arXiv subjects

Cheng Yuan

Publications and source records attributed to Cheng Yuan.

At least 19 recordsLinked to original sources

arXiv2026

On Cauchy Problems for Parabolic Equations with Rough Coefficients

The presented work investigates the Cauchy problems for parabolic equations in both non-divergence and divergence forms with rough diffusion coefficients, which commonly arise in composite media, financial pricing, and viscous fluids. Under critical regularity settings, we establish the unique solvability in optimal fractional Sobolev spaces. The first key technical step lies in constructing an effective approximation scheme with truncated and mollified diffusion coefficients $a^\epsilon(t,x)$, for which we rigorously prove the uniform preservation of high-frequency smallness. By incorporating this approximation scheme with paraproduct decomposition, Fefferman-Stein maximal inequalities, Coifman-Meyer bilinear estimates, and refined Sobolev embeddings, we close the uniform a priori estimates and then pass to the limit. Furthermore, we prove that the threshold $s < \frac{1}{2}$ is sharp by constructing explicit counterexamples. These theoretical results provide a rigorous mathematical framework in the study of Cauchy problems for parabolic equations with rough coefficients.

math.AP↗

arXiv2026

Global Well-posedness and Regularity of the Dynamical Prandtl Equation

In this paper, we study the dynamical Prandtl equation, which plays an important role in the study of the vanishing viscosity limit of the Navier--Stokes equations. Our focus is on the (Sobolev) well-posedness regime, where the given data satisfy a crucial monotonicity condition. In this case, local classical solutions have been constructed in the pioneering works of Oleinik \cite{O68,OS99}. More recently, global weak solutions were obtained in \cite{XZ04} by Xin and Zhang, and in \cite{XZZ24} by Xin, Zhang, and Zhao, where the uniqueness and interior H"older estimates of the solutions were established (in Crocco coordinates). Using a precise description of the fundamental solution to the Kolmogorov equation in the half-space, we first obtain the H"older regularity of local weak solutions up-to-boundary. We also provide a detailed proof of higher-order regularity estimates together with $W^{2,p}$ Sobolev estimates and $H^{s}$ hypoelliptic estimates, which are nontrivial. Up-to-boundary smoothness of solutions (in Crocco coordinates) is important in order to conclude the smoothness of the Prandtl solutions in the physical variables, even in the interior. It is also physically significant for applications to the Boundary Layer Theory where the dynamical Prandtl equation is essential. Using these smoothing estimates, we then prove the global existence and regularity of classical solutions to the dynamical Prandtl equation under monotonicity assumptions, which was listed by Oleinik and Samokhin in \cite{OS99} as one of the open problems. We also develop a self-contained local existence theory using weighted energy estimates and further expand the theory of global weak solutions. The main point is to incorporate all physical types of asymptotic matching of the boundary layer with the outer flow, which is expected to be useful for applications to the Navier--Stokes equations.

math.AP↗

arXiv2026

An alternating learning-based collocation method for solving inverse elliptic problems

We propose the Alternating Learning-Based Collocation (ALBC) method for solving inverse elliptic problems. Our approach employs sinusoidal shallow networks as adaptive basis generators. By alternately updating the state variable and the unknown parameter, we decompose the original nonconvex joint optimization problem into a sequence of tractable linear subproblems. This strategy effectively overcomes the fixed-basis limitations of classical collocation methods while avoiding the slow convergence typically encountered in deep learning approaches. Theoretically, we establish stability estimates and prove the convergence of the proposed algorithm. Numerical experiments on five benchmark problems demonstrate the efficacy of ALBC, which consistently outperforms the standard collocation method in accuracy. Furthermore, it achieves performance comparable to or better than that of physics-informed neural networks at a substantially lower computational cost. Finally, the method remains robust under noise levels of up to twenty percent.

math.NA↗

arXiv2026

Task-Oriented Communication for Human Action Understanding via Edge-Cloud Co-Inference

The expanding application of smart sensing has created a growing demand for the accurate understanding of human action at the network edge. Traditional approaches require massive video data to be transmitted from resource-constrained edge devices to powerful cloud servers, incurring prohibitive uplink bandwidth consumption and unacceptable latency while raising privacy concerns. To overcome these bottlenecks, we propose a task-oriented communication framework for human action understanding (TOAU) through edge-cloud collaboration. Our framework utilizes a monocular pose estimator to extract continuous joint coordinates from raw videos, followed by a vector quantized variational autoencoder (VQ-VAE) to convert these coordinates into discrete motion tokens. Consequently, only a compact sequence of codebook indices is transmitted over the network, consuming as few as 9 bits per frame and avoiding privacy leakages. At the cloud server, a lightweight projector aligns these motion tokens with the embedding space of a large vision-language model (VLM) to facilitate complex action understanding, which is trained with an efficient instruction tuning paradigm. Comprehensive evaluations on three benchmarks demonstrate that our TOAU system reduces the transmission payload to approximately 1\% and the system latency to around 20\% compared to video codec-based solutions, while delivering comparable action understanding accuracy.

eess.SP↗

arXiv2026

SCISSR: Scribble-Conditioned Interactive Surgical Segmentation and Refinement

Accurate segmentation of tissues and instruments in surgical scenes is annotation-intensive due to irregular shapes, thin structures, specularities, and frequent occlusions. While SAM models support point, box, and mask prompts, points are often too sparse and boxes too coarse to localize such challenging targets. We present SCISSR, a scribble-promptable framework for interactive surgical scene segmentation. It introduces a lightweight Scribble Encoder that converts freehand scribbles into dense prompt embeddings compatible with the mask decoder, enabling iterative refinement for a target object by drawing corrective strokes on error regions. Because all added modules (the Scribble Encoder, Spatial Gated Fusion, and LoRA adapters) interact with the backbone only through its standard embedding interfaces, the framework is not tied to a single model: we build on SAM 2 in this work, yet the same components transfer to other prompt-driven segmentation architectures such as SAM 3 without structural modification. To preserve pre-trained capabilities, we train only these lightweight additions while keeping the remaining backbone frozen. Experiments on EndoVis 2018 demonstrate strong in-domain performance, while evaluation on the out-of-distribution CholecSeg8k further confirms robustness across surgical domains. SCISSR achieves 95.41% Dice on EndoVis 2018 with five interaction rounds and 96.30% Dice on CholecSeg8k with three interaction rounds, outperforming iterative point prompting on both benchmarks.

eess.IV↗

arXiv2026

PA-Net: Precipitation-Adaptive Mixture-of-Experts for Long-Tail Rainfall Nowcasting

Precipitation nowcasting is vital for flood warning, agricultural management, and emergency response, yet two bottlenecks persist: the prohibitive cost of modeling million-scale spatiotemporal tokens from multi-variate atmospheric fields, and the extreme long-tailed rainfall distribution where heavy-to-torrential events -- those of greatest societal impact -- constitute fewer than 0.1% of all samples. We propose the Precipitation-Adaptive Network (PA-Net), a Transformer framework whose computational budget is explicitly governed by rainfall intensity. Its core component, Precipitation-Adaptive MoE (PA-MoE), dynamically scales the number of activated experts per token according to local precipitation magnitude, channeling richer representational capacity toward the rare yet critical heavy-rainfall tail. A Dual-Axis Compressed Latent Attention mechanism factorizes spatiotemporal attention with convolutional reduction to manage massive context lengths, while an intensity-aware training protocol progressively amplifies learning signals from extreme-rainfall samples. Experiment on ERA5 demonstrate consistent improvements over state-of-the-art baselines, with particularly significant gains in heavy-rain and rainstorm regimes.

cs.AI↗

arXiv2026

Surg-R1: A Hierarchical Reasoning Foundation Model for Scalable and Interpretable Surgical Decision Support with Multi-Center Clinical Validation

Surgical scene understanding demands not only accurate predictions but also interpretable reasoning that surgeons can verify against clinical expertise. However, existing surgical vision-language models generate predictions without reasoning chains, and general-purpose reasoning models fail on compositional surgical tasks without domain-specific knowledge. We present Surg-R1, a surgical Vision-Language Model that addresses this gap through hierarchical reasoning trained via a four-stage pipeline. Our approach introduces three key contributions: (1) a three-level reasoning hierarchy decomposing surgical interpretation into perceptual grounding, relational understanding, and contextual reasoning; (2) the largest surgical chain-of-thought dataset with 320,000 reasoning pairs; and (3) a four-stage training pipeline progressing from supervised fine-tuning to group relative policy optimization and iterative self-improvement. Evaluation on SurgBench, comprising six public benchmarks and six multi-center external validation datasets from five institutions, demonstrates that Surg-R1 achieves the highest Arena Score (64.9%) on public benchmarks versus Gemini 3.0 Pro (46.1%) and GPT-5.1 (37.9%), outperforming both proprietary reasoning models and specialized surgical VLMs on the majority of tasks spanning instrument localization, triplet recognition, phase recognition, action recognition, and critical view of safety assessment, with a 15.2 percentage point improvement over the strongest surgical baseline on external validation.

cs.CV↗

arXiv2026

Enhancing Neural Video Compression of Static Scenes with Positive-Incentive Noise

Static scene videos, such as surveillance feeds and videotelephony streams, constitute a dominant share of storage consumption and network traffic. However, both traditional standardized codecs and neural video compression (NVC) methods struggle to encode these videos efficiently due to inadequate usage of temporal redundancy and severe distribution gaps between training and test data, respectively. While recent generative compression methods improve perceptual quality, they introduce hallucinated details that are unacceptable in authenticity-critical applications. To overcome these limitations, we propose a positive-incentive camera (PIC) framework for static scene videos, where short-term temporal changes are reinterpreted as positive-incentive noise to facilitate NVC model finetuning. By disentangling transient variations from the persistent background, structured prior information is internalized in the compression model. During inference, the invariant component requires minimal signaling, thus reducing data transmission while maintaining pixel-level fidelity. Experiment results show that PIC achieves visually lossless reconstruction for static scenes at an extremely low compression rate of 0.009%, while the DCVC-FM baseline requires 20.5% higher Bj{\o}ntegaard delta (BD) rate. Our method provides an effective solution to trade computation for bandwidth, enabling robust video transmission under adverse network conditions and economic long-term retention of surveillance footage.

eess.IV↗

arXiv2026

Privacy-Aware Camera 2.0 Technical Report

With the increasing deployment of intelligent sensing technologies in highly sensitive environments such as restrooms and locker rooms, visual surveillance systems face a profound privacy-security paradox. Existing privacy-preserving approaches, including physical desensitization, encryption, and obfuscation, often compromise semantic understanding or fail to ensure mathematically provable irreversibility. Although Privacy Camera 1.0 eliminated visual data at the source to prevent leakage, it provided only textual judgments, leading to evidentiary blind spots in disputes. To address these limitations, this paper proposes a novel privacy-preserving perception framework based on the AI Flow paradigm and a collaborative edge-cloud architecture. By deploying a visual desensitizer at the edge, raw images are transformed in real time into abstract feature vectors through nonlinear mapping and stochastic noise injection under the Information Bottleneck principle, ensuring identity-sensitive information is stripped and original images are mathematically unreconstructable. The abstract representations are transmitted to the cloud for behavior recognition and semantic reconstruction via a "dynamic contour" visual language, achieving a critical balance between perception and privacy while enabling illustrative visual reference without exposing raw images.

cs.CV↗

arXiv2026

Beyond Static Artifacts: A Forensic Benchmark for Video Deepfake Reasoning in Vision Language Models

Current Vision-Language Models (VLMs) for deepfake detection excel at identifying spatial artifacts but overlook a critical dimension: temporal inconsistencies in video forgeries. Adapting VLMs to reason about these dynamic cues remains a distinct challenge. To bridge this gap, we propose Forensic Answer-Questioning (FAQ), a large-scale benchmark that formulates temporal deepfake analysis as a multiple-choice task. FAQ introduces a three-level hierarchy to progressively evaluate and equip VLMs with forensic capabilities: (1) Facial Perception, testing the ability to identify static visual artifacts; (2) Temporal Deepfake Grounding, requiring the localization of dynamic forgery artifacts across frames; and (3) Forensic Reasoning, challenging models to synthesize evidence for final authenticity verdicts. We evaluate a range of VLMs on FAQ and generate a corresponding instruction-tuning set, FAQ-IT. Extensive experiments show that models fine-tuned on FAQ-IT achieve advanced performance on both in-domain and cross-dataset detection benchmarks. Ablation studies further validate the impact of our key design choices, confirming that FAQ is the driving force behind the temporal reasoning capabilities of these VLMs.

cs.CV↗

arXiv2026

A Real-Time Privacy-Preserving Behavior Recognition System via Edge-Cloud Collaboration

As intelligent sensing expands into high-privacy environments such as restrooms and changing rooms, the field faces a critical privacy-security paradox. Traditional RGB surveillance raises significant concerns regarding visual recording and storage, while existing privacy-preserving methods-ranging from physical desensitization to traditional cryptographic or obfuscation techniques-often compromise semantic understanding capabilities or fail to guarantee mathematical irreversibility against reconstruction attacks. To address these challenges, this study presents a novel privacy-preserving perception technology based on the AI Flow theoretical framework and an edge-cloud collaborative architecture. The proposed methodology integrates source desensitization with irreversible feature mapping. Leveraging Information Bottleneck theory, the edge device performs millisecond-level processing to transform raw imagery into abstract feature vectors via non-linear mapping and stochastic noise injection. This process constructs a unidirectional information flow that strips identity-sensitive attributes, rendering the reconstruction of original images impossible. Subsequently, the cloud platform utilizes multimodal family models to perform joint inference solely on these abstract vectors to detect abnormal behaviors. This approach fundamentally severs the path to privacy leakage at the architectural level, achieving a breakthrough from video surveillance to de-identified behavior perception and offering a robust solution for risk management in high-sensitivity public spaces.

cs.CR↗

arXiv2025

The Law of Multi-Model Collaboration: Scaling Limits of Model Ensembling for Large Language Models

Recent advances in large language models (LLMs) have been largely driven by scaling laws for individual models, which predict performance improvements as model parameters and data volume increase. However, the capabilities of any single LLM are inherently bounded. One solution originates from intricate interactions among multiple LLMs, rendering their collective performance surpasses that of any constituent model. Despite the rapid proliferation of multi-model integration techniques such as model routing and post-hoc ensembling, a unifying theoretical framework of performance scaling for multi-model collaboration remains absent. In this work, we propose the Law of Multi-model Collaboration, a scaling law that predicts the performance limits of LLM ensembles based on their aggregated parameter budget. To quantify the intrinsic upper bound of multi-model collaboration, we adopt a method-agnostic formulation and assume an idealized integration oracle where the total cross-entropy loss of each sample is determined by the minimum loss of any model in the model pool. Experimental results reveal that multi-model systems follow a power-law scaling with respect to the total parameter count, exhibiting a more significant improvement trend and a lower theoretical loss floor compared to single model scaling. Moreover, ensembles of heterogeneous model families achieve better performance scaling than those formed within a single model family, indicating that model diversity is a primary driver of collaboration gains. These findings suggest that model collaboration represents a critical axis for extending the intelligence frontier of LLMs.

cs.LG↗

arXiv2025

Integrated Ring-based Quantum Key Distribution with Weak Measurement Enhanced Fiber-Optic Sensing Disturbance Magnitude and Location

The deep integration of quantum communication and fiber-optic sensing is pivotal for the development of next-generation multifunctional and highly reliable secure information infrastructure. Here, we present a Sagnac-loop integrated system (SLIS) that, for the first time, combines ring-based quantum key distribution (QKD) with fiber-based weak measurement (WM) enhanced sensing and disturbance localization capabilities. In the event of communication interruption due to external disturbances, the SLIS seamlessly switches to perception system, employing interference measurement and WM techniques to monitor channel disturbances. By integrating null-frequencies localization (NFL) mode, the system precisely determines the disturbance location, enabling rapid identification of security vulnerabilities along the link. Experimental results demonstrate that, over a 30 km Sagnac loop channel, the SLIS achieves a raw key generation rate of 22.4 kbps with stable operation and clear scalability toward network expansion. In terms of perception performance, the SLIS exhibits strong capability for both dynamic and quasi-static disturbances. For dynamic perturbations, the system detects transient impacts and PZT-driven frequency variations down to 100 Hz, and enables long-distance localization via NFL alignment, with improved localization performance as the disturbance position moves farther away along the loop. For quasi-static disturbances, gravitational changes as small as 100 g are resolved, corresponding to a time-delay variation of 9.81 as. This work provides a novel technical pathway toward self-diagnosing, robust quantum networks through integrated communication and sensing functionalities.

quant-ph↗

arXiv2025

Provable Diffusion Posterior Sampling for Bayesian Inversion

We propose a novel diffusion-based posterior sampling method within a plug-and-play framework. Our approach constructs a probability transport from an easy-to-sample distribution to the target posterior via a diffusion process. To initialize the sampler efficiently, we introduce a warm-start strategy for the particles. The posterior score is then approximated using a Monte Carlo estimator in which samples are generated via Langevin dynamics, avoiding the heuristic approximations prevalent in prior work. The score function driving the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior. We also establish non-asymptotic error bounds in Wasserstein-2 distance guaranteeing convergence of the proposed method even for complex, multimodal posterior distributions. We corroborate our theoretical findings with numerical experiments demonstrating the effectiveness of the method across a variety of inverse problems.

stat.ML↗

arXiv2025

See in Depth: Training-Free Surgical Scene Segmentation with Monocular Depth Priors

Pixel-wise segmentation of laparoscopic scenes is essential for computer-assisted surgery but difficult to scale due to the high cost of dense annotations. We propose depth-guided surgical scene segmentation (DepSeg), a training-free framework that utilizes monocular depth as a geometric prior together with pretrained vision foundation models. DepSeg first estimates a relative depth map with a pretrained monocular depth estimation network and proposes depth-guided point prompts, which SAM2 converts into class-agnostic masks. Each mask is then described by a pooled pretrained visual feature and classified via template matching against a template bank built from annotated frames. On the CholecSeg8k dataset, DepSeg improves over a direct SAM2 auto segmentation baseline (35.9% vs. 14.7% mIoU) and maintains competitive performance even when using only 10--20% of the object templates. These results show that depth-guided prompting and template-based classification offer an annotation-efficient segmentation approach.

cs.CV↗

arXiv2025

Information Capacity: Evaluating the Efficiency of Large Language Models via Text Compression

Recent years have witnessed the rapid advancements of large language models (LLMs) and their expanding applications, leading to soaring demands for computational resources. The widespread adoption of test-time scaling further intensifies the tension between model capability and resource consumption. However, a rigorous metric that accurately reflects an LLM's inference efficiency across diverse tokenizers, parameter counts, and model architectures remains absent. Motivated by the correlation between compression and intelligence, we introduce information capacity, a measure of model efficiency based on text compression performance relative to computational complexity. A distinctive feature of information capacity is its incorporation of tokenizer efficiency, which affects inference costs but is often neglected in LLM evaluations. We assess the information capacity of 56 open-source models and observe a consistent information capacity among different-sized models within a series. Experiments on five heterogeneous datasets reveal strong linguistic biases in mainstream LLMs. Empirical results verify the accuracy of performance prediction across model sizes based on information capacity and show the correlation between information capacity and benchmark scores. This metric can be used to quantify improvements in inference efficiency and provide insights into better scaling performance for future LLM development.

cs.AI↗

arXiv2025

Toward fast, accurate and robust AI prediction of ground states in rotating BEC

We propose an unsupervised deep learning approach for computing the ground state (GS) of rotating Bose-Einstein condensation. To minimize the energy under a mass constraint, our approach introduces two key and novel ingredients: a normalized loss function that exactly enforces the mass constraint, and a training strategy named virtual rotation acceleration that is essential for avoiding local minima and guiding the learning process to the correct quantized vortex phase. Extensive numerical experiments demonstrate the proposed approach as an effective and accurate method to predict GS across physical conditions--from slow to fast rotation and from isotropic to anisotropic confinement. Through further distillation, we establish a unified operator network capable of efficiently generalizing physical parameters across different phases. It enables rapid GS predictions while correctly capturing phase transitions and is applied for inverse problems.

cond-mat.quant-gas↗

arXiv2025

LCDS: A Logic-Controlled Discharge Summary Generation System Supporting Source Attribution and Expert Review

Despite the remarkable performance of Large Language Models (LLMs) in automated discharge summary generation, they still suffer from hallucination issues, such as generating inaccurate content or fabricating information without valid sources. In addition, electronic medical records (EMRs) typically consist of long-form data, making it challenging for LLMs to attribute the generated content to the sources. To address these challenges, we propose LCDS, a Logic-Controlled Discharge Summary generation system. LCDS constructs a source mapping table by calculating textual similarity between EMRs and discharge summaries to constrain the scope of summarized content. Moreover, LCDS incorporates a comprehensive set of logical rules, enabling it to generate more reliable silver discharge summaries tailored to different clinical fields. Furthermore, LCDS supports source attribution for generated content, allowing experts to efficiently review, provide feedback, and rectify errors. The resulting golden discharge summaries are subsequently recorded for incremental fine-tuning of LLMs. Our project and demo video are in the GitHub repository https://github.com/ycycyc02/LCDS.

cs.CL↗