arXiv subjects

Hang Du

Publications and source records attributed to Hang Du.

At least 19 recordsLinked to original sources

arXiv2026

Overlap distribution of the critical Sherrington-Kirkpatrick model

We study the distribution of the two-replica overlap $R_{1,2}$ in the Ising and spherical Sherrington-Kirkpatrick models at the critical inverse temperature $\beta = 1$. Our main result shows that in both models, $R_{1,2}$ has scale $N^{-1/3}$, and the quenched distribution of $N^{1/3} R_{1,2}$ converges to an explicit random probability measure defined in terms of the reflected $\mathrm{Airy}_1$ point process. As a consequence, we characterize the limiting value of $N^{2/3} \mathbb{E} \langle R_{1,2}^2 \rangle$, answering a question of Talagrand \cite{talagrand2011mean2}. For the spherical SK model, we obtain the limit by representing the Gibbs measure as an anisotropic Gaussian on $\mathbb{R}^N$ conditioned to have norm $\sqrt{N}$, and then passing to the $\mathrm{Airy}_1$ scaling limit at the GOE spectral edge. For the Ising SK model, the proof is based on a sphere-to-cube comparison principle showing that the quenched distributions of $N^{1/3} R_{1,2}$ under the spherical and Ising Gibbs measures asymptotically coincide. This paper is a companion to \cite{du2026fluctuations}, where we introduced a related comparison principle to identify the limiting fluctuations of the SK free energy. Most of the arguments in this paper were generated using GPT-5.6 Pro, with the aim of exploring further consequences of the ideas developed in that work.

math.PR↗

arXiv2026

Offline-Online Curriculum RL for Multimodal Reasoning

Multimodal large language models exhibit capabilities on reasoning tasks, yet often produce flawed intermediate steps while yielding correct final answers. This behavior undermines interpretability and reliability, suggesting reliance on spurious shortcuts rather than faithful reasoning. Although efforts have explored step-level supervision, distinguishing decisive steps from redundant ones remains challenging. We propose $O^2$-CritiCuRL, a novel curriculum reinforcement learning framework that introduces critical-step awareness through an iterative offline-online paradigm. In the offline stage, $O^2$-CritiCuRL conducts multi-rollout analysis over step-annotated trajectories to estimate step-level importance, allowing the framework to distill critical reasoning steps and filter out redundant ones. In the online stage, we employ a progressive step-level reinforcement learning strategy, where truncated chains guide the model to infer missing steps and refine its reasoning, thereby sharpening its focus on critical steps and overcoming the limitations of static supervision. Extensive experiments on multimodal reasoning benchmarks show that our method achieves state-of-the-art performance while delivering superior training and inference efficiency. Code is available at https://github.com/kk0013/CritiCuRL.

cs.AI↗

arXiv2026

Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime

A random geometric graph (RGG) is generated by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the unit sphere in $\mathbb{R}^d$, and then connecting each pair $(i,j)$ if $\langle x_i,x_j\rangle$ exceeds some threshold $\tau$. We study the sharp detection threshold -- the largest dimension at which the RGG can be statistically distinguished from the Erd\H{o}s--R\'enyi graph with the same edge density $p$. This threshold is conjectured to be $d \asymp (nh(p))^3$, where $h(p)=p \log \frac{1}{p} + (1-p) \log \frac{1}{1-p}$ is the binary entropy function. Previous works proved this conjecture for dense graphs with constant $p$ and, up to polylogarithmic factors, very sparse graphs with $p=\Theta(1/n)$. In this paper, we prove that detection is impossible when $d\gg (nh(p))^3$ and $d\ge (1+\epsilon) n$ for any constant $\epsilon>0$, thereby resolving the conjecture in the regime $p\gtrsim n^{-2/3}/\log n$ and improving upon the state of the art in the regime $1/n \ll p \ll n^{-2/3}/\log n$. The key to our proof is a sharp analysis of the posterior distribution of the latent points given the observed graph, obtained through an information-theoretic comparison argument combined with strong log-concavity.

math.PR↗

arXiv2026

Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature

We consider the Sherrington-Kirkpatrick spin glass model at the critical inverse temperature $\beta = 1$ with zero external field. We prove that the free energy $F_N = F_{N,\beta=1}$ of this model has variance \[ \mathrm{Var}(F_N) = \frac16 \log N + O(1)\,, \] confirming a physics prediction of Aspelmeier \cite{aspelmeier2008free}, and that the centered and scaled $F_N$ satisfies a Gaussian CLT. We also identify the critical two-replica overlap scale, proving \[ \mathbb{E} \langle R_{1,2}^2\rangle \asymp N^{-2/3}\,, \] as conjectured by Talagrand \cite{talagrand2011mean2}, together with a uniform exponential moment bound for $N^{1/3} |R_{1,2}|$. The key input is a critical reweighted moment method, in the spirit of the ``small subgraph conditioning'' technique from probabilistic combinatorics, but capable of capturing diverging fluctuations. Through this reweighting, we relate the critical SK model to the BBP critical edge, which determines the overlap and fluctuation scales.

math.PR↗

arXiv2026

Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions

We study high-dimensional inference in correlated two-view models, focusing on spectral methods for strong detection and weak recovery. We introduce a general framework, motivated by a TAP type heuristic from statistical physics, that provides a unified treatment of three canonical models: high-dimensional canonical correlation analysis, and the correlated spiked Wigner and Wishart models. Our main contribution is to construct explicit spectral algorithms in all three settings, that achieve strong detection and weak recovery down to the corresponding thresholds, where we prove matching information-theoretic lower bounds. Furthermore, our spectral procedures operate without knowledge of the model parameters, relying solely on the observed data. This demonstrates the optimality of spectral methods in these models and the broad statistical applicability of the framework.

math.ST↗

arXiv2026

MMFCTUB: Multi-Modal Financial Credit Table Understanding Benchmark

The advent of multi-modal language models (MLLMs) has spurred research into their application across various table understanding tasks. However, their performance in credit table understanding (CTU) for financial credit review remains largely unexplored due to the following barriers: low data consistency, high annotation costs stemming from domain-specific knowledge and complex calculations, and evaluation paradigm gaps between benchmark and real-world scenarios. To address these challenges, we introduce MMFCTUB (Multi-Modal Financial Credit Table Understanding Benchmark), a practical benchmark, encompassing more than 7,600 high quality CTU samples across 5 table types. MMFCTUB employ a minimally supervised pipeline that adheres to inter-table constraints and maintains data distributions consistency. The benchmark leverages capacity-driven questions and mask-and-recovery strategy to evaluate models' cross-table structure perception, domain knowledge utilization, and numerical calculation capabilities. Utilizing MMFCTUB, we conduct comprehensive evaluations of both proprietary and open-source MLLMs, revealing their strengths and limitations in CTU tasks. MMFCTUB serves as a valuable resource for the research community, facilitating rigorous evaluation of MLLMs in the domain of CTU.

cs.CE↗

arXiv2025

Perception, Understanding and Reasoning, A Multimodal Benchmark for Video Fake News Detection

The advent of multi-modal large language models (MLLMs) has greatly advanced research on video fake news detection (VFND) tasks. Existing benchmarks typically focus on the detection accuracy, while failing to provide fine-grained assessments for the entire detection process. To address these limitations, we introduce {POVFNDB (Process-oriented Video Fake News Detection Benchmark)}, a process-oriented benchmark comprising 10 tasks designed to systematically evaluate MLLMs' perception, understanding, and reasoning capabilities in VFND. This benchmark contains \textit{36,240} human-annotated question-answer (QA) in structured or open-ended formats, spanning 15 distinct evaluation dimensions that characterize different aspects of the video fake news detection process. Using POVFNDB, we conduct comprehensive evaluations on both proprietary and open-source MLLMs. Moreover, we establish a strong benchmark baseline by fine-tuning Qwen2.5VL-7B-Instruct on process-oriented chain-of-thought data constructed with our proposed POVFND-CoT framework, achieving state-of-the-art performance on VFND.

cs.CV↗

arXiv2025

IL3D: A Large-Scale Indoor Layout Dataset for LLM-Driven 3D Scene Generation

In this study, we present IL3D, a large-scale dataset meticulously designed for large language model (LLM)-driven 3D scene generation, addressing the pressing demand for diverse, high-quality training data in indoor layout design. Comprising 27,816 indoor layouts across 18 prevalent room types and a library of 29,215 high-fidelity 3D object assets, IL3D is enriched with instance-level natural language annotations to support robust multimodal learning for vision-language tasks. We establish rigorous benchmarks to evaluate LLM-driven scene generation. Experimental results show that supervised fine-tuning (SFT) of LLMs on IL3D significantly improves generalization and surpasses the performance of SFT on other datasets. IL3D offers flexible multimodal data export capabilities, including point clouds, 3D bounding boxes, multiview images, depth maps, normal maps, and semantic masks, enabling seamless adaptation to various visual tasks. As a versatile and robust resource, IL3D significantly advances research in 3D scene generation and embodied intelligence, by providing high-fidelity scene data to support environment perception tasks of embodied agents.

cs.CV↗

arXiv2025

From Easy to Hard: The MIR Benchmark for Progressive Interleaved Multi-Image Reasoning

Multi-image Interleaved Reasoning aims to improve Multi-modal Large Language Models (MLLMs) ability to jointly comprehend and reason across multiple images and their associated textual contexts, introducing unique challenges beyond single-image or non-interleaved multi-image tasks. While current multi-image benchmarks overlook interleaved textual contexts and neglect distinct relationships between individual images and their associated texts, enabling models to reason over multi-image interleaved data may significantly enhance their comprehension of complex scenes and better capture cross-modal correlations. To bridge this gap, we introduce a novel benchmark MIR, requiring joint reasoning over multiple images accompanied by interleaved textual contexts to accurately associate image regions with corresponding texts and logically connect information across images. To enhance MLLMs ability to comprehend multi-image interleaved data, we introduce reasoning steps for each instance within the benchmark and propose a stage-wise curriculum learning strategy. This strategy follows an "easy to hard" approach, progressively guiding models from simple to complex scenarios, thereby enhancing their ability to handle challenging tasks. Extensive experiments benchmarking multiple MLLMs demonstrate that our method significantly enhances models reasoning performance on MIR and other established benchmarks. We believe that MIR will encourage further research into multi-image interleaved reasoning, facilitating advancements in MLLMs capability to handle complex inter-modal tasks.

cs.CV↗

arXiv2025

Characterizing the limiting critical Potts measures on locally regular-tree-like expander graphs

For any integers $d,q\ge 3$, we consider the $q$-state ferromagnetic Potts model with an external field on a sequence of expander graphs that converges to the $d$-regular tree $\mathtt{T}_d$ in the Benjamini-Schramm sense. We show that along the critical line, any subsequential local weak limit of the Potts measures is a mixture of the free and wired Potts Gibbs measures on $\mathtt{T}_d$. Furthermore, we show the possibility of an arbitrary extent of strong phase coexistence: for any $\alpha\in [0,1]$, there exists a sequence of locally $\mathtt{T}_d$-like expander graphs $\{G_n\}$, such that the Potts measures on $\{G_n\}$ locally weakly converges to the $(\alpha,1-\alpha)$-mixture of the free and wired Potts Gibbs measures. Our result extends results of \cite{HJP23} which restrict to the zero-field case and also require $q$ to be sufficiently large relative to $d$, and results of \cite{BDS23} which restrict to the even $d$ case. We also confirm the phase coexistence prediction of \cite{BDS23}, asserting that the Potts local weak limit is a genuine mixture of the free and wired states in a generic setting. We further characterize the subsequential local weak limits of random cluster measures on such graph sequences, for any cluster parameter $q>2$ (not necessarily integer).

math.PR↗

arXiv2025

Asymptotic diameter of preferential attachment model

We study the asymptotic diameter of the preferential attachment model $\operatorname{PA}\!_n^{(m,\delta)}$ with parameters $m \ge 2$ and $\delta > 0$. Building on the recent work \cite{VZ25}, we prove that the diameter of $G_n \sim \operatorname{PA}\!_n^{(m,\delta)}$ is $(1+o(1))\log_\nu n$ with high probability, where $\nu$ is the exponential growth rate of the local weak limit of $G_n$. Our result confirms the conjecture in \cite{VZ25} and closes the remaining gap in understanding the asymptotic diameter of preferential attachment graphs with general parameters $m \ge 1$ and $\delta >-m$. Our proof follows a general recipe that relates the diameter of a random graph to its typical distance, which we expect to have applicability in a broader range of models.

math.PR↗

arXiv2025

Sharp threshold for network recovery from voter model dynamics

We investigate the problem of recovering a latent directed Erd\H{o}s-R\'enyi graph $G^*\sim \mathcal G(n,p)$ from observations of discrete voter model trajectories on $G^*$, where $np$ grows polynomially in $n$. Given access to $M$ independent voter model trajectories evolving up to time $T$, we establish that $G^*$ can be recovered \emph{exactly} with probability at least $0.9$ by an \emph{efficient} algorithm, provided that \[ M \cdot \min\{T, n\} \geq C n^2 p^2 \log n \] holds for a sufficiently large constant $C$. Here, $M\cdot \min\{T,n\}$ can be interpreted as the approximate number of effective update rounds being observed, since the voter model on $G^*$ typically reaches consensus after $\Theta(n)$ rounds, and no further information can be gained after this point. Furthermore, we prove an \emph{information-theoretic} lower bound showing that the above condition is tight up to a constant factor. Our results indicate that the recovery problem does not exhibit a statistical-computational gap.

math.PR↗

arXiv2025

Optimal recovery of correlated Erd\H{o}s-R\'enyi graphs

For two unlabeled graphs $G_1,G_2$ independently sub-sampled from an Erd\H{o}s-R\'enyi graph $\mathbf G(n,p)$ by keeping each edge with probability $s$, we aim to recover \emph{as many as possible} of the corresponding vertex pairs. We establish a connection between the recoverability of vertex pairs and the balanced load allocation in the true intersection graph of $ G_1 $ and $ G_2 $. Using this connection, we analyze the partial recovery regime where $ p = n^{-\alpha + o(1)} $ for some $ \alpha \in (0, 1] $ and $ nps^2 = \lambda = O(1) $. We derive upper and lower bounds for the recoverable fraction in terms of $ \alpha $ and the limiting load distribution $ \mu_\lambda $ (as introduced in \cite{AS16}). These bounds coincide asymptotically whenever $ \alpha^{-1} $ is not an atom of $ \mu_\lambda $. Therefore, for each fixed $ \lambda $, our result characterizes the asymptotic optimal recovery fraction for all but countably many $ \alpha \in (0, 1] $.

math.PR↗

arXiv2025

A Proof of The Changepoint Detection Threshold Conjecture in Preferential Attachment Models

We investigate the problem of detecting and estimating a changepoint in the attachment function of a network evolving according to a preferential attachment model on $n$ vertices, using only a single final snapshot of the network. Bet et al.~\cite{bet2023detecting} show that a simple test based on thresholding the number of vertices with minimum degrees can detect the changepoint when the change occurs at time $n-\Omega(\sqrt{n})$. They further make the striking conjecture that detection becomes impossible for any test if the change occurs at time $n-o(\sqrt{n}).$ Kaddouri et al.~\cite{kaddouri2024impossibility} make a step forward by proving the detection is impossible if the change occurs at time $n-o(n^{1/3}).$ In this paper, we resolve the conjecture affirmatively, proving that detection is indeed impossible if the change occurs at time $n-o(\sqrt{n}).$ Furthermore, we establish that estimating the changepoint with an error smaller than $o(\sqrt{n})$ is also impossible, thereby confirming that the estimator proposed in Bhamidi et al.~\cite{bhamidi2018change} is order-optimal.

math.PR↗

arXiv2024

Exploring What Why and How: A Multifaceted Benchmark for Causation Understanding of Video Anomaly

Recent advancements in video anomaly understanding (VAU) have opened the door to groundbreaking applications in various fields, such as traffic monitoring and industrial automation. While the current benchmarks in VAU predominantly emphasize the detection and localization of anomalies. Here, we endeavor to delve deeper into the practical aspects of VAU by addressing the essential questions: "what anomaly occurred?", "why did it happen?", and "how severe is this abnormal event?". In pursuit of these answers, we introduce a comprehensive benchmark for Exploring the Causation of Video Anomalies (ECVA). Our benchmark is meticulously designed, with each video accompanied by detailed human annotations. Specifically, each instance of our ECVA involves three sets of human annotations to indicate "what", "why" and "how" of an anomaly, including 1) anomaly type, start and end times, and event descriptions, 2) natural language explanations for the cause of an anomaly, and 3) free text reflecting the effect of the abnormality. Building upon this foundation, we propose a novel prompt-based methodology that serves as a baseline for tackling the intricate challenges posed by ECVA. We utilize "hard prompt" to guide the model to focus on the critical parts related to video anomaly segments, and "soft prompt" to establish temporal and spatial relationships within these anomaly segments. Furthermore, we propose AnomEval, a specialized evaluation metric crafted to align closely with human judgment criteria for ECVA. This metric leverages the unique features of the ECVA dataset to provide a more comprehensive and reliable assessment of various video large language models. We demonstrate the efficacy of our approach through rigorous experimental analysis and delineate possible avenues for further investigation into the comprehension of video anomaly causation.

cs.CV↗

arXiv2024

Leveraging Propagated Infection to Crossfire Mutants

Mutation testing was proposed to identify weaknesses in test suites by repeatedly generating artificially faulty versions of the software (mutants) and determining if the test suite is sufficient to detect them (kill them). When the tests are insufficient, each surviving mutant provides an opportunity to improve the test suite. We conducted a study and found that many such surviving mutants (up to 84% for the subjects of our study) are detectable by simply augmenting existing tests with additional assertions, or assertion amplification. Moreover, we find that many of these mutants are detectable by multiple existing tests, giving developers options for how to detect them. To help with these challenges, we created a technique that performs memory-state analysis to identify candidate assertions that developers can use to detect the surviving mutants. Additionally, we build upon prior research that identifies ``crossfiring'' opportunities -- tests that coincidentally kill multiple mutants. To this end, we developed a theoretical model that describes the varying granularities that crossfiring can occur in the existing test suite, which provide opportunities and options for how to kill surviving mutants. We operationalize this model to an accompanying technique that optimizes the assertion amplification of the existing tests to crossfire multiple mutants with fewer added assertions, optionally concentrated within fewer tests. Our experiments show that we can kill all surviving mutants that are detectable with existing test data with only 1.1% of the identified assertion candidates, and increasing by a factor of 6x, on average, the number of killed mutants from amplified tests, over tests that do not crossfire.

cs.SE↗

arXiv2024

Uncovering What, Why and How: A Comprehensive Benchmark for Causation Understanding of Video Anomaly

Video anomaly understanding (VAU) aims to automatically comprehend unusual occurrences in videos, thereby enabling various applications such as traffic surveillance and industrial manufacturing. While existing VAU benchmarks primarily concentrate on anomaly detection and localization, our focus is on more practicality, prompting us to raise the following crucial questions: "what anomaly occurred?", "why did it happen?", and "how severe is this abnormal event?". In pursuit of these answers, we present a comprehensive benchmark for Causation Understanding of Video Anomaly (CUVA). Specifically, each instance of the proposed benchmark involves three sets of human annotations to indicate the "what", "why" and "how" of an anomaly, including 1) anomaly type, start and end times, and event descriptions, 2) natural language explanations for the cause of an anomaly, and 3) free text reflecting the effect of the abnormality. In addition, we also introduce MMEval, a novel evaluation metric designed to better align with human preferences for CUVA, facilitating the measurement of existing LLMs in comprehending the underlying cause and corresponding effect of video anomalies. Finally, we propose a novel prompt-based method that can serve as a baseline approach for the challenging CUVA. We conduct extensive experiments to show the superiority of our evaluation metric and the prompt-based approach. Our code and dataset are available at https://github.com/fesvhtr/CUVA.

cs.CV↗

arXiv2024

1st Place Solution for ICCV 2023 OmniObject3D Challenge: Sparse-View Reconstruction

In this report, we present the 1st place solution for ICCV 2023 OmniObject3D Challenge: Sparse-View Reconstruction. The challenge aims to evaluate approaches for novel view synthesis and surface reconstruction using only a few posed images of each object. We utilize Pixel-NeRF as the basic model, and apply depth supervision as well as coarse-to-fine positional encoding. The experiments demonstrate the effectiveness of our approach in improving sparse-view reconstruction quality. We ranked first in the final test with a PSNR of 25.44614.

cs.CV↗