arXiv subjects
Publications and source records attributed to Jian Ding.
We prove that on the metric graph of $\mathbb{Z}^d$ for $d\in \{3,4,5\}$, clusters of the critical loop soup (or equivalently, clusters of the critical Gaussian free field level-set) admit a scaling limit. To the best of our knowledge, this presents the first scaling limit result for a percolation model on a three-dimensional lattice.
Although highly effective in vision and language domains, applying in-context learning to robotics remains challenging. Existing autoregressive in-context imitation methods discretize continuous actions and exacerbate the accumulation of early prediction errors through next-token prediction, limiting their generalization on unseen task configurations. Meanwhile, flow-matching policies have been explored for continuous robot control and can help mitigate compounding errors; however, in-context imitation learning within a flow-matching framework remains underexplored. To address these limitations, we introduce ContextFlow, a conditional flow-matching model that learns continuous action distributions for in-context imitation learning. ContextFlow conditions flow-based action prediction on demonstrations and observations, enabling robust generation from noisy action distributions. To better encode multimodal in-context demonstrations, we adapt perceiver-style multimodal context compressors that distill visual, proprioceptive, and action sequences into compact, task-relevant latent representations. On LIBERO, ContextFlow outperforms ICRT by 35 percentage points in average success rate on unseen task configurations, while matching the performance of the task-specific fine-tuned VLA model $\pi_0$ without any fine-tuning on unseen tasks. On real robots, it generalizes to unseen configurations of both single-arm and bimanual tasks, achieving 40% success on a new pen-uncapping configuration. Project Page: https://dingjiansw101.github.io/contextflow-page/.
Large Vision-Language Models (VLMs) now act as agents in interactive environments, where success requires coherent reasoning and decision-making across turns. Although end-to-end training in agentic environments can improve such multi-turn decision-making abilities, current methods mainly rely on either token-wise optimization over concatenated token trajectories or turn-wise optimization with uniform within-turn credit. In this work, we establish theoretical formulations for the two levels of optimization and derive a hybrid advantage that serves both objectives. Furthermore, with an appropriate choice of discount factor and learning target, we prove that a unified critic model can estimate values for both turn-wise and token-wise. As such, we propose HyGAE, an actor-critic framework that jointly optimizes token- and turn-level objectives with the hybrid advantage and unified critic. We conduct extensive evaluations of HyGAE across five multi-turn decision-making environments, where it achieves an average success rate of 91% and a significant improvement of 10% over other methods. Furthermore, we provide an in-depth analysis showing that the exact analytic form of the hybrid advantage and return is crucial for optimization. Project Page: https://wx-zhang.github.io/hygae-web/.
The evolution of e-commerce has fundamentally transformed how users search for products, shifting from simple text-based keyword queries to complex multimodal interactions that seamlessly combine product images, natural language descriptions, and mixed-intent instructions. However, existing approaches face a critical dilemma: single-modal specialist models, deployed independently for text retrieval, visual search, and voice recognition, operate in isolation and cannot handle cross-modal queries, while general-purpose vision-language models lack the domain-specific knowledge necessary for fine-grained product understanding, user behavior modeling, and commercial intent reasoning. In this work, we present Pailitao-MMSearch, one native e-commerce multimodal search foundation model designed to bridge this gap. Our approach introduces three key innovations: (1)HybSID (Hybrid Semantic ID);(2)a two-stage continual pre-training strategy; and (3)a hybrid reasoning post-training pipeline. Built upon Qwen and deployed on Taobao's Pailitao multimodal search platform, Pailitao-MMSearch achieves substantial improvements in online A/B testing, including up to +13.61\% in Gross Merchandise Volume (GMV) and +8.21\% in transaction volume compared to traditional multi-modal search pipeline, demonstrating the effectiveness of our native e-commerce multimodal search large language models.
Reconstructing articulated objects from sparse images requires recovering complete geometry, movable parts, and motion parameters. Recent methods typically separate geometry reconstruction, part reasoning, and articulation estimation into different stages. This separation can weaken consistency between shape, active parts, and motion, while also incurring substantial inference cost. We introduce Artic-O, an end-to-end, feed-forward framework for articulated object reconstruction via latent geometry learning. Instead of fitting geometry in image or view space, Artic-O maps sparse multi-state observations into a pretrained latent geometry space, where a frozen flow-matching decoder provides a complete-shape prior for recovering visible and occluded structures. To connect geometry with articulation, Artic-O fuses visual tokens, geometry latents, and point-wise decoder features in an image-grounded part-reasoning module for active-part segmentation and articulation prediction. We further train the model with a geometry-to-articulation curriculum and a decoupled two-pass strategy to balance reconstruction and part-level supervision. On PartNet-Mobility, Artic-O achieves strong reconstruction quality while being substantially more efficient than LARM, a strong prior method. It reduces Chamfer Distance, improves F-score, and achieves comparable or better articulation accuracy across most joint metrics, while reducing inference time from 9 minutes to about 0.3 seconds per object.
Multi-hop question answering requires systems to retrieve evidence from multiple documents and connect scattered facts into a coherent reasoning process. Standard retrieval-augmented generation (RAG) mainly relies on semantic similarity between a query and text chunks, and therefore often fails to model structural relations among entities, facts, and evidence units. Graph-based RAG improves this by introducing graph-structured knowledge, but pairwise edges are still limited in representing higher-order associations involving multiple entities and contexts. We propose HyCE-RAG, a Hypergraph Chain-of-Evidence Retrieval-Augmented Generation framework for explainable multi-hop question answering. HyCE-RAG organizes entities, relations, and contextual evidence into hyperedges, builds a query-aware evidence hypergraph, and performs confidence propagation over entity--hyperedge incidence structures. It then uses confidence-guided evidence assembly to select, connect, and rank evidence paths before answer generation. The scoring process jointly considers semantic relevance, entity connectivity, evidence coverage, relation reliability, extraction confidence, and propagated confidence. By providing the language model with structured evidence chains rather than flat retrieved passages, HyCE-RAG supports more faithful and interpretable reasoning. Experiments on HotpotQA, 2WikiMultihopQA, MuSiQue, and two GraphRAG-Bench subsets show that HyCE-RAG consistently outperforms standard RAG and graph-based RAG baselines in answer accuracy, context relevance, and faithfulness. These results suggest that hypergraph-based evidence organization is a promising direction for post-retrieval reasoning in complex question answering.
World models enable language-model agents to predict environment dynamics and plan before acting. In text environments, the model must learn symbolic action effects from serialized state descriptions, but the role of serialization structure remains underexplored. We present HyperWorld, a controlled study of state serialization for learned textual world models. We compare raw observations with three symbolic serializations of the same ground-truth state: independent sentences, pairwise triples, and entity-centered hyperedge units that group multiple related facts around entities and relations. All variants use the same training objective: given a state and an action, predict symbolic effects or judge the action infeasible. Across model scales, data budgets, and in-distribution and out-of-distribution test worlds, hyperedge serialization gives the clearest gains for 0.5B--1.5B models and under distribution shift. Larger models reduce the gap, and pairwise triples can match or slightly exceed hyperedges on in-distribution exact match, but hyperedges achieve the strongest out-of-distribution fact F1 and the best small-to-medium scale trade-off between feasibility detection and effect prediction. In downstream greedy planning, the hyperedge world model also attains the highest success rate among the tested representations. These results show that higher-order state organization is a simple but effective inductive bias for learned symbolic world models, especially when model capacity is limited or test environments differ from training.
Conjunctive Hierarchical Secret Sharing (CHSS) is a type of secret sharing that divides participants into multiple distinct hierarchical levels, with each level having a specific threshold. An authorized subset must simultaneously meet the threshold of all levels. Existing Chinese Remainder Theorem (CRT)-based CHSS schemes either have security vulnerabilities or have an information rate lower than $\frac{1}{2}$. In this work, we utilize the CRT for polynomial ring and one-way functions to construct an asymptotically perfect CHSS scheme. It has computational security, and permits flexible share sizes. Notably, when all shares are of equal size, our scheme is an asymptotically ideal CHSS scheme with an information rate one.
In Shamir's secret sharing scheme, all participants possess equal privileges. However, in many practical scenarios, it is often necessary to assign different levels of authority to different participants. To address this requirement, Hierarchical Secret Sharing (HSS) schemes were developed, which partitioned all participants into multiple subsets and assigned a distinct privilege level to each. Existing Chinese Remainder Theorem (CRT)-based HSS schemes benefit from flexible share sizes, but either exhibit security flaws or have an information rate less than $\frac{1}{2}$. In this work, we propose a disjunctive HSS scheme and a conjunctive HSS scheme by using the CRT for integer ring and one-way functions. Both schemes are asymptotically ideal and are proven to be secure.
Turbulence mitigation (TM) is highly ill-posed due to the stochastic nature of atmospheric turbulence. Most methods rely on multiple frames recorded by conventional cameras to capture stable patterns in natural scenarios. However, they inevitably suffer from a trade-off between accuracy and efficiency: more frames enhance restoration at the cost of higher system latency and larger data overhead. Event cameras, equipped with microsecond temporal resolution and efficient sensing of dynamic changes, offer an opportunity to break the bottleneck. In this work, we present EHETM, a high-quality and efficient TM method inspired by the superiority of events to model motions in continuous sequences. We discover two key phenomena: (1) turbulence-induced events exhibit distinct polarity alternation correlated with sharp image gradients, providing structural cues for restoring scenes; and (2) dynamic objects form spatiotemporally coherent ``event tubes'' in contrast to irregular patterns within turbulent events, providing motion priors for disentangling objects from turbulence. Based on these insights, we design two complementary modules that respectively leverage polarity-weighted gradients for scene refinement and event-tube constraints for motion decoupling, achieving high-quality restoration with few frames. Furthermore, we construct two real-world event-frame turbulence datasets covering atmospheric and thermal cases. Experiments show that EHETM outperforms SOTA methods, especially under scenes with dynamic objects, while reducing data overhead and system latency by approximately 77.3% and 89.5%, respectively. Our code is available at: https://github.com/Xavier667/EHETM.
Disjunctive Hierarchical Secret Sharing (DHSS) scheme is a secret sharing scheme in which the set of all participants is partitioned into disjoint subsets. Each disjoint subset is said to be a level, and different levels have different degrees of trust and different thresholds. If the number of cooperating participants from a given level falls to meet its threshold, the shortfall can be compensated by participants from higher levels. Many ideal DHSS schemes have been proposed, but they often suffer from big share sizes. Conversely, existing non-ideal DHSS schemes achieve small share sizes, yet they fail to be both secure and asymptotically ideal simultaneously. In this work, we present an explicit construct of an asymptotically ideal DHSS scheme by using a polynomial, multiple linear homogeneous recurrence relations and one-way functions. Although our scheme has computational security and many public values, it has a small share size and the dealer is required polynomial time.
Disjunctive Hierarchical Secret Sharing (DHSS)} scheme is a type of secret sharing scheme in which the set of all participants is partitioned into disjoint subsets, and each subset is said to be a level with different degrees of trust and different thresholds. In this work, we focus on the Chinese Remainder Theorem (CRT)-based DHSS schemes due to their ability to accommodate flexible share sizes. We point out that the ideal DHSS scheme of Yang et al. (ISIT, 2024) and the asymptotically ideal DHSS scheme of Tiplea et al. (IET Information Security, 2021) are insecure. Consequently, existing CRT-based DHSS schemes either exhibit security flaws or have an information rate less than $\frac{1}{2}$. To address these limitations, we propose a CRT-based asymptotically perfect DHSS scheme that supports flexible share sizes. Notably, our scheme is asymptotically ideal when all shares are equal in size. Its information rate achieves one and it has computational security.
For the Gaussian free field on the metric graph of $\mathbb{Z}^d$ ($d\ge 3$), we consider the heterochromatic two-arm probability, i.e., the probability that two points $v$ and $v'$ are contained in distinct clusters of opposite signs with diameters at least $N$. For all $d\ge 3$ except the critical dimension $d_c=6$, we prove that this probability is asymptotically proportional to $N^{-[(\frac{d}{2}+1)\land 4]}$. Furthermore, we prove that conditioned on this two-arm event, the volume growth of each involved cluster is comparable to that of a typical (unconditioned) cluster; precisely, each cluster has a volume of order $M^{(\frac{d}{2}+1)\land 4}$ within a box of size $M$.
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.
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 $5/2$.
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.
By recent works of B\"aumler [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.
We study the critical long-range percolation on $\mathbb{Z}$, where an edge connects $i$ and $j$ independently with probability $1-\exp\{-\beta\int_i^{i+1}\int_j^{j+1}|u-v|^{-2}{\rm d} u{\rm d} v\}$ for $|i-j|>1$ for some fixed $\beta>0$ 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 $n^{\delta(\beta)}$ for some $\delta(\beta)\in (0,1)$.