arXiv subjects

Lu Liu

Publications and source records attributed to Lu Liu.

At least 19 recordsLinked to original sources

arXiv2026

There is no maximal $K$-degree

The Kolmogorov complexity of a string characterize how complex it is to describe the string. If every prefix of a real $x$ is more complex to describe than every prefix (of the same length) of real $y$, then it is seen as $x$ is more complex to describe than $y$. It is wondered if there is a real $x$ so that no other reals are strictly more complex (to describe) than $x$. The behavior of Kolmogorov complexity functions generated by reals (namely $n\mapsto$ the minimal description length of the real) is quite chaos. Therefore, it is widely believed that there are many reals that are maximally complex to describe. For instance, it is conjectured that all random enough reals have maximal $K$-degree. In this paper, it is shown that there is no real with maximal $K$-degree. Actually, for almost all real $x$, we can uniformly computably find another real whose $K$-degree is strictly above $x$.

math.LO↗

arXiv2026

Traffic Congestion Control for ARZ Model with an Arbitrarily Large Input Delay

This paper addresses the stabilization problem for Aw-Rascle-Zhang (ARZ) traffic model in the presence of an arbitrarily large input delay. The linearized ARZ model is a $2 \times 2$ hyperbolic partial differential equation (PDE) system with proximal reflection, which introduces significant analytical challenges when combined with input delays. To tackle this problem, we propose a backstepping-based boundary controller capable of stabilizing the linearized ARZ model under these conditions. The input delay is modeled as a transport PDE, which reformulates the entire system into a $3 \times 3$ hyperbolic PDE system. A backstepping transformation is designed to map the original system into a stable target system, enabling the design of a delay-compensated controller. A key technical contribution of this work is that for hyperbolic PDEs with delays, we develop a characteristic-region-wise construction for kernel functions subject to two boundary constraints and close the proof via successive approximation. Another contribution is that we utilize the small-gain theorem for input-to-state stability (ISS) of hyperbolic PDEs. Two simulations are provided to illustrate the effectiveness of the proposed delay-compensated controller: one compares it with a controller without compensation, and the other employs real traffic vehicle data to validate its effectiveness.

eess.SY↗

arXiv2026

GraFT: A Training-Free Framework for Spatial Reasoning in Multimodal Large Language Models via 3D Scene Graphs

3D spatial reasoning underpins understanding and acting in the physical world, yet it remains unreliable in current multimodal large language models (MLLMs). These models falter at precise geometric measurement, at transforming between egocentric and allocentric viewpoints, and at grounding fine-grained appearance. The most common remedies fine-tune the model on large-scale curated spatial-reasoning datasets or attach dedicated encoders for 3D geometry, which typically couples the solution to costly supervision and a specific backbone. We instead introduce GraFT, a training-free framework that supplies the missing 3D structure through a compact, easily maintained 3D scene graph (3DSG). From this 3DSG, GraFT provides three spatial reasoning capabilities: (1) deterministic geometry through symbolic tools, (2) allocentric layout through a bird's-eye-view (BEV) rendering, and (3) visual-attribute grounding through task-relevant egocentric frames. On ScanQA, GraFT improves every metric over the same-backbone baseline, raising CIDEr by 27%. On VSI-Bench, GraFT improves frozen MLLMs by up to 65%, surpassing every proprietary and general-purpose open-source baseline, and several prominent fine-tuned spatial models.

cs.CV↗

arXiv2026

Projection-Free Bandit Online Optimization for Multi-Agent Systems with Dynamic Regret

This paper investigates distributed online optimization for multi-agent dynamical systems with constrained inputs and time-varying cost functions. While online convex optimization offers a principal framework for sequential decision-making, existing online learning and optimization algorithms typically require accurate system models, limiting their applicability in practical settings. To overcome this challenge, we propose a distributed bandit online feedback optimization algorithm that relies solely on real-time input-output data. The algorithm employs a smoothing zeroth-order one-point estimator to construct local gradient approximations directly from cost evaluations. Additionally, to enforce input constraints effectively, we integrate a projection-free conditional gradient update, making the algorithm well-suited for online and large-scale settings. Furthermore, we establish a sublinear dynamic regret bound that depends on a temporal variation measure of system non-stationarity. Finally, numerical simulations demonstrate the effectiveness of the proposed algorithm.

cs.DC↗

arXiv2026

ReGround-Surg: Reliability-Guided Anchor Grounding for Referring Surgical Video Segmentation

Referring surgical video segmentation requires segmenting a target instrument or tissue region across video frames according to a natural language expression. Recent Segment Anything Model 2 (SAM2) based two-stage methods (e.g., ReSurgSAM2) first ground the referred target in an initial or selected frame, then propagate the selected mask via tracking. Although effective, their performance is highly sensitive to the quality of the initial grounded mask: once an incorrect anchor is selected, subsequent tracking tends to propagate the error. This issue is especially challenging in surgical videos due to visually similar instruments, occlusion, and complex tissue-tool interactions. To address this issue, we propose ReGround-Surg, a lightweight reliability-guided anchor grounding framework to improve SAM2-based referring surgical video segmentation. It first predicts a text-conditioned spatial reliability map from the referring expression and current-frame visual features. The map is then reused in two complementary branches: a Gated Side Adapter enhances expression-relevant visual regions before text-to-vision fusion, while a Reliability-Weighted Vision-to-Text Attention module suppresses off-target visual evidence during prompt-token aggregation. Experiments on Ref-EndoVis17 and Ref-EndoVis18 show consistent improvements over state-of-the-art methods across three evaluation splits with negligible speed reduction. Code is publicly available at https://github.com/JiaxinWen1/ReGround-Surg.

cs.CV↗

arXiv2026

MissDiag: Diagnostic Evaluation of Incomplete-Knowledge Robustness in KGQA and KG-RAG

Knowledge graph question answering (KGQA) and knowledge-graph-based retrieval-augmented generation (KG-RAG) aim to ground answers in explicit graph evidence, but real-world knowledge graphs are often sparse, outdated, and incomplete. Existing robustness evaluations usually report aggregate changes in answer quality after evidence is removed or perturbed, which measures sensitivity to incomplete support but leaves the source of degradation under-specified: the same score change can conflate the type of missing evidence, the response of the evaluated system, and the sensitivity of the answer-matching protocol. To address this gap, we propose \textbf{MissDiag}, a diagnostic evaluation framework for incomplete-knowledge robustness in KGQA and KG-RAG. MissDiag keeps the question and gold answer fixed while applying structurally typed missingness interventions to benchmark-provided support graphs, enabling paired comparisons that decompose robustness changes by evidence type, system response, and evaluation protocol rather than reducing them to a single aggregate score drop. Experiments across multiple system families show that incomplete-knowledge robustness is better understood as a typed degradation phenomenon than as a uniform property: answer-adjacent evidence loss produces the largest observed degradation, source-context removal is often neutral and can be beneficial, and semantic answer matching changes absolute scores while preserving the main typed degradation patterns. By transforming aggregate robustness measurement into typed diagnostic attribution, MissDiag provides a more interpretable basis for comparing, diagnosing, and stress-testing KGQA and KG-RAG systems under incomplete knowledge.

cs.CL↗

arXiv2026

Offline Multi-Agent Reinforcement Learning with a Physics-Informed World Model for Cooperative Mixed Traffic Control

This study investigates cooperative control of connected and automated vehicles (CAVs) at partially observable highway bottlenecks in mixed traffic, aiming to mitigate congestion without relying on complete global traffic states or online trial-and-error. We propose a physics-informed world model-based offline multi-agent reinforcement learning framework that reconstructs a physically interpretable global traffic state from local CAV observation-action histories, with coupled macroscopic-microscopic traffic dynamics providing physics-based supervision. A probabilistic ensemble world model learns traffic-state transitions and system rewards, while model disagreement quantifies epistemic uncertainty. Multi-step imagined rollouts with pessimistic rewards and uncertainty-driven truncation are then used for offline policy learning. Experiments in a SUMO-based on-ramp bottleneck using approximately $1\times10^6$ offline transitions show that physics supervision improves state reconstruction and world-model prediction accuracy.

cs.MA↗

arXiv2026

Step-Level On-Policy Distillation: Interpolating Between On-Policy Distillation and Supervised Fine-Tuning

On-policy distillation (OPD) aligns a student model with a teacher's logit distribution on student-generated trajectories. This approach has achieved strong empirical gains and can often surpass conventional off-policy distillation with substantially less data. However, standard token-level OPD can provide only fragmented corrections along an erroneous student trajectory and cannot unfold a complete and correct repair path. Motivated by this limitation, we propose \emph{Step-Level On-Policy Distillation} (SOPD), which combines the long-horizon correction of supervised fine-tuning (SFT) with the on-policy advantage of OPD to provide step-level supervision over complete student-generated trajectories. We show that, at different limits of step length, SOPD reduces to SFT or approximates OPD. Compared with SFT, the teacher responses in SOPD are conditioned on student trajectories and therefore align more closely with student-visited states; compared with OPD, SOPD provides longer-horizon corrections rather than fragmented token-level guidance. Across both reasoning and agent tasks, SOPD substantially outperforms conventional SFT and OPD. For example, on ALFWorld, SOPD improves the average success rate by 13.4 points over Vanilla OPD. We hope this work offers a new perspective for future research on distillation methods.

cs.CL↗

arXiv2026

SAIN: Structure-Aware Interactive Navigation with Active Dialogue Grounding for Mobile Robot

Most existing vision-language navigation tasks assume that instructions are complete and unambiguous. However, real-world robots often encounter natural human instructions that are ambiguous, underspecified, or incomplete, requiring them to resolve such uncertainties through active questioning. Interactive Instance Goal Navigation (IIGN) requires an embodied agent to find the specific instance under an ambiguous category-level instruction through active dialogue. However, existing dialogue-enabled methods often consume oracle answers as transient textual context for immediate decisions, rather than persistent spatial or object-centric structured state. We present SAIN, a zero-shot framework that turns active dialogue into persistent navigation state. Instead of consuming oracle answers as one-step text hints, SAIN compiles them into target evidence, route-level corridor memory, and object-candidate labels. These states are stored in structured value, room, graph, and object memories, then consumed by a unified policy for frontier ranking and final target approach. On the VL-LN IIGN benchmark, SAIN improves SR from 20.2 to 25.4 and SPL from 13.07 to 14.17 over the strongest reported dialogue-enabled baseline, while requiring no task-specific policy training. The results support dialogue-to-state conversion as an effective zero-shot mechanism for long-horizon interactive instance navigation. Project website: https://zorattc.github.io/SAIN/

cs.RO↗

arXiv2026

LifelongCrossNav: Persistent 3D Semantic Memory for Cross-Floor Multi-Object Navigation

Object-goal navigation has made substantial progress in semantic perception and exploration, yet persistent memory for multi-object navigation and cross-floor navigation are still commonly addressed separately. We present LifelongCrossNav, a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. Within each episode, the agent receives an ordered sequence of object-goal queries while continuously maintaining a shared sparse 3D semantic voxel memory. This memory incrementally accumulates geometric structure, traversability states, and vision-language features, allowing subsequent object-goal queries to retrieve previously acquired scene information without rebuilding the map. To support persistent search across floors, LifelongCrossNav combines support-aware 3D traversability mapping, stair-specific perception, and direction-aware stair traversal. A unified navigation policy coordinates same-floor frontier exploration, live and historical point-of-interest retrieval, stair navigation, and target-object search and approach. We further introduce HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes, including a dedicated subset in which completing the full sequence of object-goal subtasks requires at least one floor transition. Experimental results show that LifelongCrossNav consistently outperforms a representative planar persistent semantic-map baseline on HM3D-MFMON, demonstrating that persistent 3D semantic memory and cross-floor traversability modeling effectively support sequential multi-object navigation in multi-floor environments. Project page: https://flageval-baai.github.io/LifelongCrossNavPage.

cs.RO↗

arXiv2026

MDLMPE: Distribution Aware Positional Encoding for Masked Diffusion Language Models

Masked diffusion language models (MDLMs) enable parallel generation and bidirectional context modeling, but their positional context differs fundamentally from that of autoregressive (AR) models. Whereas AR decoding exposes a contiguous prefix, MDLM denoising produces dynamic, non-contiguous configurations of revealed and masked tokens. Conventional positional encodings such as RoPE capture sequence order and pairwise displacement but remain insensitive to this evolving token-availability structure. To address this limitation, we propose MDLMPE, a positional encoding designed specifically for masked diffusion. To the best of our knowledge, MDLMPE is the first method to make positional representations explicitly aware of the changing revealed/masked configuration. It represents token availability as a binary sequence, applies distance-aware Gaussian weighting, and projects the resulting pattern through a cosine basis to obtain distribution-aware positional features. These features are added to token embeddings and mapped by a lightweight MLP to angular offsets that modulate the standard RoPE phases. Extensive experiments on LLaDA and DREAM demonstrate that MDLMPE generally outperforms conventional positional encoding methods across supervised fine-tuning, pretraining, zero-shot evaluation, and block-diffusion settings. Further ablations show that the complete combination of availability state, Gaussian locality, spectral basis, and embedding injection yields the strongest result. These results establish the evolving token-availability distribution as a useful positional signal for masked diffusion language models.

cs.CL↗

arXiv2026

OASIS: Occlusion-aware Single-image Hand Avatar Reconstruction via 3D Gaussian Splatting

Single-image 3D hand avatar reconstruction is fundamentally ill-posed and particularly challenging due to limited visual evidence under severe self-occlusion and the complex pose-dependent deformation of highly articulated hands. Existing methods predominantly rely on implicit NeRF-style representations, whose volumetric fitting is computationally expensive and often struggles to preserve fine-grained hand details. In this work, we present OASIS, a tailored 3D Gaussian Splatting framework for single-image hand avatar reconstruction. To faithfully encode sparse image-specific appearance cues in single-view reconstruction, we construct geometry-aligned visual evidence tokens by explicitly aligning input image observations with 3D hand geometry and context-adaptively tokenizing the resulting visual evidence. Since severe self-occlusion makes the reliability of image evidence inherently visibility-dependent, we introduce a visibility-conditioned point-image attention to reliably transfer visual evidence to geometric tokens, yielding occlusion-aware Gaussian features for faithful and robust reconstruction. To further capture non-rigid deformation of articulated hands, we introduce a Feature-on-Mesh representation to enable Gaussian deformation to be guided by local surface stretching. Under this framework, we adopt a one-shot adaptation scheme that learns a shared hand prior from multi-identity training data and then fits it to a target image for target-specific reconstruction. Extensive experiments show that OASIS outperforms existing baselines in both visual fidelity and efficiency across challenging poses and in-the-wild scenarios, and further demonstrates strong versatility in downstream applications such as text-to-avatar generation and texture editing.

cs.CV↗

arXiv2026

CinemaTraj: Composing Atomic Camera Trajectories for 3D Scenes with LLM Agents

Automatically generating cinematically expressive camera trajectories through 3D scenes from natural language descriptions is a challenging task of high practical value, with applications ranging from real-estate advertising to virtual tour creation. Existing methods either lack true 3D spatial awareness by relying on 2D image priors, or treat trajectory generation as a geometric path planning problem divorced from cinematographic semantics. We present CinemaTraj, a framework that reframes camera trajectory planning as a language-grounded spatial reasoning problem. Given a set of RGB-D images and a user prompt, CinemaTraj equips an LLM agent with a structured 3D scene graph: the agent decomposes the prompt into a sequence of atomic cinematographic movements (dolly, orbit, crane, pan, tilt, zoom, arc). Each movement is instantiated via a novel parametric trajectory representation that is both cinematographically expressive and optimizable for collision avoidance. The scene graph acts as a structured spatial prior, grounding the agent's reasoning in accurate geometric and semantic knowledge of the environment. CinemaTraj further generates synchronized voiceover and subtitles aligned with camera motion, producing narrated cinematic video outputs. We evaluate CinemaTraj on real-world ScanNet++ environments, and show that it produces prompt-faithful, collision-free trajectories with high cinematographic quality, outperforming existing approaches on prompt alignment, trajectory quality, and safety metrics.

cs.CV↗

arXiv2026

Moving Alphabet: A Controlled Study of Training Data for Text-to-Video Generation

Text-to-video generation has advanced significantly over the past five years through scaling of model size, data, and compute. Unlike model architecture, training data is often underexplored. Real-world data curation is complex and non-trivial, involving clip selection from raw videos and captioning to create video-text pairs for learning text-to-video mappings. We study how data distribution and caption quality impact text-to-video models. To enable controlled experiments, we introduce Moving Alphabet, a procedural testbed that renders letters with varying fonts, colors, sizes, and positions, moving in different directions and speeds against a black background. This design allows precise control over data distribution and caption quality by corrupting ground-truth metadata. Our experiments yield three findings: a) a diverse and balanced distribution of video content and duration is critical for generalization; b) caption quality significantly affects both model performance and training efficiency, suggesting that text-to-video models are bounded by video understanding capabilities; and c) classifier-free guidance and fine-tuning on high-quality data provide partial recovery from models trained on corrupted captions, but cannot fully compensate for poor pre-training data. We believe these insights can inform the development of large-scale text-to-video models, and we advocate for greater attention to the science of pre-training data.

cs.CV↗

arXiv2026

Hindman's theorem does not code $\emptyset^{(\omega)}$ in one application

We prove that for every non-arithmetic set~$C$ and every arithmetic finite coloring of~$\mathbb{N}$, there is an infinite set $H \subseteq \mathbb{N}$ whose non-empty finite sums of distinct elements is monochromatic, and $C$ is not $H$-computable. We also study restrictions of Hindman's theorem to simple colorings.

math.LO↗

arXiv2026

Thinking More, Harnessing Better: State Machine Guided Harness Automatic Generation with Project Digestion and Workflow Decomposition

High-quality fuzz harnesses are essential for effective gray-box fuzzing. While Large Language Models (LLMs) offer promise for automating this task, existing one-turn generation methods suffer from hallucinations and inadequate coverage due to coarse-grained function targeting and misaligned generation workflows. We present SynapseFlow, an automatic harness generator that addresses these limitations through two key innovations: dataflow-aware function aggregation and a staged, rollback-enabled generation workflow decomposition. SynapseFlow first analyzes source code to construct Structural Flow Graphs and extract coherent Function Triplets. It then synthesizes harnesses via a decomposed four-stage process governed by a staged rollback algorithm to ensure correctness. We evaluated SynapseFlow on 25 real-world open-source software projects. The experimental results indicate that SynapseFlow outperforms state-of-the-art tools (OSS-Fuzz-Gen, CKGFuzzer, PromeFuzz), achieving 3.07$\times$, 1.71$\times$, and 4.26$\times$ higher branch coverage, and 1.77$\times$, 1.51$\times$, and 1.36$\times$ higher bug detection rates, respectively. Most importantly, SynapseFlow discovered 7 previously unreported bugs (5 assigned CVEs), demonstrating its practical effectiveness in real-world bug discovery.

cs.CR↗

arXiv2026

Robust Stabilization of Linear Markov-Jumping Hyperbolic PDEs with Boundary Input Delay

This paper studies the robust stabilization of 2 $\times$ 2 linear hyperbolic partial differential equations (PDEs) with Markov-jumping parameters and boundary input delay. The main challenge arises from the simultaneous presence of stochastic parameter variations and input delay, which complicates both the stability analysis and controller design. To address this issue, a nominal delay-compensating backstepping controller is first designed for a fixed nominal system. Applying the nominal transformation to the stochastic system yields a target system with additional perturbation terms induced by parameter mismatch. A mode-independent Lyapunov functional is then constructed to establish a pathwise exponential estimate, which directly implies mean-square exponential stability under an explicit small-mismatch condition. The proposed analysis provides a direct robustness certificate for nominal delay compensation without using mode-dependent Lyapunov functionals. Finally, we present simulation results and discuss how the conservative small-mismatch condition should be interpreted for the numerical example.

eess.SY↗

arXiv2026

CPR: Chained Perceptual Refinement for Coarse-to-Fine Medical Image Classification

High resolution medical images contain fine grained, spatially sparse cues that are critical for diagnosis, yet preserving full resolution incurs substantial computational and memory costs. Most deep models process images uniformly, leading to redundant computation or loss of diagnostic detail under downsampling. We propose Chained Perceptual Refinement, CPR, a coarse to fine framework that formulates medical image analysis as a sequential global to local decision process. Starting from a low resolution global view, CPR dynamically predicts the location and spatial extent of refinement regions, extracts high resolution evidence from the original image, and incrementally integrates it with global context. By keeping the backbone input size fixed while contracting the perceptual field, CPR preserves diagnostic fidelity with constant peak GPU memory. Extensive experiments on five medical imaging datasets and multiple backbone architectures demonstrate that CPR consistently outperforms both fixed resolution and multi scale state of the art baselines, achieving improvements of up to 2.27 percentage points over the second best method. It also achieves up to a 19.6 fold reduction in GFLOPs at matched accuracy, establishing a superior accuracy and efficiency trade off for high resolution medical image analysis. The code is available on GitHub.

cs.CV↗