arXiv subjects

Wen Huang

Publications and source records attributed to Wen Huang.

At least 73 records · Page 4Linked to original sources

arXiv2025

Pointwise convergence of some continuous-time polynomial ergodic averages

In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in \mathbb{R}$, $Q\in \mathbb{R}[t]$ with $\text{deg}\ Q\ge 2$. Let $(X,\mathcal{X},μ, (T^{t})_{t\in \mathbb{R}})$ and $(X,\mathcal{X},μ, (S^{t})_{t\in \mathbb{R}})$ be two measurable flows. Then for any $f_1, f_2, g\in L^{\infty}(μ)$, the limit \begin{equation*} \lim\limits_{M\to\infty}\frac{1}{M}\int_{0}^{M}f_1(T^{t}x)f_2(T^{at}x)g(S^{Q(t)}x)dt \end{equation*} exists for $μ$-a.e. $x\in X$. In particular, we are able to build a pointwise ergodic theorem involving geodesic flow and horocycle flow.

math.DS↗

arXiv2025

SLRQA: A Sparse Low-Rank Quaternion Model for Color Image Processing with Convergence Analysis

In this paper, we propose a Sparse Low-rank Quaternion Approximation (SLRQA) model for color image processing problems with noisy observations. %Different from the existing color image processing models, The proposed SLRQA is a quaternion model that combines low-rankness and sparsity priors without an initial rank estimation. %Furthermore, it does not need an initial rank estimate. A proximal linearized ADMM (PL-ADMM) algorithm is proposed to solve SLRQA and the global convergence is guaranteed under standard assumptions. %where only one variable is linearized. When the observation is noise-free, a limiting case of the SLRQA, called SLRQA-NF, is proposed. Subsequently, a proximal linearized ADMM (PL-ADMM-NF) algorithm for SLRQA-NF is given. Since SLRQA-NF does not satisfy a widely-used assumption for global convergence of ADMM-type algorithms, we propose a novel assumption, under which the global convergence of PL-ADMM-NF is established. In numerical experiments, we verify the effectiveness of quaternion representation. Furthermore, for color image denoising and color image inpainting problems, SLRQA and SLRQA-NF demonstrate superior performance both quantitatively and visually when compared with some state-of-the-art methods.

math.OC↗

arXiv2025

Generalizable Audio Deepfake Detection via Latent Space Refinement and Augmentation

Advances in speech synthesis technologies, like text-to-speech (TTS) and voice conversion (VC), have made detecting deepfake speech increasingly challenging. Spoofing countermeasures often struggle to generalize effectively, particularly when faced with unseen attacks. To address this, we propose a novel strategy that integrates Latent Space Refinement (LSR) and Latent Space Augmentation (LSA) to improve the generalization of deepfake detection systems. LSR introduces multiple learnable prototypes for the spoof class, refining the latent space to better capture the intricate variations within spoofed data. LSA further diversifies spoofed data representations by applying augmentation techniques directly in the latent space, enabling the model to learn a broader range of spoofing patterns. We evaluated our approach on four representative datasets, i.e. ASVspoof 2019 LA, ASVspoof 2021 LA and DF, and In-The-Wild. The results show that LSR and LSA perform well individually, and their integration achieves competitive results, matching or surpassing current state-of-the-art methods.

eess.AS↗

arXiv2025

Constraints on the orbital flux phase in $A$V$_3$Sb$_5$ from polar Kerr effect

The $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) family of Kagome metals hosts unconventional charge density wave order whose nature is still an open puzzle. Accumulated evidences point to a time-reversal symmetry breaking orbital flux phase that carries loop currents. Such an order may support anomalous Hall effect. However, the polar Kerr effect measurements that probe the a.c. anomalous Hall conductivity seems to have yielded contradictory results. We first argue on symmetry grounds that some previously proposed orbital flux order, most notably the one with Star-of-David distortion, shall not give rise to anomalous Hall or polar Kerr effects. We further take the tri-hexagonal orbital flux phase as an exemplary Kagome flux order that does exhibit anomalous Hall response, and show that the Kerr rotation angle at two relevant experimental optical frequencies generally reaches microradians to sub-milliradians levels. A particularly sharp resonance enhancement is observed at around $\hbar ω=1$ eV, suggesting exceedingly large Kerr rotation at the corresponding probing frequencies not yet accessed by previous experiments. Our study can help to interpret the Kerr measurements on $A$V$_3$Sb$_5$ and to eventually resolve the nature of their CDW order.

cond-mat.mes-hall↗

arXiv2025

Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order

Understanding the formation of novel pair density waves (PDWs) in strongly correlated electronic systems remains challenging. Recent mean-field studies suggest that PDW phases may arise in strong-coupling multiband superconductors by virtue of the quantum geometric properties of paired electrons. However, scrutiny through sophisticated many-body calculations has been lacking. Employing large-scale density matrix renormalization group calculations, we obtain in the strong-coupling regime the phase diagram as a function of doping concentration and a tuning interaction parameter for a simple two-orbital model that incorporates quantum geometric effects. The phase diagram reveals a robust PDW phase spanning a broad range of parameters, characterized by a Luttinger parameter $K_{sc} \sim 0.3$ and the absence of coexisting competing spin or charge density wave orders. The observed pairing field configuration aligns with the phenomenological understanding that quantum geometry can promote PDW formation. Our study provides the most compelling numerical evidence to date for quantum-geometry-facilitated intrinsic PDW order in strongly correlated systems, paving the way for further exploration of novel PDW orders and quantum geometric effects in such systems.

cond-mat.str-el↗

arXiv2024

Ergodicity and Mixing of Sublinear Expectation System and Applications

We utilize an ergodic theory framework to explore sublinear expectation theory. Specifically, we investigate the pointwise Birkhoff's ergodic theorem for invariant sublinear expectation systems. By further assuming that these sublinear expectation systems are ergodic, we derive stronger results. Furthermore, we relax the conditions for the law of large numbers and the strong law of large numbers under sublinear expectations from independent and identical distribution to $α$-mixing. These results can be applied to a class of stochastic differential equations driven by $G$-Brownian motion (i.e., $G$-SDEs), such as $G$-Ornstein-Uhlenbeck processes. As byproducts, we also obtain a series of applications for classical ergodic theory and capacity theory.

math.PR↗

arXiv2024

Finite ergodic components for upper probabilities

Under the notion of ergodicity of upper probability in the sense of Feng and Zhao (2021) that any invariant set either has capacity $0$ or its complement has capacity 0, we introduce the definition of finite ergodic components (FEC). We prove an invariant upper probability has FEC if and only if it is in the regime that any invariant set has either capacity $0$ or capacity $1$, proposed by Cerreia-Vioglio, Maccheroni, and Marinacci (2016). Furthermore, this is also equivalent to that the eigenvalue $1$ of the Koopman operator is of finite multiplicity, while in the ergodic upper probability regime, as in the classical ergodic probability case, the eigenvalue $1$ of the Koopman operator is simple. Additionally, we obtain the equivalence of the law of large numbers with multiple values, the asymptotic independence and the FEC. Furthermore, we apply these to obtain the corresponding results for non-invariant probabilities.

math.PR↗

arXiv2024

Ergodicity and Mixing of invariant capacities and applications

We introduce the notion of common conditional expectation to investigate Birkhoff's ergodic theorem and subadditive ergodic theorem for invariant upper probabilities. If in addition, the upper probability is ergodic, we construct an invariant probability to characterize the limit of the ergodic mean. Moreover, this skeleton probability is the unique ergodic probability in the core of the upper probability, that is equal to all probabilities in the core on all invariant sets. We have the following applications of these two theorems: $\bullet$ provide a strong law of large numbers for ergodic stationary sequence on upper probability spaces; $\bullet$ prove the multiplicative ergodic theorem on upper probability spaces; $\bullet$ establish a criterion for the ergodicity of upper probabilities in terms of independence. Furthermore, we introduce and study weak mixing for capacity preserving systems. Using the skeleton idea, we also provide several characterizations of weak mixing for invariant upper probabilities. Finally, we provide examples of ergodic and weakly mixing capacity preserving systems. As applications, we obtain new results in the classical ergodic theory. e.g. in characterizing dynamical properties on measure preserving systems, such as weak mixing, periodicity. Moreover, we use our results in the nonlinear theory to obtain the asymptotic independence, Birkhoff's type ergodic theorem, subadditive ergodic theorem, and multiplicative ergodic theorem for non-invariant probabilities.

math.PR↗

arXiv2024

Data-Efficient Low-Complexity Acoustic Scene Classification via Distilling and Progressive Pruning

The goal of the acoustic scene classification (ASC) task is to classify recordings into one of the predefined acoustic scene classes. However, in real-world scenarios, ASC systems often encounter challenges such as recording device mismatch, low-complexity constraints, and the limited availability of labeled data. To alleviate these issues, in this paper, a data-efficient and low-complexity ASC system is built with a new model architecture and better training strategies. Specifically, we firstly design a new low-complexity architecture named Rep-Mobile by integrating multi-convolution branches which can be reparameterized at inference. Compared to other models, it achieves better performance and less computational complexity. Then we apply the knowledge distillation strategy and provide a comparison of the data efficiency of the teacher model with different architectures. Finally, we propose a progressive pruning strategy, which involves pruning the model multiple times in small amounts, resulting in better performance compared to a single step pruning. Experiments are conducted on the TAU dataset. With Rep-Mobile and these training strategies, our proposed ASC system achieves the state-of-the-art (SOTA) results so far, while also winning the first place with a significant advantage over others in the DCASE2024 Challenge.

cs.SD↗

arXiv2024

Prototype and Instance Contrastive Learning for Unsupervised Domain Adaptation in Speaker Verification

Speaker verification system trained on one domain usually suffers performance degradation when applied to another domain. To address this challenge, researchers commonly use feature distribution matching-based methods in unsupervised domain adaptation scenarios where some unlabeled target domain data is available. However, these methods often have limited performance improvement and lack generalization in various mismatch situations. In this paper, we propose Prototype and Instance Contrastive Learning (PICL), a novel method for unsupervised domain adaptation in speaker verification through dual-level contrastive learning. For prototype contrastive learning, we generate pseudo labels via clustering to create dynamically updated prototype representations, aligning instances with their corresponding class or cluster prototypes. For instance contrastive learning, we minimize the distance between different views or augmentations of the same instance, ensuring robust and invariant representations resilient to variations like noise. This dual-level approach provides both high-level and low-level supervision, leading to improved generalization and robustness of the speaker verification model. Unlike previous studies that only evaluated mismatches in one situation, we have conducted relevant explorations on various datasets and achieved state-of-the-art performance currently, which also proves the generalization of our method.

eess.AS↗

arXiv2024

Quantum geometric superfluid weight in multiband superconductors: A microscopic interpretation

Even in non-interacting limit, electrons on different Bloch bands of a multiband system do not move as if they are oblivious to the presence of one another. Instead, they move in concert by virtue of a non-Abelian interband Berry connection. While the impact of this quantum geometric attribute manifests most famously through the Hall response of topological bands, the geometric effects in superconductors have attracted significant recent attention. In particular, much has been discussed about the quantum-metric-induced superfluid weight (SW) in flatband superconductors. In this study, we revisit the geometric SW in generic multiband superconductors and trace its origin to a series of microscopic processes. We separately derive the SW of models containing only intraband Cooper pairing and those involving interband pairing. Two classes of processes enabled by the so-called interband velocity (or the closely related interband Berry connection) are identified: one resembles the transfer of Cooper pairs between different bands, and the other corresponds to virtual single-electron back-and-forth tunneling between the bands. The former contribution manifests as effective Josephson coupling between the multiband superconducting order parameters, while the latter constitutes the only source of SW for a superconducting flatband well isolated from other bands. We further numerically evaluate the SW of a simple two-band superconductor with trivial band topology, showcasing how the geometric contribution is sensitive to the details of the multiband pairing configuration. In particular, we highlight an intriguing scenario of negative SW, which may pave way for the formation of novel pair density wave order. Our study provides deeper and more intuitive insight into the origin and nature of the SW induced by the quantum geometry of paired Bloch states.

cond-mat.supr-con↗

arXiv2024

Unified Audio Event Detection

Sound Event Detection (SED) detects regions of sound events, while Speaker Diarization (SD) segments speech conversations attributed to individual speakers. In SED, all speaker segments are classified as a single speech event, while in SD, non-speech sounds are treated merely as background noise. Thus, both tasks provide only partial analysis in complex audio scenarios involving both speech conversation and non-speech sounds. In this paper, we introduce a novel task called Unified Audio Event Detection (UAED) for comprehensive audio analysis. UAED explores the synergy between SED and SD tasks, simultaneously detecting non-speech sound events and fine-grained speech events based on speaker identities. To tackle this task, we propose a Transformer-based UAED (T-UAED) framework and construct the UAED Data derived from the Librispeech dataset and DESED soundbank. Experiments demonstrate that the proposed framework effectively exploits task interactions and substantially outperforms the baseline that simply combines the outputs of SED and SD models. T-UAED also shows its versatility by performing comparably to specialized models for individual SED and SD tasks on DESED and CALLHOME datasets.

eess.AS↗

arXiv2024

Multiple recurrence without commutativity

We study multiple recurrence without commutativity in this paper. We show that for any two homeomorphisms $T,S: X\rightarrow X$ with $(X,T)$ and $(X,S)$ being minimal, there is a residual subset $X_0$ of $X$ such that for any $x\in X_0$ and any nonlinear integral polynomials $p_1,\ldots, p_d$ vanishing at $0$, there is some subsequence $\{n_i\}$ of $\mathbb Z$ with $n_i\to \infty$ satisfying $$ S^{n_i}x\to x,\ T^{p_1(n_i)}x\to x, \ldots,\ T^{p_d(n_i)}x\to x,\ i\to\infty.$$

math.DS↗

arXiv2024

On the analysis of optimization with fixed-rank matrices: a quotient geometric view

We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on $\mathcal{M}_k^{m\times n}$ -- the set of $m\times n$ real matrices with a fixed rank $k$. Our analysis is based on a quotient geometric view of $\mathcal{M}_k^{m\times n}$: by identifying this set with the quotient manifold of a two-term product space $\mathbb{R}_*^{m\times k}\times \mathbb{R}_*^{n\times k}$ of matrices with full column rank via matrix factorization, we find an explicit form for the update rule of the RGD algorithm, which leads to a novel approach to analysing their convergence behavior in rank-constrained optimization. We then deduce some interesting properties that reflect how RGD distinguishes from other matrix factorization algorithms such as those based on the Euclidean geometry. In particular, we show that the RGD algorithm is not only faster than Euclidean gradient descent but also does not rely on balancing techniques to ensure its efficiency while the latter does. We further show that this RGD algorithm is guaranteed to solve matrix sensing and matrix completion problems with linear convergence rate under the restricted positive definiteness property. Numerical experiments on matrix sensing and completion are provided to demonstrate these properties.

math.OC↗

arXiv2024

Evidence chain for time-reversal symmetry-breaking kagome superconductivity

Superconductivity and magnetism are antagonistic quantum matter, while their intertwining has long been considered in frustrated-lattice systems1-3. In this work, we utilize scanning tunneling microscopy and muon spin resonance to discover time-reversal symmetry-breaking superconductivity in kagome metal Cs(V,Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a full-gap superconducting state. Under perturbations of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of unusual interference effect under time-reversal symmetry-breaking. The correlation between internal magnetism, Bogoliubov quasi-particles, and pairing modulation provides a chain of experimental clues for time-reversal symmetry-breaking kagome superconductivity.

cond-mat.supr-con↗

arXiv2024

Local Differential Privacy in Graph Neural Networks: a Reconstruction Approach

Graph Neural Networks have achieved tremendous success in modeling complex graph data in a variety of applications. However, there are limited studies investigating privacy protection in GNNs. In this work, we propose a learning framework that can provide node privacy at the user level, while incurring low utility loss. We focus on a decentralized notion of Differential Privacy, namely Local Differential Privacy, and apply randomization mechanisms to perturb both feature and label data at the node level before the data is collected by a central server for model training. Specifically, we investigate the application of randomization mechanisms in high-dimensional feature settings and propose an LDP protocol with strict privacy guarantees. Based on frequency estimation in statistical analysis of randomized data, we develop reconstruction methods to approximate features and labels from perturbed data. We also formulate this learning framework to utilize frequency estimates of graph clusters to supervise the training procedure at a sub-graph level. Extensive experiments on real-world and semi-synthetic datasets demonstrate the validity of our proposed model.

cs.LG↗

arXiv2024

A counterexample on multiple convergence without commutativity

It is shown that there exist a probability space $(X,{\mathcal X},μ)$, two ergodic measure preserving transformations $T,S$ acting on $(X,{\mathcal X},μ)$ with $h_μ(X,T)=h_μ(X,S)=0$, and $f, g \in L^\infty(X,μ)$ such that the limit \begin{equation*} \lim_{N\to\infty}\frac{1}{N}\sum_{n=0}^{N-1} f(T^{n}x)g(S^{n}x) \end{equation*} does not exist in $L^2(X,μ)$.

math.DS↗

arXiv2024

Visual Hallucinations of Multi-modal Large Language Models

Visual hallucination (VH) means that a multi-modal LLM (MLLM) imagines incorrect details about an image in visual question answering. Existing studies find VH instances only in existing image datasets, which results in biased understanding of MLLMs' performance under VH due to limited diversity of such VH instances. In this work, we propose a tool called VHTest to generate a diverse set of VH instances. Specifically, VHTest finds some initial VH instances in existing image datasets (e.g., COCO), generates a text description for each VH mode, and uses a text-to-image generative model (e.g., DALL-E-3) to generate VH images based on the text descriptions. We collect a benchmark dataset with 1,200 VH instances in 8 VH modes using VHTest. We find that existing MLLMs such as GPT-4V, LLaVA-1.5, and MiniGPT-v2 hallucinate for a large fraction of the instances in our benchmark. Moreover, we find that fine-tuning an MLLM using our benchmark dataset reduces its likelihood to hallucinate without sacrificing its performance on other benchmarks. Our benchmarks are publicly available: https://github.com/wenhuang2000/VHTest.

cs.CV↗