.

cs.RO↗

arXiv2021

Protonation-induced discrete superconducting phases in bulk FeSe single crystals

The superconducting transition temperature, $T_{\rm{c}}$, of FeSe can be significantly enhanced several-fold by applying pressure, electron doping, intercalating spacing layer, and reducing dimensionality. Various ordered electronic phases, such as nematicity and spin density waves, have also been observed accompanying high-$T_{\rm{c}}$ superconductivity. Investigation on the evolution of the electronic structure with $T_{\rm{c}}$ is essential to understanding electronic behavior and high-$T_{\rm{c}}$ superconductivity in FeSe and its derived superconductors. In this report, we have found a series of discrete superconducting phases, with a maximum $T_{\rm{c}}$ up to 44 K, in H$^+$-intercalated FeSe single crystals using an ionic liquid gating method. Accompanied with the increase of $T_{\rm{c}}$, suppression of the nematic phase and evolution from non-Fermi-liquid to Fermi-liquid behavior was observed. An abrupt change in the Fermi surface topology was proposed to explain the discrete superconducting phases. A band structure that favors the high-$T_{\rm{c}}$ superconducting phase was also revealed.

cond-mat.supr-con↗

arXiv2021

Relation-aware Heterogeneous Graph for User Profiling

User profiling has long been an important problem that investigates user interests in many real applications. Some recent works regard users and their interacted objects as entities of a graph and turn the problem into a node classification task. However, they neglect the difference of distinct interaction types, e.g. user clicks an item v.s.user purchases an item, and thus cannot incorporate such information well. To solve these issues, we propose to leverage the relation-aware heterogeneous graph method for user profiling, which also allows capturing significant meta relations. We adopt the query, key, and value mechanism in a transformer fashion for heterogeneous message passing so that entities can effectively interact with each other. Via such interactions on different relation types, our model can generate representations with rich information for the user profile prediction. We conduct experiments on two real-world e-commerce datasets and observe a significant performance boost of our approach.

cs.IR↗