arXiv subjects

Jian Ding

Publications and source records attributed to Jian Ding.

At least 37 records · Page 2Linked to original sources

arXiv2026

Percolation of thick points of the log-correlated Gaussian field in high dimensions

We prove that the set of thick points of the log-correlated Gaussian field contains an unbounded path in sufficiently high dimensions. This contrasts with the two-dimensional case, where Aru, Papon, and Powell (2023) showed that the set of thick points is totally disconnected. This result has an interesting implication for the exponential metric of the log-correlated Gaussian field: in sufficiently high dimensions, when the parameter $ξ$ is large, the set-to-set distance exponent (if it exists) is negative. This suggests that a new phase may emerge for the exponential metric, which does not appear in two dimensions. In addition, we establish similar results for the set of thick points of the branching random walk. As an intermediate result, we also prove that the critical probability for fractal percolation converges to 0 as $d \to \infty$.

math.PR↗

arXiv2026

Separation and cut edge in macroscopic clusters for metric graph Gaussian free fields

We prove that for the Gaussian free field (GFF) on the metric graph of $\mathbb{Z}^d$ (for all $d\ge 3$ except the critical dimension $d_c=6$), with uniformly positive probability there exist two distinct sign clusters of diameter at least $cN$ within a box of size $N$ such that their graph distance is less than $N^{-[(d-2)\vee (2d-8)]}$. This phenomenon contrasts sharply with the two-dimensional case, where the distance between two macroscopic clusters is typically on the order of their diameters, following from the basic property of the scaling limit ``conformal loop ensembles'' $\mathrm{CLE}_4$ (Sheffield-Werner'2001). As a byproduct, we derive that the number of pivotal edges for the one-arm event (i.e., the sign cluster containing the origin has diameter at least $N$) is typically of order $N^{(\frac{d}{2}-1)\land 2}$. This immediately implies that for the incipient infinite cluster (IIC) of the metric graph GFF, the dimension of cut edges (i.e., edges whose removal disconnects the IIC) equals $(\frac{d}{2}-1)\land 2$. Translated in the language of critical loop soups (whose clusters, by the isomorphism theorem, have the same distribution as GFF sign clusters), this leads to the analogous estimates where the counterpart of a pivotal edge is a pivotal loop at scale $1$. This result hints at the new and possibly surprising idea that already in dimension $3$, microscopic loops (even those at scale $1$) play a crucial role in the construction of macroscopic loop clusters.

math.PR↗

arXiv2026

On the gap between cluster dimensions of loop soups on $\mathbb{R}^3$ and the metric graph of $\mathbb{Z}^3$

The question of understanding the scaling limit of metric graph critical loop soup clusters and its relation to loop soups in the continuum appears to be one of the subtle cases that reveal interesting new scenarios about scaling limits, with a mixture of macroscopic and microscopic randomness. In the present paper, we show that in three dimensions, scaling limits of the metric graph clusters are strictly larger than the clusters of the limiting continuum Brownian loop soup. We actually show that the upper box counting dimension of the latter clusters is strictly smaller than $5/2$, while that of the former is $5/2$.

math.PR↗

arXiv2025

iMotion-LLM: Instruction-Conditioned Trajectory Generation

We introduce iMotion-LLM, a large language model (LLM) integrated with trajectory prediction modules for interactive motion generation. Unlike conventional approaches, it generates feasible, safety-aligned trajectories based on textual instructions, enabling adaptable and context-aware driving behavior. It combines an encoder-decoder multimodal trajectory prediction model with a pre-trained LLM fine-tuned using LoRA, projecting scene features into the LLM input space and mapping special tokens to a trajectory decoder for text-based interaction and interpretable driving. To support this framework, we introduce two datasets: 1) InstructWaymo, an extension of the Waymo Open Motion Dataset with direction-based motion instructions, and 2) Open-Vocabulary InstructNuPlan, which features safety-aligned instruction-caption pairs and corresponding safe trajectory scenarios. Our experiments validate that instruction conditioning enables trajectory generation that follows the intended condition. iMotion-LLM demonstrates strong contextual comprehension, achieving 84% average accuracy in direction feasibility detection and 96% average accuracy in safety evaluation of open-vocabulary instructions. This work lays the foundation for text-guided motion generation in autonomous driving, supporting simulated data generation, model interpretability, and robust safety alignment testing for trajectory generation models. Our code, pre-trained model, and datasets are available at: https://vision-cair.github.io/iMotion-LLM/.

cs.CV↗

arXiv2025

Dynamical random field Ising model at zero temperature

In this paper, we study the evolution of the zero-temperature random field Ising model as the mean of the external field $M$ increases from $-\infty$ to $\infty$. We focus on two types of evolutions: the ground state evolution and the Glauber evolution. For the ground state evolution, we investigate the occurrence of global avalanche, a moment where a large fraction of spins flip simultaneously from minus to plus. In two dimensions, no global avalanche occurs, while in three or higher dimensions, there is a phase transition: a global avalanche happens when the noise intensity is small, but not when it is large. Additionally, we study the zero-temperature Glauber evolution, where spins are updated locally to minimize the Hamiltonian. Our results show that for small noise intensity, in dimensions $d =2$ or $3$, most spins flip around a critical time $c_d = \frac{2 \sqrt{d}}{1 + \sqrt{d}}$ (but we cannot decide whether such flipping occurs simultaneously or not). We also connect this process to polluted bootstrap percolation and solve an open problem on it.

math.PR↗

arXiv2025

InfiniBench: A Benchmark for Large Multi-Modal Models in Long-Form Movies and TV Shows

Understanding long-form videos, such as movies and TV episodes ranging from tens of minutes to two hours, remains a significant challenge for multi-modal models. Existing benchmarks often fail to test the full range of cognitive skills needed to process these temporally rich and narratively complex inputs. Therefore, we introduce InfiniBench, a comprehensive benchmark designed to evaluate the capabilities of models in long video understanding rigorously. InfiniBench offers:(1) Over 1,000 hours of video content, with an average video length of 53 minutes. (2) The largest set of question-answer pairs for long video comprehension, totaling around 87.7 K. (3) Eight diverse skills that span both grounding-based (e.g., scene transitions, character actions) and reasoning-based (e.g., deep context understanding, multi-event linking). (4) Rich annotation formats, including both multiple-choice and open-ended questions. We conducted an in-depth evaluation across both commercial (GPT-4o, Gemini 2.0 Flash) and most recent open-source vision-language models such as Qwen2.5-VL, InternVL3.0). Results reveal that:(1) Models struggle across the board: Even the best model, GPT-4o, achieves only 47.1 % on grounding-based skills, with most models performing near or just above random chance. (2) Strong reliance on world knowledge: Models achieve surprisingly high scores using only metadata (e.g., video titles), highlighting a tendency to rely on pre-trained knowledge rather than actual visual or temporal understanding. (3) Multi-Modal Importance: When provided with full video and subtitle context, however, models show substantial improvements, confirming the critical role of multimodal input in video understanding. InfiniBench is publicly available at https://vision-cair.github.io/Infinibench

cs.CV↗

arXiv2025

When LLMs step into the 3D World: A Survey and Meta-Analysis of 3D Tasks via Multi-modal Large Language Models

As large language models (LLMs) evolve, their integration with 3D spatial data (3D-LLMs) has seen rapid progress, offering unprecedented capabilities for understanding and interacting with physical spaces. This survey provides a comprehensive overview of the methodologies enabling LLMs to process, understand, and generate 3D data. Highlighting the unique advantages of LLMs, such as in-context learning, step-by-step reasoning, open-vocabulary capabilities, and extensive world knowledge, we underscore their potential to significantly advance spatial comprehension and interaction within embodied Artificial Intelligence (AI) systems. Our investigation spans various 3D data representations, from point clouds to Neural Radiance Fields (NeRFs). It examines their integration with LLMs for tasks such as 3D scene understanding, captioning, question-answering, and dialogue, as well as LLM-based agents for spatial reasoning, planning, and navigation. The paper also includes a brief review of other methods that integrate 3D and language. The meta-analysis presented in this paper reveals significant progress yet underscores the necessity for novel approaches to harness the full potential of 3D-LLMs. Hence, with this paper, we aim to chart a course for future research that explores and expands the capabilities of 3D-LLMs in understanding and interacting with the complex 3D world. To support this survey, we have established a project page where papers related to our topic are organized and listed: https://github.com/ActiveVisionLab/Awesome-LLM-3D.

cs.CV↗

arXiv2025

Detecting Correlation Efficiently in Stochastic Block Models: Breaking Otter's Threshold in the Entire Supercritical Regime

Consider a pair of sparse correlated stochastic block models $\mathcal S(n,\tfracλ{n},ε;s)$ subsampled from a common parent stochastic block model with two symmetric communities, average degree $λ=O(1)$, divergence parameter $ε\in (0,1)$ and subsampling probability $s$. For all $ε\in(0,1)$ and $Δ>0$, we construct a statistic based on the combination of two low-degree polynomials and show that there exists a sufficiently small constant $δ=δ(ε,λ,Δ)>0$ such that if $ε^2 λs>1+Δ$ and $s>\sqrtα-δ$ where $α\approx 0.338$ is Otter's constant, this statistic can distinguish this model and a pair of independent stochastic block models $\mathcal S(n,\tfrac{λs}{n},ε)$ with probability $1-o(1)$. We also provide an efficient algorithm that approximates this statistic in polynomial time. The crux of our statistic's construction lies in a carefully curated family of multigraphs called \emph{decorated trees}, which enables effective aggregation of the community signal and graph correlation by leveraging the counts of the same decorated tree while suppressing the undesirable correlations among counts of different decorated trees. We believe such construction may be of independent interest.

cs.DS↗

arXiv2025

Efficiently matching random inhomogeneous graphs via degree profiles

In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending the matching algorithm via degree profiles by Ding, Ma, Wu and Xu (2021), we obtain an efficient matching algorithm as long as the minimal average degree is at least $Ω(\log^{2} n)$ and the minimal correlation is at least $1 - O(\log^{-2} n)$.

cs.DS↗

arXiv2025

Kestrel: 3D Multimodal LLM for Part-Aware Grounded Description

In this paper, we introduce Part-Aware Point Grounded Description (PaPGD), a challenging task aimed at advancing 3D multimodal learning for fine-grained, part-aware segmentation grounding and detailed explanation of 3D objects. Existing 3D datasets largely focus on either vision-only part segmentation or vision-language scene segmentation, lacking the fine-grained multimodal segmentation needed for robotic navigation and interaction in real-world environments. To address this gap, we present the 3DCoMPaT Grounded Instructions (3DCoMPaT-GrIn) Dataset, a comprehensive resource that pairs rich point cloud descriptions with corresponding part-level segmentation masks. This dataset encompasses extensive samples designed for both PaPGD and fine-grained single-part grounding tasks. To tackle the inherent challenges of grounding objects and generating grounded descriptions at the part level, we propose Kestrel, a part-aware 3D multimodal large language model that integrates an advanced language model for nuanced language comprehension with multi-level point feature propagation and query refinement mechanism to enhance spatial reasoning at the part level. The extensive experiments demonstrate that Kestrel effectively bridges the gap between part-aware language understanding and 3D segmentation grounding, paving the way for more robust and interpretable 3D object comprehension that meets the demands of real-world robotic applications. Project page at https://feielysia.github.io/Kestrel.github.io/

cs.CV↗

arXiv2025

A computational transition for detecting correlated stochastic block models by low-degree polynomials

Detection of correlation in a pair of random graphs is a fundamental statistical and computational problem that has been extensively studied in recent years. In this work, we consider a pair of correlated (sparse) stochastic block models $\mathcal{S}(n,\tfracλ{n};k,ε;s)$ that are subsampled from a common parent stochastic block model $\mathcal S(n,\tfracλ{n};k,ε)$ with $k=O(1)$ symmetric communities, average degree $λ=O(1)$, divergence parameter $ε$, and subsampling probability $s$. For the detection problem of distinguishing this model from a pair of independent Erdős-Rényi graphs with the same edge density $\mathcal{G}(n,\tfrac{λs}{n})$, we focus on tests based on \emph{low-degree polynomials} of the entries of the adjacency matrices, and we determine the threshold that separates the easy and hard regimes. More precisely, we show that this class of tests can distinguish these two models if and only if $s> \min \{ \sqrtα, \frac{1}{λε^2} \}$, where $α\approx 0.338$ is the Otter's constant and $\frac{1}{λε^2}$ is the Kesten-Stigum threshold. Combining a reduction argument in \cite{Li25+}, our hardness result also implies low-degree hardness for partial recovery and detection (to independent block models) when $s< \min \{ \sqrtα, \frac{1}{λε^2} \}$. Finally, our proof of low-degree hardness is based on a conditional variant of the low-degree likelihood calculation.

math.PR↗

arXiv2025

Diffusion-Based Imaginative Coordination for Bimanual Manipulation

Bimanual manipulation is crucial in robotics, enabling complex tasks in industrial automation and household services. However, it poses significant challenges due to the high-dimensional action space and intricate coordination requirements. While video prediction has been recently studied for representation learning and control, leveraging its ability to capture rich dynamic and behavioral information, its potential for enhancing bimanual coordination remains underexplored. To bridge this gap, we propose a unified diffusion-based framework for the joint optimization of video and action prediction. Specifically, we propose a multi-frame latent prediction strategy that encodes future states in a compressed latent space, preserving task-relevant features. Furthermore, we introduce a unidirectional attention mechanism where video prediction is conditioned on the action, while action prediction remains independent of video prediction. This design allows us to omit video prediction during inference, significantly enhancing efficiency. Experiments on two simulated benchmarks and a real-world setting demonstrate a significant improvement in the success rate over the strong baseline ACT using our method, achieving a \textbf{24.9\%} increase on ALOHA, an \textbf{11.1\%} increase on RoboTwin, and a \textbf{32.5\%} increase in real-world experiments. Our models and code are publicly available at https://github.com/return-sleep/Diffusion_based_imaginative_Coordination.

cs.RO↗

arXiv2025

Uniqueness and dimension for the geodesic of the critical long-range percolation metric

By recent works of Bäumler [2] and of the authors of this paper [5], the (limiting) random metric for the critical long-range percolation was constructed. In this paper, we prove the uniqueness of the geodesic between two fixed points, for which an important ingredient of independent interest is the continuity of the metric distribution. In addition, we establish the Hausdorff dimension of the geodesics.

math.PR↗

arXiv2025

The polynomial growth of effective resistances in one-dimensional critical long-range percolation

We study the critical long-range percolation on $\mathbb{Z}$, where an edge connects $i$ and $j$ independently with probability $1-\exp\{-β\int_i^{i+1}\int_j^{j+1}|u-v|^{-2}{\rm d} u{\rm d} v\}$ for $|i-j|>1$ for some fixed $β>0$ and with probability 1 for $|i-j|=1$. Viewing this as a random electric network where each edge has a unit conductance, we show that the effective resistances from 0 to $[-n,n]^c$ and from the interval $[-n,n]$ to $[-2n,2n]^c$ (conditioned on no edge joining $[-n,n]$ and $[-2n,2n]^c$) both grow like $n^{δ(β)}$ for some $δ(β)\in (0,1)$.

math.PR↗

arXiv2025

Efficient Tuning of Large Language Models for Knowledge-Grounded Dialogue Generation

Large language models (LLMs) demonstrate remarkable text comprehension and generation capabilities but often lack the ability to utilize up-to-date or domain-specific knowledge not included in their training data. To address this gap, we introduce KEDiT, an efficient method for fine-tuning LLMs for knowledge-grounded dialogue generation. KEDiT operates in two main phases: first, it employs an information bottleneck to compress retrieved knowledge into learnable parameters, retaining essential information while minimizing computational overhead. Second, a lightweight knowledge-aware adapter integrates these compressed knowledge vectors into the LLM during fine-tuning, updating less than 2\% of the model parameters. The experimental results on the Wizard of Wikipedia and a newly constructed PubMed-Dialog dataset demonstrate that KEDiT excels in generating contextually relevant and informative responses, outperforming competitive baselines in automatic, LLM-based, and human evaluations. This approach effectively combines the strengths of pretrained LLMs with the adaptability needed for incorporating dynamic knowledge, presenting a scalable solution for fields such as medicine.

cs.CL↗

arXiv2025

Distilling Implicit Multimodal Knowledge into Large Language Models for Zero-Resource Dialogue Generation

Integrating multimodal knowledge into large language models (LLMs) represents a significant advancement in dialogue generation capabilities. However, the effective incorporation of such knowledge in zero-resource scenarios remains a substantial challenge due to the scarcity of diverse, high-quality dialogue datasets. To address this, we propose the Visual Implicit Knowledge Distillation Framework (VIKDF), an innovative approach aimed at enhancing LLMs for enriched dialogue generation in zero-resource contexts by leveraging implicit multimodal knowledge. VIKDF comprises two main stages: knowledge distillation, using an Implicit Query Transformer to extract and encode visual implicit knowledge from image-text pairs into knowledge vectors; and knowledge integration, employing a novel Bidirectional Variational Information Fusion technique to seamlessly integrate these distilled vectors into LLMs. This enables the LLMs to generate dialogues that are not only coherent and engaging but also exhibit a deep understanding of the context through implicit multimodal cues, effectively overcoming the limitations of zero-resource scenarios. Our extensive experimentation across two dialogue datasets shows that VIKDF outperforms existing state-of-the-art models in generating high-quality dialogues. The code is available at https://github.com/zhangbo-nlp/VIKDF.

cs.CL↗

arXiv2025

Quasi-multiplicativity and regularity for metric graph Gaussian free fields

We prove quasi-multiplicativity for critical level-sets of Gaussian free fields (GFF) on the metric graphs $\widetilde{\mathbb{Z}}^d$ ($d\ge 3$). Specifically, we study the probability of connecting two general sets located on opposite sides of an annulus with inner and outer radii both of order $N$, where additional constraints are imposed on the distance of each set to the annulus. We show that for all $d \ge 3$ except the critical dimension $d=6$, this probability is of the same order as $N^{(6-d)\land 0}$ (serving as a correction factor) times the product of the two probabilities of connecting each set to the closer boundary of this annulus. The analogue for $d=6$ is also derived, although the upper and lower bounds differ by a divergent factor of $N^{o(1)}$. Notably, it was conjectured by Basu and Sapozhnikov (2017) that quasi-multiplicativity without correction factor holds for Bernoulli percolation on $\mathbb{Z}^d$ when $3\le d<6$ and fails when $d>6$. In high dimensions (i.e., $d>6$), taking into account the similarity between the metric graph GFF and Bernoulli percolation (which was proposed by Werner (2016) and later partly confirmed by the authors (2024)), our result provides support to the conjecture that Bernoulli percolation exhibits quasi-multiplicativity with correction factor $N^{6-d}$. During our proof of quasi-multiplicativity, numerous regularity properties, which are interesting in their own right, were also established. A crucial application of quasi-multiplicativity is proving the existence of the incipient infinite cluster (IIC), which has been completed by Basu and Sapozhnikov (2017) for Bernoulli percolation for $3\le d<6$. Inspired by their work, in a companion paper, we also utilize quasi-multiplicativity to establish the IIC for metric graph GFFs, for all $d\ge 3$ except for the critical dimension $6$.

math.PR↗

arXiv2025

Incipient infinite clusters and volume growth for Gaussian free fields and loop soups on metric graphs

In this paper, we establish the existence and equivalence of four types of incipient infinite clusters (IICs) for the critical Gaussian free field (GFF) level-set and the critical loop soup on the metric graph $\widetilde{\mathbb{Z}}^d$ for all $d\ge 3$ except the critical dimension $d=6$. These IICs are defined as four limiting conditional probabilities, involving different conditionings and various ways of taking limits: (1) conditioned on $\{0 \leftrightarrow{} \partial B(N)\}$ at criticality (where $0$ is the origin of $\mathbb{Z}^d$, and $\partial B(N)$ is the boundary of the box $B(N)$ centered at $0$ with side length $2N$), and letting $N\to \infty$; (2) conditioned on $\{0\leftrightarrow{} \infty\}$ at super-criticality, and letting the parameter tend to the critical threshold; (3) conditioned on $\{0 \leftrightarrow{} x\}$ at criticality (where $x\in \mathbb{Z}^d$ is a lattice point), and letting $x\to \infty$; (4) conditioned on the event that the capacity of the critical cluster containing $0$ exceeds $T$, and letting $T\to \infty$. Our proof employs a robust framework of Basu and Sapozhinikov (2017) for constructing IICs as in (1) and (2) for Bernoulli percolation in low dimensions (i.e., $3\le d\le 5$), where a key hypothesis on the quasi-multiplicativity is proved in our companion paper. We further show that conditioned on $\{0 \leftrightarrow{} \partial B(N)\}$, the volume of the critical cluster containing $0$ within $B(M)$ is typically of order $M^{(\frac{d}{2}+1)\land 4}$, as long as $N\gg M$. This phenomenon indicates that the critical cluster of the GFF or the loop soup exhibits self-similarity, which supports Werner's conjecture (2016) that such cluster has a scaling limit. Moreover, the exponent of $M^{(\frac{d}{2}+1)\land 4}$ matches the conjectured fractal dimension of the scaling limit proposed by Werner (2016).

math.PR↗