arXiv subjects

Hongliang Lu

Publications and source records attributed to Hongliang Lu.

At least 19 recordsLinked to original sources

arXiv2026

Stability and exact extremal colourings for the Alon--Frankl--Lovász bound

The Alon--Frankl--Lovász theorem states that every $q$-colouring of the edges of the complete $r$-uniform hypergraph on $n$ vertices contains a monochromatic matching of size $\lfloor(n+q-1)/(r+q-1)\rfloor$. For fixed uniformity $r$ and number of colours $q$, we prove a stability theorem: every colouring whose largest monochromatic matching has size at most $n/(r+q-1)+o(n)$ differs from a threshold extremal colouring on only $o(n^r)$ edges. We also give a necessary and sufficient structural characterization of all extremal colourings for sufficiently large $n$. The proofs combine rigidity of fractional covering weights with an extension argument for prescribed matchings. These results answer, for sufficiently large orders, the stability and extremal-colouring questions posed by Gishboliner, Glock, Michaeli and Sgueglia.

math.CO↗

arXiv2026

Ore-degree conditions for hypergraph matchings

Let $σ_k(H)$ be the minimum sum of the vertex degrees over all non-edges of an $n$-vertex $k$-uniform hypergraph $H$. For every $k\ge3$, $n\geq ks$ and sufficiently large $n$, we establish a sharp Ore-type degree condition that forces a matching of size $s$ in $H$. Specifically, we prove that if \[ σ_k(H)>\max\left\{ k\left(\binom{n-1}{k-1}-\binom{n-s}{k-1}\right), (k-c)\binom{ks-2}{k-1}\right\}, \] then $H$ has a matching of size $s$, where $c=n-ks+1$. In particular, this proves a conjecture of Balogh, Palmer and Raeisi for $k\geq 3$ and sufficiently large $n$.

math.CO↗

arXiv2026

Commit While Futures Agree: Consequence-Aware Adaptive Action Chunking for Robot Manipulation

Action-chunking policies predict multi-step control sequences, but a fundamental question remains: how much of a predicted action chunk should be committed before replanning? Existing systems typically execute a fixed-length prefix, implicitly assuming that the same execution horizon remains trustworthy across states. Some adaptive methods estimate this horizon from the similarity or stability of predicted actions. However, different actions may lead to the same successful outcome, whereas similar actions can produce different futures, suggesting that commitment should be determined by agreement among imagined futures rather than by similarity in action space. To this end, we propose Consequence-Aware Adaptive Action Chunking (CA$^3$C), an inference-time framework built on a simple principle: commit while imagined futures agree, and replan when they diverge. Without modifying or retraining the base policy, CA$^3$C uses an action-conditioned world model to imagine the future consequences of multiple candidate action chunks under the same sampling noise. Using these imagined consequences, we formulate execution-horizon estimation as a Bayesian change-point inference problem and select the execution candidate through future consensus. Across multiple simulation benchmarks and real-world robot manipulation tasks, CA$^3$C consistently improves diverse action-chunking policies, achieving up to a 71.8% relative reduction in failure rate over the corresponding base policies.

cs.RO↗

arXiv2026

Perfect Matching in $k$-Partite $k$-Uniform Hypergraphs

A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph whose vertex set is partitioned into $k$ classes of the same size and whose edges meet every class in exactly one vertex. Lo and Markström (2014) determined the minimum vertex-degree threshold for perfect matchings when $k=3$, and Lu, Wang and Yuan recently determined it when $k=4$. We prove the corresponding exact result for every fixed $k\ge5$ and all sufficiently large class sizes. The close case follows from the general theorem of Lu, Wang and Yuan. For the non-closed case, we extend their stability result from the 3-partite setting to arbitrary partite uniformity, using the probability-tail rigidity theorem of Cao, Liu and Zhang, thereby replacing the earlier weighted lemma.

math.CO↗

arXiv2026

From Likelihood to Utility: Quality-Axis Diffusion for End-to-End Autonomous Driving

Diffusion models have become a dominant paradigm for end-to-end autonomous driving, yet existing planners organize trajectory generation along the Gaussian-noise axis, treating driving utility only as an auxiliary guidance or selection signal. We instead formulate diffusion along a driving-quality axis. We propose QualiDrive, which constructs scene-specific quality ladders by ranking observed trajectories according to measured driving utility and learns to reverse this ordered degradation through ordered low-to-high-quality refinement. Each reverse step is conditioned on the scene, ego state, current trajectory, and target quality level, progressively refining trajectories toward higher driving quality. On NAVSIM, QualiDrive achieves 94.5 PDMS on v1 and a state-of-the-art 92.74 EPDMS on v2. QualiDrive improves Oracle EPDMS only modestly over endpoint-only quality supervision (98.52 to 98.57), but substantially increases the fractions of candidates above 0.95 and 0.98 EPDMS from 12.94%/9.71% to 21.53%/15.93%, raising selected EPDMS from 92.63 to 92.74. These results suggest that diffusion is not merely a process of denoising, but one of progressive quality-ordered refinement.

cs.RO↗

arXiv2026

EvoAD: Self-Evolving Autonomous Driving via Latent World-Model Guided Post-hoc Reflection

End-to-end autonomous driving systems have achieved rapid progress by learning unified policies that map sensor observations directly to driving trajectories. However, once deployed, these systems typically remain frozen: they may repeat similar decisions in similar scenes, and failures can only be addressed through costly data collection and retraining. This sharply contrasts with human drivers, who improve lifelong through experience, memory, and reflection. In this work, we ask whether autonomous driving systems can achieve similar post-deployment self-evolution to human drivers. We propose EvoAD, a self-evolving autonomous driving framework via latent world-model guided post-hoc reflection. EvoAD stores driving experiences in a bird's-eye-view feature memory pool, retrieves scene-relevant precedents according to geometric and semantic similarity, and uses a latent world model to evaluate the future consequences of candidate trajectories in a compact planning-oriented space. Instead of treating memory as external textual contexts or using world models only for pre-action simulation, EvoAD transforms executed driving outcomes into reusable improvement signals for future decisions. This enables the system to diagnose how prior trajectories could have been improved and to refine behavior in similar future scenarios without retraining the base driving policy. Experiments on NAVSIM v1 and v2 show consistent improvements across reflection rounds and state-of-the-art performance, demonstrating the potential of world models as reflective mechanisms for post-deployment self-evolution in autonomous driving.

cs.RO↗

arXiv2026

EditWM: Event-Decomposed World Modeling with Incremental Correction for End-to-End Autonomous Driving

World models support autonomous driving by predicting the scene evolution associated with candidate trajectories. Driving dynamics differ in predictability, motivating a distinction between regular evolution and event-induced deviations that call for selective correction. We propose EditWM, a world model that decomposes future prediction into normal evolution and event-driven incremental correction in compact visual feature space. A trajectory-conditioned normal predictor provides the base forecast and is then frozen for correction learning. A correction decoder compares this forecast with observation history and planned actions, producing a bounded feature update whose contribution is regulated by a learned gate. The corrected future features condition trajectory scoring through candidate-specific cross-attention, linking world modeling to plan selection. At inference, EditWM uses only past and current observations, ego state, and candidate trajectories. Across all 12,146 NAVSIM navtest scenes, expert-trajectory-conditioned evaluation shows a 5.35\% reduction in future-feature MSE over Normal, with improvements in 83.54\% of scenes. The system achieves 91.05 EPDMS on a 100-point scale using the official EPDMS evaluator. These results demonstrate improved future-feature prediction and competitive trajectory selection when corrected future representations are integrated into planning.

cs.RO↗

arXiv2026

Exact Minimum $d$-Degree Thresholds for Hypergraph Perfect Matchings

For fixed integers $k\ge3$ and $1\le d\le k-1$ and sufficiently large $n\in k\mathbb N$, we establish the sharp minimum $d$-degree thresholds that forces perfect matching in every $n$-vertex $k$-uniform hypergraphs. This was conjectued by Treglown and Zhao, and the $d=1$ case was conjectued by Kühn, Osthus and Treglown.

math.CO↗

arXiv2026

Energy-Aware Wind-Resilient Routing for Truck-Assisted Multi-UAV Delivery under Wind Uncertainty

Energy feasibility under wind uncertainty is a critical safety issue for low-altitude air-ground delivery. In truck-UAV systems, UAVs complete assigned deliveries and safely return to a mobile truck or depot, while wind-induced propulsion costs vary online and are only partially observable. Existing routing methods often rely on static or deterministic energy models, which may underestimate headwind, crosswind, battery-voltage, and return-feasibility risks. This paper proposes Energy-Aware Wind-Resilient Routing (EWR), an online risk-sensitive planning framework for wind-aware and energy-safe UAV routing. The delivery environment is represented as a time-dependent directed energy graph whose edge costs are updated using delayed noisy wind estimates, payload states, and conservative uncertainty margins. Experiments using synthetic delivery graphs with replayed wind logs from a public truck-UAV delivery dataset show that EWR improves mission success rates and reduces wind-induced return failures.

eess.SY↗

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.

cs.RO↗

arXiv2026

Perfect matching in 4-partite 4-uniform hypergraphs

A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph such that every edge intersects each partition class in exactly one vertex, where each partition class has size $n$. Lo and Markström (2014) determined the minimum vertex-degree threshold for perfect matchings in balanced $3$-partite $3$-graphs. In this paper, we determine the minimum vertex-degree threshold for balanced $4$-partite $4$-graphs. The proof relies on a reduction framework for $k$-partite $k$-graphs, through which the existence of a perfect fractional matching is converted into a finite-dimensional optimization problem.

math.CO↗

arXiv2026

On the codegree threshold for Hamilton $\ell$-cycles in $k$-uniform hypergraphs

In this note, we resolve the remaining open case of a conjecture by Han and Zhao concerning the codegree threshold for Hamilton $\ell$-cycles in $k$-uniform hypergraphs. Specifically, we prove that for integers $k\ge 3$, $3k/4\le \ell<k$, with $k\not\equiv 0 \pmod{k-\ell}$, and for all sufficiently large $n$ divisible by $k-\ell$, every $n$-vertex $k$-uniform hypergraph $H$ satisfying \[ δ_{k-1}(H)\ge \frac{n}{(k-\ell)\left\lceil \frac{k}{k-\ell}\right\rceil} \] contains a Hamilton $\ell$-cycle. Our proof builds on the framework of Gan, Han and Xu, and refines their argument to obtain, at the exact threshold, the required family of paths.

math.CO↗

arXiv2026

Diffusion-based 4D Trajectory Prediction and Distributed Control for UAV Swarms

Accurate 4D trajectory prediction and closed-loop tracking are essential for Unmanned Aerial Vehicle (UAV) swarms to achieve safe and efficient operations in complex low-altitude environments such as urban airspaces, industrial sites, and indoor facilities. However, this task remains challenging due to intrinsic nonlinearity of UAV swarm dynamics and strict real-time constraints of swarm formation control. To address these challenges, we propose a unified framework that couples coarse-to-fine trajectory forecasting with uncertainty-aware Distributed Nonlinear Model Predictive Control (DNMPC). Our approach features two key innovations: 1) a dimension-decoupled trajectory prediction module that reduces computational complexity by forecasting axis-wise motion, and 2) a diffusion-based residual dynamics refinement module that captures temporally correlated dynamic uncertainties. These refined predictions are then integrated into a DNMPC loop to ensure formation stability. We also introduce a synchronized multi-scenario 4D UAV swarm dataset spanning six representative airspace scenarios. The dataset contains over \textbf{7,900} frames of synchronized three-UAV trajectories with frame-level annotations of speed intention and target sector. Extensive experiments demonstrate that our approach outperforms state-of-the-art baselines, reducing trajectory tracking error by up to \textbf{10-15\%} and achieving sub-\textbf{0.07\,m} average tracking error in complex urban and industrial environments, while maintaining real-time inference speeds of 34 FPS (sub-30 ms latency) suitable for agile flight.

cs.RO↗

arXiv2026

A spectral condition for perfect matchings in 3-partite 3-graphs

Let $H$ be a 3-partite 3-uniform hypergraph whose three vertex classes all have size $n$. For a vertex $v \in V(H)$, the link graph $N_H(v)$ is defined on $V(H)\setminus\{v\}$ with edge set $\{e\setminus\{v\}: v\in e\in E(H)\}$, and we denote by $ρ(N_H(v))$ its spectral radius. We prove that for every $α>0$ there exists $n_0$ such that for all $n\ge n_0$ the following holds: if \[ ρ\bigl(N_H(v)\bigr) > \left(\frac{\sqrt{2}}{2}+α\right)n \] for every vertex $v\in V(H)$, then $H$ contains a perfect matching. This spectral condition is asymptotically best possible.

math.CO↗

arXiv2026

Towards the Erdős matching conjecture for 4-uniform hypergraphs: stability and applications

A famous conjecture of Erdős asserts that for $k\ge 3$, the maximum number of edges in an $n$-vertex $k$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom{n}{k}-\binom{n-s}{k},\binom{sk+k-1}{k}\}$. This problem has been central in extremal combinatorics, with substantial progress in the literature, including a complete solution for $k=3$ due to the first author. In this paper, we make progress towards the $4$-uniform case, proving the conjecture for $n\ge 5s$ and sufficiently large $n$, thereby taking a first step analogous to the $3$-uniform case. The main technical contribution is a stability result of independent interest. We further apply this stability to resolve two new instances of conjectures on the minimum $d$-degree threshold for matchings in $5$- and $6$-uniform hypergraphs, in a strengthened form.

math.CO↗

arXiv2026

Curvature-driven revival of charge density waves in non-Euclidean space

Strongly correlated quantum states, such as charge density waves (CDWs), are exquisitely sensitive to Fermi surface topology and lattice symmetry, and are typically quenched by heavy carrier doping. In two-dimensional (2D) systems, however, macroscopic geometric curvature emerges as a novel structural degree of freedom to modulate microscopic quantum coherence. This raises a compelling physical question: can non-Euclidean geometric deformations compete with extreme electronic perturbations to reshape, or even revive, a quenched macroscopic quantum order? Here, by constructing monolayer TiSe$_2$-NbSe$_2$ heterostructure on a BLG/SiC substrate for the first time, we report the curvature-driven revival of a frustrated charge order in a non-Euclidean space. Low-temperature angle-resolved photoemission spectroscopy (ARPES) reveals a massive interfacial charge transfer, which destroys the global Fermi surface nesting and completely suppresses the long-range CDW order in Euclidean flat regions. Strikingly, high-resolution scanning tunneling microscopy (STM) reveals that a novel, non-linear CDW state miraculously survives, remaining strictly localized within morphologically distorted, non-Euclidean nanoscale curved regions. Atomistic simulations unravel the structural origin of this phenomenon, demonstrating that interfacial twist and lattice mismatch spontaneously generate a corrugated superlattice.

cond-mat.mtrl-sci↗

arXiv2026

Does Visual Information Play a Decisive Role in Vision-Language-Action Model Driving Behavior?

Vision-Language-Action (VLA) models have demonstrated promising capability in autonomous driving, highlighting the potential of unified multimodal architectures for jointly modeling perception and planning. However, how current VLA-based driving behavior is grounded in visual information remains poorly understood. Existing evaluation protocols mainly focus on aggregate performance metrics, lacking structured and practical diagnostics to quantify visual-behavior dependency. In this work, we introduce a structured multi-level visual perturbation framework to analyze visual-behavior dependency in VLA-based driving models systematically. The framework organizes controlled visual perturbations along three complementary dimensions: channellevel degradation, information-level disruption, and structurelevel modification. We apply it to VLA-based driving systems and evaluate behavioral responses under both open-loop trajectory prediction and interactive closed-loop safety evaluation. Experimental results reveal evaluation-dependent dependency patterns and uneven visual grounding across abstraction levels. These findings call for more structured analyses and principled design of VLA driving models to better understand how visual information shapes behavior and develop safer, more robust systems.

cs.CV↗

arXiv2026

Constructing Industrial-Scale Optimization Modeling Benchmark

Optimization modeling underpins decision-making in logistics, manufacturing, energy, and finance, yet translating natural-language requirements into correct optimization formulations and solver-executable code remains labor-intensive. Although large language models (LLMs) have been explored for this task, evaluation is still dominated by toy-sized or synthetic benchmarks, masking the difficulty of industrial problems with $10^{3}$--$10^{6}$ (or more) variables and constraints. A key bottleneck is the lack of benchmarks that align natural-language specifications with reference formulations/solver code grounded in real optimization models. To fill in this gap, we introduce MIPLIB-NL, built via a structure-aware reverse construction methodology from real mixed-integer linear programs in MIPLIB~2017. Our pipeline (i) recovers compact, reusable model structure from flat solver formulations, (ii) reverse-generates natural-language specifications explicitly tied to this recovered structure under a unified model--data separation format, and (iii) performs iterative semantic validation through expert review and human--LLM interaction with independent reconstruction checks. This yields 223 one-to-one reconstructions that preserve the mathematical content of the original instances while enabling realistic natural-language-to-optimization evaluation. Experiments show substantial performance degradation on MIPLIB-NL for systems that perform strongly on existing benchmarks, exposing failure modes invisible at toy scale.

cs.LG↗