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Lu Liu

Publications and source records attributed to Lu Liu.

At least 37 records · Page 2Linked to original sources
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

GradientStabilizer:Fix the Norm, Not the Gradient

Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence. Widely used safeguards such as gradient clipping mitigate these failures but require threshold tuning and indiscriminately truncate large updates. We propose GradientStabilizer, a lightweight, drop-in gradient transform that preserves the instantaneous gradient direction while replacing the update magnitude with a statistically stabilized estimate derived from running gradient-norm statistics. We prove that the resulting stabilized magnitude is uniformly bounded on spike steps, independent of the spike size, and show how this boundedness controls optimizer state evolution in adaptive methods. Across LLM pre-training (FP16), quantization-aware pre-training (FP4), ImageNet classification, reinforcement learning, and time-series forecasting, GradientStabilizer consistently improves training stability, widens stable learning-rate regions, and reduces divergence relative to clipping-based baselines, even substantially reducing Adam's sensitivity to weight-decay strength. Code will be released soon.

cs.LG↗
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 $\emptyset^{(ω)}$ 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

Stable (2+1)-dimensional soliton and breather molecules in a cold Rydberg atomic gas

We investigate the formation of stable (2+1)-dimensional spatial-domain optical soliton molecules and breather molecules in a gas of Rydberg atoms, highlighting the role of the nonlocal nonlinearity, which is generated by the electromagnetically induced transparency in the Rydberg medium. The setting supports diverse species of large-size polygonal soliton molecules, including rectangular and oblique rhombuses, checkerboard cells, and hexagons. The analysis identifies two distinct formation regimes. In the case of moderately nonlocality, the long-range interactions alone stabilize the soliton molecules in the static form. In contrast, in the strongly nonlocal regime, initially imposed rotation is required to generate a centrifugal force that counteracts the strong attraction, resulting in stably rotating soliton molecules. The rotation period can be controlled by adjusting the system parameters. Furthermore, appropriate initial velocities can induce inherent breathing dynamics in the solitons, leading to the formation of breather molecules. Tuning the initial velocity, one can control the evolution of soliton molecules and breather molecules and even realize their mutual conversion. Our study offers a new scheme for engineering soliton molecules and breather molecules, and suggests new possibilities for the design of data processing and transmission in optical systems.

physics.optics↗
arXiv2026

The reverse mathematics of the Ordered Variable Word theorem

In this article, we study the reverse mathematics of variable word theorems used in the proof of the Dual Ramsey theorem. We prove that the Ordered Variable Word theorem does not imply Ramsey's theorem for pairs and that every computable instance admits a solution of low${}_2$ degree. This is used to prove the Carlson-Simpson Lemma and the Open Dual Ramsey theorem over~$\mathsf{ACA}_0$, thereby answering some 40-years old open questions. These results have consequences in the reverse mathematics of structural Ramsey theory.

math.LO↗
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↗
arXiv2026

ATOM-Bench: A Real-World Benchmark for Atomic Skills and Compositional Generalization in Manipulation Policies

Generalist manipulation policies are increasingly presented as foundation models for robotic control, but their real-world generalization remains difficult to diagnose. A policy may succeed on demonstrated tasks while still failing to execute fine-grained atomic skills or recombine learned skills in new task structures. We introduce \textbf{ATOM-Bench}, a real-world benchmark for evaluating both atomic skills and compositional generalization in manipulation policies. ATOM-Bench factorizes tabletop manipulation into motor atoms and instruction atoms, and contains 30 atomic tasks and 24 held-out compositional tasks across paired single-arm and dual-arm robot tracks. We collect 3,000 human demonstrations for atomic fine-tuning and release both the demonstration data and evaluation rollout data to support reproducible real-world evaluation. Policies are fine-tuned on atomic tasks and evaluated on both atomic skill acquisition and held-out compositional tasks. We further introduce Atomic Score (AS) and Compositional Failure Share (CFS) to distinguish failures caused by weak atomic skills from failures caused by limited compositional reuse. Through 2,700 physical rollouts on five representative manipulation policies, we find that current policies can acquire simple instruction-grounding skills, but still struggle with fine-grained motor atoms, counting, and logical filtering. More importantly, strong atomic performance does not reliably transfer to held-out compositional tasks. ATOM-Bench provides a diagnostic testbed for studying whether failures arise from weak motor execution, poor instruction grounding, or limited compositional reuse.

cs.RO↗
arXiv2026

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

cs.CL↗
arXiv2026

Group Sequential Sample Size for Comparing Two Survival Probabilities at a Specific Time Point

We propose a novel method that simultaneously determines the sample size for testing two survival probabilities at a pre-specified ltime while guaranteeing type I error control in both fixed and group-sequential trial designs. Simulations across varying hypothesized differences, failure distributions, censoring proportions, and nominal powers demonstrate consistent performance, while interim analyses highlight reduced type I error and increased power at each look, regardless of the underlying failure time distribution or spending function. Importantly, our method is especially useful for evaluating survival outcomes at a fixed time in randomized trials where one treatment arm includes neoadjuvant therapy prior to surgery while the other involves surgery alone. Furthermore, it is advantageous when the proportional hazards assumption is not satisfied, as often occurs in immunotherapy trials with delayed or time-varying treatment effects or crossing survival curves. The method is also applicable to randomized phase II trials, where smaller sample sizes and the use of intermediate or surrogate time-to-event endpoints demand efficient data use and robust error control. We illustrate the approach with motivating examples in renal and prostate cancer. An accompanying R Shiny application enables investigators to compute sample sizes interactively, facilitating practical trial planning in diverse settings.

stat.ME↗
arXiv2026

Phase diagram of the extended chequerboard $J-Q$ model

The chequerboard $J-Q$ model was proposed to describe the direct phase transition from the antiferromagnetic (AFM) state to the plaquette-sin glet (PS) solid state observed in SrCu$_2({\rm BO}_3)_2$. In this paper, we present a Monte Carlo study of the ground state of an extended ve rsion of this model. For all parameters investigated, we find only a direct first-order phase transitions from the AFM to the PS phase, with no intermediate phase between them. On the transition line, the system exhibits an emergent $O(4)$ symmetry. Furthermore, we find that the Bi nder ratio of the columnar valence-bond solid state can be used to locate the phase transition. It exhibits a monotonic finite-size scaling b ehavior, allowing for a precise determination of the transition point.

cond-mat.str-el↗
arXiv2026

LL-Bench: Rethinking Low-Level Vision Evaluation in the Era of Large-Scale Generative Models

Large-scale generative models have demonstrated remarkable capabilities across image generation and editing tasks. However, their performance in low-level vision tasks, which require pixel-wise control, remains insufficiently studied. To address this gap, we introduce \textbf{LL-Bench}, a comprehensive \textbf{Benchmark} for evaluating the capabilities of large-scale generative models on \textbf{L}ow-\textbf{L}evel vision tasks. The benchmark comprises 2,469 real-world degraded images covering 16 low-level degradation tasks, and 28,919 restored images produced by 10 state-of-the-art large-scale generative models and 21 conventional restoration models, which are annotated with 152,020 expert-level pairwise human preferences and 28,334 quality scores. Built upon LL-Bench, we present a systematic diagnosis that reveals the performance boundaries and unique failure modes of large-scale generative models across diverse low-level vision tasks, compared with conventional representative restoration approaches. Moreover, we investigate the effectiveness of current quality evaluation metrics on LL-Bench, which exhibit significant discrepancy with human ratings. To better align restored-image quality assessment with human preferences, we further propose \textbf{LL-Score}, an MLLM-based evaluator that captures both restoration quality and hallucination existence. Extensive experiments demonstrate that LL-score not only outperforms existing image quality assessment metrics, but also serves as a promising reward model for training generative models on low-level vision tasks.

cs.CV↗
arXiv2026

FedAdaVR: Adaptive Variance Reduction for Robust Federated Learning under Limited Client Participation

Federated learning (FL) encounters substantial challenges due to heterogeneity, leading to gradient noise, client drift, and partial client participation errors, the last of which is the most pervasive but remains insufficiently addressed in current literature. In this paper, we propose FedAdaVR, a novel FL algorithm aimed at solving heterogeneity issues caused by sporadic client participation by incorporating an adaptive optimiser with a variance reduction technique. This method takes advantage of the most recent stored updates from clients, even when they are absent from the current training round, thereby emulating their presence. Furthermore, we propose FedAdaVR-Quant, which stores client updates in quantised form, significantly reducing the memory requirements (by 50%, 75%, and 87.5%) of FedAdaVR while maintaining highly competitive model performance. We analyse the convergence behaviour of FedAdaVR under general nonconvex conditions and prove that our proposed algorithm can eliminate partial client participation error. Extensive experiments conducted on multiple datasets, under both independent and identically distributed (IID) and non-IID settings, demonstrate that FedAdaVR consistently outperforms state-of-the-art baseline methods.

cs.LG↗
arXiv2026

Measurement-Device-Independent Entanglement Quantification in a Fully Connected Time-Bin Quantum Network

Fully connected quantum networks enable scalable quantum communication, yet reliable entanglement characterization without trusting measurement devices remains challenging. Here we experimentally demonstrate measurement-device-independent (MDI) entanglement verification and quantification in a time-bin-encoded fully connected quantum network. Using a broadband periodically poled lithium niobate on insulator source combined with dense wavelength-division multiplexing, we distribute all six pairwise entangled links among four users over 20-km fiber channels, preserving high-fidelity entanglement without active stabilization of the long-distance fiber links. We show that conventional entanglement witnesses can fail under untrusted measurement conditions. By encoding trusted input states in the polarization degree of freedom of the same photons, we realize MDI measurements without ancillary photons or additional experimental resources. Both entanglement verification and quantification are obtained from the same measurement dataset. Our results establish a practical and scalable approach for reliable entanglement characterization in quantum networks.

quant-ph↗