arXiv subjects

Lujia Wang

Publications and source records attributed to Lujia Wang.

At least 19 recordsLinked to original sources

arXiv2026

Balanced even cycles in signed graphs:Tur\'an bounds, double covers, and parity obstructions

We study Tur\'an problems for balanced even cycles in simple signed graphs, where signed subgraphs are considered up to switching. For every balanced bipartite signed graph, the signed and ordinary Tur\'an numbers differ by at most a factor of two. Our main structural results concern the underlying graphs that admit a signing in which every $2k$-cycle is unbalanced. We characterize these graphs by the absence of an odd dependence among their $2k$-cycle incidence vectors, give a cohomological formulation, and construct subgraph-minimal obstructions of arbitrarily large order. In particular, there is no finite forbidden-subgraph characterization. We also give an exact closed-walk criterion for cycles in double covers and derive a direct signed breadth-first-search upper bound. As applications, we prove \[ \hex(n,C_{+4})=\left(\frac{\sqrt2}{2}+o(1)\right)n^{3/2} \] and study the signed hexagon number $R_6(n)=\hex(n,\{C_{-3},C_{+6}\})$. We characterize the underlying graphs counted by $R_6$ and express it as an extremal problem for ordinary $C_6$-free graphs with a prescribed involution. For every sufficiently large $n$, we construct examples with $\Omega(n^{4/3})$ edges, and we give an equivariant construction attaining the coefficient obtained from the F\"uredi--Naor--Verstra\"ete lower bound by double-cover transfer. Finally, we give $n$-vertex $C_{+10}$-free signed graphs with $\Omega(n^{6/5})$ edges and use octagon examples to illustrate the limitations of theta-freeness as a signing criterion.

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arXiv2026

LIRA: Local Cross-Layer Information Routing for Vision-Language-Action Decoding

Vision-Language-Action (VLA) models transform representations from pretrained vision-language models (VLMs) into robot actions, yet the interface that routes intermediate VLM features into action decoders remains underexplored. Existing designs either expose only a narrow part of the representation hierarchy or rigidly match each decoder block to one VLM layer, restricting access to complementary task evidence across depths. We introduce LIRA, a local cross-layer action-conditioning mechanism that formulates VLM-to-action conditioning as depth-aware information routing. LIRA operates on task-token features and LIRA Query features derived from intermediate VLM states, then assigns each Parallel Fusion Block a depth-aligned local window centered on its corresponding VLM layer. Parallel Fusion Blocks aggregate neighboring LIRA Query features and integrate them with task-token features and proprioceptive inputs before action prediction. This routing interface leaves the backbone architecture, action decoder, and supervised training recipe unchanged. Across LIBERO, LIBERO-Plus, CALVIN ABC$\rightarrow$D, and real-world manipulation, LIRA improves the principal aggregate metrics over the VLA-Adapter baseline under the same 0.5B-parameter configuration. In zero-shot transfer to LIBERO-Plus, LIRA increases average success from 59.1% to 78.0%, an 18.9-point gain indicating improved robustness under controlled distribution shifts.

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arXiv2026

DreamTrajectory: Trajectory-Guided Action Generation with World Model Alignment for Mobile Manipulation

Mobile manipulation requires a robot to coordinate base and arm motion under continuously changing viewpoints and contact conditions, within an action space far larger than that of fixed-base manipulation. Existing Vision-Language-Action (VLA) policies are limited in two respects. (i)They map observations directly to whole-body action chunks, searching this large action space without an explicit task-space motion plan, which makes coordinated base--arm prediction imprecise. (ii)They execute the predicted chunk open-loop, without checking whether the actions can realize the motion the policy intended, so control errors and unmodeled contacts accumulate into a gap between planned and realized motion. We present DreamTrajectory, a trajectory-guided framework for language-conditioned mobile manipulation that introduces one component for each limitation. Addressing(i), DreamTrajectory jointly predicts an intention-level end-effector trajectory and a whole-body action chunk in a single action expert, so that the trajectory explicitly guides base--arm action generation instead of remaining implicit. Addressing(ii), a lightweight trajectory world model predicts the trajectory that a candidate action chunk would induce, and a test-time search--predict--score procedure selects the candidate best aligned with the planned trajectory. On MS-HAB, trajectory guidance raises average success from 32.3% to 47.5% and test-time refinement further to 54.8%, with the largest gains on contact-rich articulated-object tasks. On three real-world mobile manipulation tasks, the corresponding average success rates are 63.3%, 81.7%, and 90.0%.

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arXiv2026

Winding number and circular coloring

In 1996, Youngs proved a surprising theorem that quadrangulations of the projective plane could never have chromatic number exactly 3. This sparked a lot of interest, and the result has been further developed in many directions over the past decades. For example, the result is strengthened by considering the circular chromatic number, which is a real-valued lower bound on the chromatic number. The circular chromatic number of a quadrangulation cannot be in the interval (2,4). This parameter allows a generalization to larger even faces, for which a similar gap exists. In this work, we place these results into a framework based on the notion of winding number using extensions of colorings to continuous mappings. This yields unified and simplified proofs of gaps in the circular chromatic number for graphs with a distinguished set of directed even cycles. This generalizes the setting of graphs embedded on surfaces where every face is even. We further establish an analogous gap phenomenon when all faces are of a given odd length, previously known only in the case of triangulations. For example, we conclude that if G is a graph embedded on the projective plane such that all faces are 5-cycles, then either its circular chromatic number is 5/2 or at least 3, the former being the case only if G is Eulerian and every noncontractible facial walk is of odd length...

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arXiv2026

TactileReflex: Noise-Statistics-Driven Vision-Tactile Reflex Control for Force-Sensitive Manipulation

Manipulating fragile deformable containers, such as disposable plastic cups filled with liquid, demands real-time grip-force adaptation within an extremely narrow force margin: insufficient force causes slip, while excessive force irreversibly deforms the thin wall. Existing approaches struggle to achieve such force-sensitive manipulation tasks. We propose a noise-statistics-based calibration-driven reflex control paradigm with vision-based tactile sensing: by analyzing the sensor's intrinsic noise characteristics (via a brief static-hold-and-unload protocol), we directly derive all controller thresholds, eliminating external force calibration, trial-and-error manual tuning, or material-specific physical models. Instantiating this paradigm, we present TactileReflex, a three-channel closed-loop controller that extracts three image-level proxies, shear intensity ($S_y$), contact intensity ($F_n$), and center of pressure ($C$), from dual visuo-tactile sensors and drives prioritized reflex channels at ~12 Hz for slip suppression, weight-adaptive release, and force protection. Each channel closes the loop directly on its proxy via noise-derived thresholds. Ablation demonstrates that only the full three-channel system is able to prevent irreversible container deformation (5/5 success vs. at most 1/5 for partial configurations). In a dynamic pouring task, fixed-effort baselines fail in all 10 attempts due to pose drift, while TactileReflex achieves 9/10 success across two water volumes. As a self-contained and interpretable controller, TactileReflex can serve as a plug-and-play safety layer beneath high-level manipulation pipelines, including haptic-free VR teleoperation and vision-language-action (VLA) policies.

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arXiv2026

HCSG: Human-Centric Semantic-Geometric Reasoning for Vision-Language Navigation

VLN has achieved remarkable progress by scaling data and model capacity. However, the assumption of a static environment breaks down in real-world indoor scenarios, where robots inevitably encounter dynamic pedestrians. Existing human-aware approaches typically treat humans merely as moving obstacles based on implicit visual cues, lacking the explicit reasoning required to interpret human intentions or maintain social norms. To address this, we propose HCSG, the first human-centric framework for VLN. This framework provides a robust foundation for safe, socially intelligent navigation in dynamic human-robot environments that shifts the paradigm from passive collision avoidance to active human behavior understanding. Specifically, HCSG introduces a unified Human Understanding Module that synergizes two key capabilities: (i) geometric forecasting, which predicts human pose and trajectory to anticipate future motion dynamics; and (ii) semantic interpretation, which leverages a Vision-Language Model (VLM) to generate natural language descriptions of human actions and intentions. These semantic-geometric representations are fused into the agent's topological map for instruction-conditioned planning. Furthermore, a social distance loss is introduced to enforce socially compliant interaction distances. Extensive experiments on the HA-VLNCE benchmark demonstrate that HCSG significantly outperforms state-of-the-art methods, achieving a 14% improvement in Success Rate and a 34% reduction in Collision Rate. Our project can be seen at https://haoxuanxu1024.github.io/HCSG/.

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arXiv2026

PosterReward: Unlocking Accurate Evaluation for High-Quality Graphic Design Generation

Recent advancements in the text-rendering capabilities of image generation models have made the end-to-end creation of graphic design content, such as posters, increasingly feasible. However, existing reward models fall short of accurately assessing design quality, as they primarily focus on global image aesthetics while overlooking the critical dimensions of typography and layout. Furthermore, the scarcity of domain-specific preference data remains a significant bottleneck, which limits the further development of graphic design evaluation and generation. To bridge this gap, we introduce an automated pipeline to construct a high-quality dataset of 70k poster preferences by leveraging the consensus of multiple Multi-modal Large Language Models (MLLMs) to simulate human-like judgment. Utilizing this dataset, we develop PosterReward, a reward model specifically designed for high-precision poster assessment through a cascaded, multi-stage training strategy. We also provide multiple variants of the model to cater to different application scenarios. Finally, we introduce PosterRewardBench and PosterBench to evaluate the performance of existing reward models in poster assessment and the generation capabilities of current text-to-image models in poster creation, respectively.

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arXiv2025

LucidFlux: Caption-Free Photo-Realistic Image Restoration via a Large-Scale Diffusion Transformer

Image restoration (IR) aims to recover images degraded by unknown mixtures while preserving semanticsconditions under which discriminative restorers and UNet-based diffusion priors often oversmooth, hallucinate, or drift. We present LucidFlux, a caption-free IR framework that adapts a large diffusion transformer (Flux.1) without image captions. Our LucidFlux introduces a lightweight dual-branch conditioner that injects signals from the degraded input and a lightly restored proxy to respectively anchor geometry and suppress artifacts. Then, a timestep- and layer-adaptive modulation schedule is designed to route these cues across the backbones hierarchy, in order to yield coarse-to-fine and context-aware updates that protect the global structure while recovering texture. After that, to avoid the latency and instability of text prompts or Vision-Language Model (VLM) captions, we enforce caption-free semantic alignment via SigLIP features extracted from the proxy. A scalable curation pipeline further filters large-scale data for structure-rich supervision. Across synthetic and in-the-wild benchmarks, our LucidFlux consistently outperforms strong open-source and commercial baselines, and ablation studies verify the necessity of each component. LucidFlux shows that, for large DiTs, when, where, and what to condition onrather than adding parameters or relying on text promptsis the governing lever for robust and caption-free image restoration in the wild.

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arXiv2025

An Erdos-Gallai conjecture for signed graphs

For every natural number $p$, we show that the maximum negative girth among the class of signed graphs on $n$ vertices with balanced chromatic number at least $p$ is between $(1/e)n^{1/(p-1)}$ and $2(p-1) n^{1/(p-1)}$. This extends a conjecture of Erd\H{o}s and Gallai to signed graphs.

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arXiv2025

Odd Hadwiger's conjecture for the complements of Kneser graphs

A generalization of the four-color theorem, Hadwiger's conjecture is considered as one of the most important and challenging problems in graph theory, and odd Hadwiger's conjecture is a strengthening of Hadwiger's conjecture by way of signed graphs. In this paper, we prove that odd Hadwiger's conjecture is true for the complements $\overline{K}(n,k)$ of the Kneser graphs $K(n,k)$, where $n\geq 2k \ge 4$. This improves a result of G. Xu and S. Zhou (2017) which states that Hadwiger's conjecture is true for this family of graphs. Moreover, we prove that $\overline{K}(n,k)$ contains a 1-shallow complete minor of a special type with order no less than the chromatic number $\chi(\overline{K}(n,k))$, and in the case when $7 \le 2k+1 \le n \le 3k-1$ the gap between the odd Hadwiger number and chromatic number of $\overline{K}(n,k)$ is $\Omega(1.5^{k})$.

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arXiv2025

Fractional balanced chromatic number of signed subcubic graphs

A signed graph is a pair $(G,\sigma)$, where $G$ is a graph and $\sigma: E(G)\rightarrow \{-, +\}$, called signature, is an assignment of signs to the edges. Given a signed graph $(G,\sigma)$ with no negative loops, a balanced $(p,q)$-coloring of $(G,\sigma)$ is an assignment $f$ of $q$ colors to each vertex from a pool of $p$ colors such that each color class induces a balanced subgraph, i.e., no negative cycles. Let $(K_4,-)$ be the signed graph on $K_4$ with all edges being negative. In this work, we show that every signed (simple) subcubic graph admits a balanced $(5,3)$-coloring except for $(K_4,-)$ and signed graphs switching equivalent to it. For this particular signed graph the best balanced colorings are $(2p,p)$-colorings.

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arXiv2025

PD-VLA: Accelerating Vision-Language-Action Model Integrated with Action Chunking via Parallel Decoding

Vision-Language-Action (VLA) models demonstrate remarkable potential for generalizable robotic manipulation. The performance of VLA models can be improved by integrating with action chunking, a critical technique for effective control. However, action chunking linearly scales up action dimensions in VLA models with increased chunking sizes. This reduces the inference efficiency. To tackle this problem, we propose PD-VLA, the first parallel decoding framework for VLA models integrated with action chunking. Our framework reformulates autoregressive decoding as a nonlinear system solved by parallel fixed-point iterations. This approach preserves model performance with mathematical guarantees while significantly improving decoding speed. In addition, it enables training-free acceleration without architectural changes, as well as seamless synergy with existing acceleration techniques. Extensive simulations validate that our PD-VLA maintains competitive success rates while achieving 2.52 times execution frequency on manipulators (with 7 degrees of freedom) compared with the fundamental VLA model. Furthermore, we experimentally identify the most effective settings for acceleration. Finally, real-world experiments validate its high applicability across different tasks.

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arXiv2024

Colouring signed analogues of Kneser, Schrijver, and Borsuk graphs

The Kneser signed graph $\KS(n,k)$, $k\leq n$, is the graph whose vertices are signed $k$-subsets of $[n]$ (i.e. $k$-subsets $S$ of $\{ \pm 1, \pm 2, \ldots, \pm n\}$ such that $S\cap (-S)=\emptyset$). Two vertices $A$ and $B$ are adjacent with a positive edge if $A\cap (-B)=\emptyset$ and with a negative edge if $A\cap B=\emptyset$. We prove that the balanced chromatic number of $\KS(n,k)$ is $n-k+1$. We then introduce the signed analogue of Schrijver graphs and show that they form vertex-critical subgraphs of $\KS(n,k)$ with respect to balanced colouring. Further connection to topological methods, in particular, connection to Borsuk signed graphs is also considered.

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arXiv2024

Real-Time Metric-Semantic Mapping for Autonomous Navigation in Outdoor Environments

The creation of a metric-semantic map, which encodes human-prior knowledge, represents a high-level abstraction of environments. However, constructing such a map poses challenges related to the fusion of multi-modal sensor data, the attainment of real-time mapping performance, and the preservation of structural and semantic information consistency. In this paper, we introduce an online metric-semantic mapping system that utilizes LiDAR-Visual-Inertial sensing to generate a global metric-semantic mesh map of large-scale outdoor environments. Leveraging GPU acceleration, our mapping process achieves exceptional speed, with frame processing taking less than 7ms, regardless of scenario scale. Furthermore, we seamlessly integrate the resultant map into a real-world navigation system, enabling metric-semantic-based terrain assessment and autonomous point-to-point navigation within a campus environment. Through extensive experiments conducted on both publicly available and self-collected datasets comprising 24 sequences, we demonstrate the effectiveness of our mapping and navigation methodologies. Code has been publicly released: https://github.com/gogojjh/cobra

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arXiv2024

MGCBS: An Optimal and Efficient Algorithm for Solving Multi-Goal Multi-Agent Path Finding Problem

With the expansion of the scale of robotics applications, the multi-goal multi-agent pathfinding (MG-MAPF) problem began to gain widespread attention. This problem requires each agent to visit pre-assigned multiple goal points at least once without conflict. Some previous methods have been proposed to solve the MG-MAPF problem based on Decoupling the goal Vertex visiting order search and the Single-agent pathfinding (DVS). However, this paper demonstrates that the methods based on DVS cannot always obtain the optimal solution. To obtain the optimal result, we propose the Multi-Goal Conflict-Based Search (MGCBS), which is based on Decoupling the goal Safe interval visiting order search and the Single-agent pathfinding (DSS). Additionally, we present the Time-Interval-Space Forest (TIS Forest) to enhance the efficiency of MGCBS by maintaining the shortest paths from any start point at any start time step to each safe interval at the goal points. The experiment demonstrates that our method can consistently obtain optimal results and execute up to 7 times faster than the state-of-the-art method in our evaluation.

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arXiv2024

FusionPortableV2: A Unified Multi-Sensor Dataset for Generalized SLAM Across Diverse Platforms and Scalable Environments

Simultaneous Localization and Mapping (SLAM) technology has been widely applied in various robotic scenarios, from rescue operations to autonomous driving. However, the generalization of SLAM algorithms remains a significant challenge, as current datasets often lack scalability in terms of platforms and environments. To address this limitation, we present FusionPortableV2, a multi-sensor SLAM dataset featuring sensor diversity, varied motion patterns, and a wide range of environmental scenarios. Our dataset comprises $27$ sequences, spanning over $2.5$ hours and collected from four distinct platforms: a handheld suite, a legged robots, a unmanned ground vehicle (UGV), and a vehicle. These sequences cover diverse settings, including buildings, campuses, and urban areas, with a total length of $38.7km$. Additionally, the dataset includes ground-truth (GT) trajectories and RGB point cloud maps covering approximately $0.3km^2$. To validate the utility of our dataset in advancing SLAM research, we assess several state-of-the-art (SOTA) SLAM algorithms. Furthermore, we demonstrate the dataset's broad application beyond traditional SLAM tasks by investigating its potential for monocular depth estimation. The complete dataset, including sensor data, GT, and calibration details, is accessible at https://fusionportable.github.io/dataset/fusionportable_v2.

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arXiv2024

PALoc: Advancing SLAM Benchmarking with Prior-Assisted 6-DoF Trajectory Generation and Uncertainty Estimation

Accurately generating ground truth (GT) trajectories is essential for Simultaneous Localization and Mapping (SLAM) evaluation, particularly under varying environmental conditions. This study introduces a systematic approach employing a prior map-assisted framework for generating dense six-degree-of-freedom (6-DoF) GT poses for the first time, enhancing the fidelity of both indoor and outdoor SLAM datasets. Our method excels in handling degenerate and stationary conditions frequently encountered in SLAM datasets, thereby increasing robustness and precision. A significant aspect of our approach is the detailed derivation of covariances within the factor graph, enabling an in-depth analysis of pose uncertainty propagation. This analysis crucially contributes to demonstrating specific pose uncertainties and enhancing trajectory reliability from both theoretical and empirical perspectives. Additionally, we provide an open-source toolbox (https://github.com/JokerJohn/Cloud_Map_Evaluation) for map evaluation criteria, facilitating the indirect assessment of overall trajectory precision. Experimental results show at least a 30\% improvement in map accuracy and a 20\% increase in direct trajectory accuracy compared to the Iterative Closest Point (ICP) \cite{sharp2002icp} algorithm across diverse campus environments, with substantially enhanced robustness. Our open-source solution (https://github.com/JokerJohn/PALoc), extensively applied in the FusionPortable\cite{Jiao2022Mar} dataset, is geared towards SLAM benchmark dataset augmentation and represents a significant advancement in SLAM evaluations.

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arXiv2024

Enhancing Campus Mobility: Achievements and Challenges of Autonomous Shuttle "Snow Lion''

The rapid evolution of autonomous vehicles (AVs) has significantly influenced global transportation systems. In this context, we present ``Snow Lion'', an autonomous shuttle meticulously designed to revolutionize on-campus transportation, offering a safer and more efficient mobility solution for students, faculty, and visitors. The primary objective of this research is to enhance campus mobility by providing a reliable, efficient, and eco-friendly transportation solution that seamlessly integrates with existing infrastructure and meets the diverse needs of a university setting. To achieve this goal, we delve into the intricacies of the system design, encompassing sensing, perception, localization, planning, and control aspects. We evaluate the autonomous shuttle's performance in real-world scenarios, involving a 1146-kilometer road haul and the transportation of 442 passengers over a two-month period. These experiments demonstrate the effectiveness of our system and offer valuable insights into the intricate process of integrating an autonomous vehicle within campus shuttle operations. Furthermore, a thorough analysis of the lessons derived from this experience furnishes a valuable real-world case study, accompanied by recommendations for future research and development in the field of autonomous driving.

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