arXiv subjects

Yi Han

Publications and source records attributed to Yi Han.

At least 55 records · Page 3Linked to original sources

arXiv2025

Modeling, Analysis, and Control of Continuous-Time Weighted-Median Opinion Dynamics

Simple yet predictive mathematical models are essential for mechanistic understanding of opinion evolution in social groups. The weighted-median mechanism has recently been proposed as a well-founded alternative to conventional DeGroot-type opinion dynamics. However, the original weighted-median model excludes compromise behavior, as individuals directly adopt their neighbors' opinions without forming intermediate values. In this paper, we introduce a parsimonious continuous-time extension of the weighted-median model by incorporating individual inertia, allowing opinions to move gradually toward the neighbors' weighted median. Empirical evidence shows that this model outperforms both the original weighted-median and DeGroot models with inertia in predicting opinion shifts. We provide a complete theoretical analysis of the proposed dynamics: the equilibria are characterized and shown to be Lyapunov stable; global convergence is established via the Bony-Brezis method, yielding necessary and sufficient conditions for consensus from arbitrary initial states. In addition, we derive a graph-theoretic condition for persistent disagreement and a necessary and sufficient condition for steering the system to any prescribed consensus value through constant external inputs to a subset of individuals. These results reveal how a social group's resilience to external manipulation fundamentally depends on its internal network structure.

eess.SY↗

arXiv2025

Reverse Diffusion Sequential Monte Carlo Samplers

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using approximate score functions, they can suffer from accumulating errors due to time discretization and imperfect score estimation. In this work, we introduce a principled SMC framework that formalizes diffusion-based samplers as proposals while systematically correcting for their biases. The core idea is to construct informative intermediate target distributions that progressively steer the sampling trajectory toward the final target distribution. Although ideal intermediate targets are intractable, we develop exact approximations using quantities from the score estimation-based proposal, without requiring additional model training or inference overhead. The resulting sampler, termed Reverse Diffusion Sequential Monte Carlo, enables consistent sampling and unbiased estimation of the target's normalization constant under mild conditions. We demonstrate the effectiveness of our method on a range of synthetic targets and real-world Bayesian inference problems.

stat.CO↗

arXiv2025

When Agents Trade: Live Multi-Market Trading Benchmark for LLM Agents

Although Large Language Model (LLM)-based agents are increasingly used in financial trading, it remains unclear whether they can reason and adapt in live markets, as most studies test models instead of agents, cover limited periods and assets, and rely on unverified data. To address these gaps, we introduce Agent Market Arena (AMA), the first lifelong, real-time benchmark for evaluating LLM-based trading agents across multiple markets. AMA integrates verified trading data, expert-checked news, and diverse agent architectures within a unified trading framework, enabling fair and continuous comparison under real conditions. It implements four agents, including InvestorAgent as a single-agent baseline, TradeAgent and HedgeFundAgent with different risk styles, and DeepFundAgent with memory-based reasoning, and evaluates them across GPT-4o, GPT-4.1, Claude-3.5-haiku, Claude-sonnet-4, and Gemini-2.0-flash. Live experiments on both cryptocurrency and stock markets demonstrate that agent frameworks display markedly distinct behavioral patterns, spanning from aggressive risk-taking to conservative decision-making, whereas model backbones contribute less to outcome variation. AMA thus establishes a foundation for rigorous, reproducible, and continuously evolving evaluation of financial reasoning and trading intelligence in LLM-based agents.

cs.CL↗

arXiv2025

Cross-Lingual Sponsored Search via Dual-Encoder and Graph Neural Networks for Context-Aware Query Translation in Advertising Platforms

Cross-lingual sponsored search is crucial for global advertising platforms, where users from different language backgrounds interact with multilingual ads. Traditional machine translation methods often fail to capture query-specific contextual cues, leading to semantic ambiguities that negatively impact click-through rates (CTR) and conversion rates (CVR). To address this challenge, we propose AdGraphTrans, a novel dual-encoder framework enhanced with graph neural networks (GNNs) for context-aware query translation in advertising. Specifically, user queries and ad contents are independently encoded using multilingual Transformer-based encoders (mBERT/XLM-R), and contextual relations-such as co-clicked ads, user search sessions, and query-ad co-occurrence-are modeled as a heterogeneous graph. A graph attention network (GAT) is then applied to refine embeddings by leveraging semantic and behavioral context. These embeddings are aligned via contrastive learning to reduce translation ambiguity. Experiments conducted on a cross-lingual sponsored search dataset collected from Google Ads and Amazon Ads (EN-ZH, EN-ES, EN-FR pairs) demonstrate that AdGraphTrans significantly improves query translation quality, achieving a BLEU score of 38.9 and semantic similarity (cosine score) of 0.83, outperforming strong baselines such as mBERT and M2M-100. Moreover, in downstream ad retrieval tasks, AdGraphTrans yields +4.67% CTR and +1.72% CVR improvements over baseline methods. These results confirm that incorporating graph-based contextual signals with dual-encoder translation provides a robust solution for enhancing cross-lingual sponsored search in advertising platforms.

stat.ME↗

arXiv2025

MultiFinBen: Benchmarking Large Language Models for Multilingual and Multimodal Financial Application

Real-world financial analysis involves information across multiple languages and modalities, from reports and news to scanned filings and meeting recordings. Yet most existing evaluations of LLMs in finance remain text-only, monolingual, and largely saturated by current models. To bridge these gaps, we present MultiFinBen, the first expert-annotated multilingual (five languages) and multimodal (text, vision, audio) benchmark for evaluating LLMs in realistic financial contexts. MultiFinBen introduces two new task families: multilingual financial reasoning, which tests cross-lingual evidence integration from filings and news, and financial OCR, which extracts structured text from scanned documents containing tables and charts. Rather than aggregating all available datasets, we apply a structured, difficulty-aware selection based on advanced model performance, ensuring balanced challenge and removing redundant tasks. Evaluating 21 leading LLMs shows that even frontier multimodal models like GPT-4o achieve only 46.01% overall, stronger on vision and audio but dropping sharply in multilingual settings. These findings expose persistent limitations in multilingual, multimodal, and expert-level financial reasoning. All datasets, evaluation scripts, and leaderboards are publicly released.

cs.CL↗

arXiv2025

Finite rank perturbation of non-Hermitian random matrices: heavy tail and sparse regimes

We revisit the problem of perturbing a large, i.i.d. random matrix by a finite rank error. It is known that when elements of the i.i.d. matrix have finite fourth moment, then the outlier eigenvalues of the perturbed matrix are close to the outlier eigenvalues of the error, as long as the perturbation is relatively small. We first prove that under a merely second moment condition, for a large class of perturbation matrix with bounded rank and bounded operator norm, the outlier eigenvalues of perturbed matrix still converge to that of the perturbation. We then prove that for a matrix with i.i.d. Bernoulli $(d/n)$ entries or Bernoulli $(d_n/n)$ entries with $d_n=n^{o(1)}$, the same result holds for perturbation matrices with a bounded number of nonzero elements.

math.PR↗

arXiv2025

RoboBrain 2.0 Technical Report

We introduce RoboBrain 2.0, our latest generation of embodied vision-language foundation models, designed to unify perception, reasoning, and planning for complex embodied tasks in physical environments. It comes in two variants: a lightweight 7B model and a full-scale 32B model, featuring a heterogeneous architecture with a vision encoder and a language model. Despite its compact size, RoboBrain 2.0 achieves strong performance across a wide spectrum of embodied reasoning tasks. On both spatial and temporal benchmarks, the 32B variant achieves leading results, surpassing prior open-source and proprietary models. In particular, it supports key real-world embodied AI capabilities, including spatial understanding (e.g., affordance prediction, spatial referring, trajectory forecasting) and temporal decision-making (e.g., closed-loop interaction, multi-agent long-horizon planning, and scene graph updating). This report details the model architecture, data construction, multi-stage training strategies, infrastructure and practical applications. We hope RoboBrain 2.0 advances embodied AI research and serves as a practical step toward building generalist embodied agents. The code, checkpoint and benchmark are available at https://superrobobrain.github.io.

cs.RO↗

arXiv2025

Spectral radius concentration for inhomogeneous random matrices with independent entries

Let $A$ be a square random matrix of size $n$, with mean zero, independent but not identically distributed entries, with variance profile $S$. When entries are i.i.d. with unit variance, the spectral radius of $n^{-1/2}A$ converges to $1$ whereas the operator norm converges to 2. Motivated by recent interest in inhomogeneous random matrices, in particular non-Hermitian random band matrices, we formulate general upper bounds for $ρ(A)$, the spectral radius of $A$, in terms of the variance $S$. We prove (1) after suitable normalization $ρ(A)$ is bounded by $1+ε$ up to the optimal sparsity $σ_*\gg (\log n)^{-1/2}$ where $σ_*$ is the largest standard deviation of an individual entry; (2) a small deviation inequality for $ρ(A)$ capturing fluctuation beyond the optimal scale $σ_*^{-1}$; (3) a large deviation inequality for $ρ(A)$ with Gaussian entries and doubly stochastic variance; and (4) boundedness of $ρ(A)$ in certain heavy-tailed regimes with only $2+ε$ finite moments and inhomogeneous variance profile $S$. The proof relies heavily on the trace moment method.

math.PR↗

arXiv2025

The smallest singular value for rectangular random matrices with Lévy entries

Let $X=(x_{ij})\in\mathbb{R}^{N\times n}$ be a rectangular random matrix with i.i.d. entries (we assume $N/n\to\mathbf{a}>1$), and denote by $σ_{min}(X)$ its smallest singular value. When entries have mean zero and unit second moment, the celebrated work of Bai-Yin and Tikhomirov show that $n^{-\frac{1}{2}}σ_{min}(X)$ converges almost surely to $\sqrt{\mathbf{a}}-1.$ However, little is known when the second moment is infinite. In this work we consider symmetric entry distributions satisfying $\mathbb{P}(|x_{ij}|>t)\sim t^{-α}$ for some $α\in(0,2)$, and prove that $σ_{min}(X)$ can be determined up to a log factor with high probability: for any $D>0$, with probability at least $1-n^{-D}$ we have $$C_1n^{\frac{1}α}(\log n)^\frac{2(α-2)}α\leq σ_{min}(X)\leq C_2n^{\frac{1}α}(\log n)^\frac{α-2}{2α}$$ for some constants $C_1,C_2>0$. The upper bound was derived in a recent work of Bao, Lee and Xu \cite{bao2024phase2} but the lower bound is new and answers a problem posed in that paper in a weaker form. This appears to be the first determination of $σ_{min}(X)$ in the $α$-stable case with a correct leading order of $n$, as previous anti-concentration arguments only yield lower bound $n^\frac{1}{2}$. The same lower bound holds for $σ_{min}(X+B)$ for any fixed rectangular matrix $B$ with no assumption on its operator norm. The case of diverging aspect ratio is also computed.

math.PR↗

arXiv2025

Symmetric matrices with banded heavy tail noise: local law and eigenvector delocalization

In this work we consider deterministic, symmetric matrices with heavy-tailed noise imposed on entries within a fixed distance $K$ to the diagonal. The most important example is discrete 1d random Schrödinger operator defined on $0,1,\cdots,N$ where the potentials imposed on the diagonal have heavy-tailed distributions and in particular may not have a finite variance. We assume the noise is of the form $N^{-\frac{1}α}ξ$ where $ξ$ are some i.i.d. random potentials. We investigate the local spectral statistics under various assumptions on $ξ$: when it has all moments but the moment explodes as $N$ gets large; when it has finite $α+δ$-moment for some $δ>0$; and when it is the $α$-stable law. We prove in the first two cases that a local law for each element of Green function holds at the almost optimal scale with high probability. As a bi-product we derive Wegner estimate, eigenvalue rigidity and eigenvector de-localization in the infinity norm. For the case of $α$-stable potentials imposed on discrete 1d Laplacian, we prove that (i) Green function entries are bounded with probability tending to one, implying eigenvectors are de-localized in the infinity norm; (ii) with positive probability some entries of the Green function do not converge to that of the deterministic matrix; and (iii) the trace of Green function converges to the Stieltjes transform of arcsine law with probability tending to one. These findings are in contrast to properties of Levy matrices recently uncovered. We extend our results to other scaling in front of the noise and derive local laws on the corresponding intermediate scales, and further extend to Wigner matrices perturbed by finite band heavy-tail noise.

math.PR↗

arXiv2025

AIS Data-Driven Maritime Monitoring Based on Transformer: A Comprehensive Review

With the increasing demands for safety, efficiency, and sustainability in global shipping, Automatic Identification System (AIS) data plays an increasingly important role in maritime monitoring. AIS data contains spatial-temporal variation patterns of vessels that hold significant research value in the marine domain. However, due to its massive scale, the full potential of AIS data has long remained untapped. With its powerful sequence modeling capabilities, particularly its ability to capture long-range dependencies and complex temporal dynamics, the Transformer model has emerged as an effective tool for processing AIS data. Therefore, this paper reviews the research on Transformer-based AIS data-driven maritime monitoring, providing a comprehensive overview of the current applications of Transformer models in the marine field. The focus is on Transformer-based trajectory prediction methods, behavior detection, and prediction techniques. Additionally, this paper collects and organizes publicly available AIS datasets from the reviewed papers, performing data filtering, cleaning, and statistical analysis. The statistical results reveal the operational characteristics of different vessel types, providing data support for further research on maritime monitoring tasks. Finally, we offer valuable suggestions for future research, identifying two promising research directions. Datasets are available at https://github.com/eyesofworld/Maritime-Monitoring.

cs.AI↗

arXiv2025

Lightweight Defense Against Adversarial Attacks in Time Series Classification

As time series classification (TSC) gains prominence, ensuring robust TSC models against adversarial attacks is crucial. While adversarial defense is well-studied in Computer Vision (CV), the TSC field has primarily relied on adversarial training (AT), which is computationally expensive. In this paper, five data augmentation-based defense methods tailored for time series are developed, with the most computationally intensive method among them increasing the computational resources by only 14.07% compared to the original TSC model. Moreover, the deployment process for these methods is straightforward. By leveraging these advantages of our methods, we create two combined methods. One of these methods is an ensemble of all the proposed techniques, which not only provides better defense performance than PGD-based AT but also enhances the generalization ability of TSC models. Moreover, the computational resources required for our ensemble are less than one-third of those required for PGD-based AT. These methods advance robust TSC in data mining. Furthermore, as foundation models are increasingly explored for time series feature learning, our work provides insights into integrating data augmentation-based adversarial defense with large-scale pre-trained models in future research.

cs.LG↗

arXiv2025

Exponential ergodicity of stochastic heat equations with Hölder coefficients

We investigate the stochastic heat equation driven by space-time white noise defined on an abstract Hilbert space, assuming that the drift and diffusion coefficients are both merely Hölder continuous. Random field SPDEs are covered as special examples. We give the first proof that there exists a unique in law mild solution when the diffusion coefficient is $β$ - Hölder continuous for $β>\frac{3}{4}$ and uniformly non-degenerate, and that the drift is locally Hölder continuous. Meanwhile, assuming the existence of a suitable Lyapunov function for the SPDE, we prove that the solution converges exponentially fast to the unique invariant measure with respect to a typical Wasserstein distance. Our technique generalizes when the SPDE has a Burgers type non-linearity $(-A)^{\vartheta}F(X_t)$ for any $\vartheta\in(0,1)$, where $F$ is $\vartheta+ε$- Hölder continuous and has linear growth. For $\vartheta\in(\frac{1}{2},1)$ this result is new even in the case of additive noise.

math.PR↗

arXiv2025

Repeated singular values of a random symmetric matrix and decoupled singular value estimates

Let $A_n$ be a random symmetric matrix with Bernoulli $\{\pm 1\}$ entries. For any $κ>0$ and two real numbers $λ_1,λ_2$ with a separation $|λ_1-λ_2|\geq κn^{1/2}$ and both lying in the bulk $[-(2-κ)n^{1/2},(2-κ)n^{1/2}]$, we prove a joint singular value estimate $$ \mathbb{P}(σ_{min}(A_n-λ_i I_n)\leqεn^{-1/2};i=1,2)\leq Cε^2+2e^{-cn}. $$ For general subgaussian distribution and a mesoscopic separation $|λ_1-λ_2|\geq κn^{-1/2+σ},σ>0$ we prove the same estimate with $e^{-cn}$ replaced by an exponential type error. This means that extreme behaviors of the least singular value at two locations can essentially be decoupled all the way down to the exponential scale when the two locations are separated. As a corollary, we prove that all the singular values of $A_n$ in $[κn^{1/2},(2-κ)n^{1/2}]$ are distinct with probability $1-e^{-cn}$, and with high probability the minimal gap between these singular values has order at least $n^{-3/2}$. This justifies, in a strong quantitative form, a conjecture of Vu up to $(1-κ)$-fraction of the spectrum for any $κ>0$.

math.PR↗

arXiv2025

NeRF-Based Transparent Object Grasping Enhanced by Shape Priors

Transparent object grasping remains a persistent challenge in robotics, largely due to the difficulty of acquiring precise 3D information. Conventional optical 3D sensors struggle to capture transparent objects, and machine learning methods are often hindered by their reliance on high-quality datasets. Leveraging NeRF's capability for continuous spatial opacity modeling, our proposed architecture integrates a NeRF-based approach for reconstructing the 3D information of transparent objects. Despite this, certain portions of the reconstructed 3D information may remain incomplete. To address these deficiencies, we introduce a shape-prior-driven completion mechanism, further refined by a geometric pose estimation method we have developed. This allows us to obtain a complete and reliable 3D information of transparent objects. Utilizing this refined data, we perform scene-level grasp prediction and deploy the results in real-world robotic systems. Experimental validation demonstrates the efficacy of our architecture, showcasing its capability to reliably capture 3D information of various transparent objects in cluttered scenes, and correspondingly, achieve high-quality, stables, and executable grasp predictions.

cs.RO↗

arXiv2025

Convergence and consensus analysis of a class of best-response opinion dynamics

Opinion dynamics aims to understand how individuals' opinions evolve through local interactions. Recently, opinion dynamics have been modeled as network games, where individuals update their opinions in order to minimize the social pressure caused by disagreeing with others. In this paper, we study a class of best response opinion dynamics introduced by Mei et al., where a parameter $α> 0$ controls the marginal cost of opinion differences, bridging well-known mechanisms such as the DeGroot model ($α= 2$) and the weighted-median model ($α= 1$). We conduct theoretical analysis on how different values of $α$ affect the system's convergence and consensus behavior. For the case when $α> 1$, corresponding to increasing marginal costs, we establish the convergence of the dynamics and derive graph-theoretic conditions for consensus formation, which is proved to be similar to those in the DeGroot model. When $α< 1$, we show via a counterexample that convergence is not always guaranteed, and we provide sufficient conditions for convergence and consensus. Additionally, numerical simulations on small-world networks reveal how network structure and $α$ together affect opinion diversity.

math.DS↗

arXiv2025

Recommendation System in Advertising and Streaming Media: Unsupervised Data Enhancement Sequence Suggestions

Sequential recommendation is an extensively explored approach to capturing users' evolving preferences based on past interactions, aimed at predicting their next likely choice. Despite significant advancements in this domain, including methods based on RNNs and self-attention, challenges like limited supervised signals and noisy data caused by unintentional clicks persist. To address these challenges, some studies have incorporated unsupervised learning by leveraging local item contexts within individual sequences. However, these methods often overlook the intricate associations between items across multiple sequences and are susceptible to noise in item co-occurrence patterns. In this context, we introduce a novel framework, Global Unsupervised Data-Augmentation (UDA4SR), which adopts a graph contrastive learning perspective to generate more robust item embeddings for sequential recommendation. Our approach begins by integrating Generative Adversarial Networks (GANs) for data augmentation, which serves as the first step to enhance the diversity and richness of the training data. Then, we build a Global Item Relationship Graph (GIG) based on all user interaction sequences. Subsequently, we employ graph contrastive learning on the refined graph to enhance item embeddings by capturing complex global associations. To model users' dynamic and diverse interests more effectively, we enhance the CapsNet module with a novel target-attention mechanism. Extensive experiments show that UDA4SR significantly outperforms state-of-the-art approaches.

cs.IR↗

arXiv2025

Simplicity of singular value spectrum of random matrices and two-point quantitative invertibility

Let $A$ be an $n\times n$ random matrix with independent, identically distributed mean 0, variance 1 subgaussian entries. We prove that $$ \mathbb{P}(A\text{ has distinct singular values})\geq 1-e^{-cn} $$ for some $c>0$, confirming a conjecture of Vu. This result is then generalized to singular values of rectangular random matrices with i.i.d. entries. We also prove that for two fixed real numbers $λ_1,λ_2$ with a sufficient lower bound on $|λ_1-λ_2|$, we have a joint singular value small ball estimate for any $ε>0$ $$ \mathbb{P}(σ_{min}(A-λ_1I_n)\leqεn^{-1/2},σ_{min}(A-λ_2I_n)\leqεn^{-1/2})\leq Cε^2+e^{-cn}, $$ where $σ_{min}(A)$ is the minimal singular value of a square matrix $A$ and $I_n$ is the identity matrix. For much smaller $|λ_1-λ_2|$ we derive a similar estimate with $C$ replaced by $C\sqrt{n}/|λ_1-λ_2|$. This generalizes the one-point estimate of Rudelson and Vershynin, which proves $\mathbb{P}(σ_{min}(A)\leq εn^{-1/2})\leq Cε+e^{-cn}$. Analogous two-point bounds are proven when $A$ has i.i.d. real and complex parts, with $ε^4$ in place of $ε^2$ on the right hand side of the estimate and for any complex numbers $λ_1,λ_2$. These two point estimates can be used to derive strong anticoncentration bounds for an arbitrary linear combination of two eigenvalues of $A$.

math.PR↗