arXiv subjects
Publications and source records attributed to Yuguang Zhang.
This note proves orbifold versions of Kobayashi's theorem. The main result asserts that a compact Kähler orbifold with non-negative Ricci curvature, along with certain conditions regarding singularities, is simply connected.
Unsupervised Domain Adaptation (UDA) aims to mitigate performance degradation when training and testing data are sampled from different distributions. While significant progress has been made in enhancing overall accuracy, most existing methods overlook performance disparities across categories-an issue we refer to as category fairness. Our empirical analysis reveals that UDA classifiers tend to favor certain easy categories while neglecting difficult ones. To address this, we propose Virtual Label-distribution-aware Learning (VILL), a simple yet effective framework designed to improve worst-case performance while preserving high overall accuracy. The core of VILL is an adaptive re-weighting strategy that amplifies the influence of hard-to-classify categories. Furthermore, we introduce a KL-divergence-based re-balancing strategy, which explicitly adjusts decision boundaries to enhance category fairness. Experiments on commonly used datasets demonstrate that VILL can be seamlessly integrated as a plug-and-play module into existing UDA methods, significantly improving category fairness.
This paper proves a convergence theorem for the push-forward Wiener measures on holonomy groups via stochastic parallel transports along convergent metric connections.
In recent years, Transformers have achieved remarkable progress in computer vision tasks. However, their global modeling often comes with substantial computational overhead, in stark contrast to the human eye's efficient information processing. Inspired by the human eye's sparse scanning mechanism, we propose a \textbf{S}parse \textbf{S}can \textbf{S}elf-\textbf{A}ttention mechanism ($\rm{S}^3\rm{A}$). This mechanism predefines a series of Anchors of Interest for each token and employs local attention to efficiently model the spatial information around these anchors, avoiding redundant global modeling and excessive focus on local information. This approach mirrors the human eye's functionality and significantly reduces the computational load of vision models. Building on $\rm{S}^3\rm{A}$, we introduce the \textbf{S}parse \textbf{S}can \textbf{Vi}sion \textbf{T}ransformer (SSViT). Extensive experiments demonstrate the outstanding performance of SSViT across a variety of tasks. Specifically, on ImageNet classification, without additional supervision or training data, SSViT achieves top-1 accuracies of \textbf{84.4\%/85.7\%} with \textbf{4.4G/18.2G} FLOPs. SSViT also excels in downstream tasks such as object detection, instance segmentation, and semantic segmentation. Its robustness is further validated across diverse datasets.
Federated learning (FL) enables collaborative model training across decentralized clients without sharing local data, but is challenged by heterogeneity in data, computation, and communication. Pretrained vision-language models (VLMs), with their strong generalization and lightweight tuning via prompts, offer a promising solution. However, existing federated prompt-learning methods rely only on text prompts and overlook joint label-domain distribution shifts. In this paper, we propose a personalized FL framework based on dual-prompt learning and cross fusion, termed pFedDC. Specifically, each client maintains both global and local prompts across vision and language modalities: global prompts capture common knowledge shared across the federation, while local prompts encode client-specific semantics and domain characteristics. Meanwhile, a cross-fusion module is designed to adaptively integrate prompts from different levels, enabling the model to generate personalized representations aligned with each client's unique data distribution. Extensive experiments across nine datasets with various types of heterogeneity show that pFedDC consistently outperforms state-of-the-art methods.
This paper proves that the universal covering of a compact Kähler manifold with small positive sectional curvature in a certain sense is contractible.
This short paper shows a topological obstruction of the existence of certain Lagrangian submanifolds in symplectic $4m$-manifolds.
We demonstrate a fully-integrated multipurpose microwave frequency identification system on silicon-on-insulator platform. Thanks to its multipurpose features, the chip is able to identify different types of microwave signals, including single-frequency, multiple-frequency, chirped and frequency-hopping microwave signals, as well as discriminate instantaneous frequency variation among the frequency-modulated signals. This demonstration exhibits fully integrated solution and fully functional microwave frequency identification, which can meet the requirements in reduction of size, weight and power for future advanced microwave photonic processor.
Silicon microring modulator (Si-MRM) has become one of the most promising compact modulators to meet the increasing capacity requirements of the next generation optical interconnection. The limited electro-optical (E-O) bandwidth, low modulation efficiency, and inherent modulation nonlinearity are the major factors that limit the Si-MRM modulation speed. To address these issues, we comprehensively optimize the Si-MRM from the device to the modulation and the signal processing. Large modulation bandwidth over 67GHz is achieved in our newly fabricated Si-MRM. Additionally, the laser wavelength and bias voltage of Si-MRM are optimized to significantly improve the modulation performance. Finally, we comprehensively study the theoretical model of modulation nonlinearity in Si-MRM, especially transient nonlinearity. A bidirectional gate recurrent unit (Bi-GRU) neural network with minor modification is applied to compensate for the nonlinear impairments. With all these efforts, we experimentally demonstrate a 302 Gbps Si-MRM-based O-band optical interconnection and achieve 300 Gbps transmission over a 1-km standard single-mode fiber using the discrete multitone modulation format with bit and power loading (BPL-DMT).
In this paper, we show that a smooth 4-manifold diffeomorphic to a complex hypersurface in $\mathbb{CP}^3 $ of degree $d\geq 5$ can be decomposed as the union of $d(d-4)^2$ copies of 4-dimensional pair-of-pants and certain subsets of K3 surfaces.
We prove that the twisted Kahler-Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi-Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when studying the collapsing of Ricci-flat Kahler metrics on Calabi-Yau manifolds, and of the Kahler-Ricci flow on compact Kahler manifolds with semiample canonical bundle and intermediate Kodaira dimension. Our results allow us to understand their collapsed Gromov-Hausdorff limits when the base is smooth and the discriminant has simple normal crossings.
We prove a convergence result for a family of Yang-Mills connections over an elliptic $K3$ surface $M$ as the fibers collapse. In particular, assume $M$ is projective, admits a section, and has singular fibers of Kodaira type $I_1$ and type $II$. Let $Ξ_{t_k}$ be a sequence of $SU(n)$ connections on a principal $SU(n)$ bundle over $M$, that are anti-self-dual with respect to a sequence of Ricci flat metrics collapsing the fibers of $M$. Given certain non-degeneracy assumptions on the spectral covers induced by $\bar\partial_{Ξ_{t_k}}$, we show that away from a finite number of fibers, the curvature $F_{Ξ_{t_k}}$ is locally bounded in $C^0$, the connections converge along a subsequence (and modulo unitary gauge change) in $L^p_1$ to a limiting $L^p_1$ connection $Ξ_0$, and the restriction of $Ξ_0$ to any fiber is $C^{1,α}$ gauge equivalent to a flat connection with holomorphic structure determined by the sequence of spectral covers. Additionally, we relate the connections $Ξ_{t_k}$ to a converging family of special Lagrangian multi-sections in the mirror HyperKähler structure, addressing a conjecture of Fukaya in this setting.
Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a compact metric space which is a half-dimensional special Kahler manifold outside a singular set of real Hausdorff codimension 2 and is homeomorphic to the base projective space.
This note studies the equivalencies among convergences of Ricci-flat Kähler-Einstein metrics on Calabi-Yau manifolds, cohomology classes and potential functions.
We study the long-time behavior of the Kahler-Ricci flow on compact Kahler manifolds. We give an almost complete classification of the singularity type of the flow at infinity, depending only on the underlying complex structure. If the manifold is of intermediate Kodaira dimension and has semiample canonical bundle, so that it is fibered by Calabi-Yau varieties, we show that parabolic rescalings around any point on a smooth fiber converge smoothly to a unique limit, which is the product of a Ricci-flat metric on the fiber and of a flat metric on Euclidean space. An analogous result holds for collapsing limits of Ricci-flat Kahler metrics.
We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first Chern class.
For a certain maximal unipotent family of Abelian varieties over the punctured disc, we show that after a base change, one can complete the family over a disc such that the whole degeneration can be simultaneously balanced embedded into a projective space by the theta functions. Then we study the relationship between the balanced filling-in and the Gromov-Hausdorff limit of flat Kähler metrics on the nearby fibers.
The parity-time symmetry (PT symmetry) breaking phenomenon is investigated in a coupled nanobeam cavity system. An exceptional point is observed during the tuning of the relation of the gain/loss and coupling strength of the closely placed nanobeam pairs. The PT symmetry concept can be applied to realize unidirectional light propagation and single mode operation lasers, which may allow for a new way to harness the optical signal in photonic integrated circuits. Otherwise, operating at this particular exceptional point, sensitivity of tiny perturbation detection can be enhanced greatly compared with conventional sensors.