arXiv subjects

Yidong Luo

Publications and source records attributed to Yidong Luo.

12 recordsLinked to original sources

arXiv2026

Stokes-Informed Diffusion for Robust Linear Polarization Estimation

Polarization cues benefit applications such as material detection and de-reflection, yet acquiring them typically requires dedicated hardware. This motivates us to estimate the linear polarization from a single RGB image. However, the task is inherently ill-posed, with the Angle of Polarization (AoP) becoming particularly unstable in weak polarization regions, where the polarimetric signal is overwhelmed by noise, leading to erratic angle estimates. To address these limitations, we propose GenPolar, a Stokes-informed diffusion framework grounded in the Mueller formalism from an intensity observation. Specifically, GenPolar predicts channel-wise linear Stokes components (S1,S2) from intensity S0, from which degree of linear polarization (DoLP) and AoP are analytically derived; AoP is further supervised with an observability-aware loss. In addition, to enable efficient and high-fidelity inference, we adopt a two-stage training strategy. Firstly, a multi-step conditional diffusion model is trained with a physics-based loss. Subsequently, we distill it into a one-step generator, which further supports stable Low-Rank Adaptation (LoRA) of the VAE encoder to mitigate domain-specific autoencoding bias. Extensive experiments across rotating-polarizer, division-of-focal-plane, and hybrid datasets demonstrate that GenPolar achieves state-of-the-art performance in both DoLP fidelity and AoP stability. Crucially, these improvements translate to significant and consistent gains in downstream applications, including material detection and de-reflection.

cs.CV↗

arXiv2026

GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs

Configuring the hyperparameters of Mixed-integer programming (MIP) solvers is a high-dimensional, instance-dependent optimization problem where suboptimal settings can degrade solving time by orders of magnitude. Default configurations are often suboptimal, while traditional tuning methods either suffer from the ``cold-start'' problem and inefficient search or heavily rely on expert experience. This paper introduces \textbf{GRIMIP} (\textbf{\underline{G}}eneral \textbf{\underline{R}}easoning for \textbf{\underline{I}}nstance-specific \textbf{\underline{MIP}} configuration), a novel hybrid intelligence framework that synergistically integrates the semantic reasoning capabilities of Large Language Models (LLMs) with the sample-efficient search of Bayesian Optimization (BO). GRIMIP enables the LLM to function as a complete probabilistic surrogate within the BO loop, significantly improving performance and reducing sampling and evaluation costs. On seven benchmarks including MIPLIB, GRIMIP achieves over 40\% reduction in Primal-Dual Integral on hard instances, outperforming SMAC and other LLM-assisted BO methods. By granting LLMs sufficient autonomy, GRIMIP combines the expert-level reasoning of LLMs with the efficient search of BO, achieving state-of-the-art performance.

cs.LG↗

arXiv2026

PolarVSR: A Unified Framework and Benchmark for Continuous Space-Time Polarization Video Reconstruction

Polarimetric imaging captures surface polarization characteristics, such as the Degree of Linear Polarization (DoLP) and the Angle of Polarization (AoP). In mainstream Division of-Focal-Plane (DoFP) color polarization imaging, recovering polarization parameters from captured mosaic arrays remains a challenging inverse problem. Existing DoFP cameras also face hardware bottlenecks and often cannot support high-frame-rate acquisition, limiting polarimetric imaging in dynamic video tasks. These limitations motivate joint spatial and temporal enhancement. To this end, we propose the first space-time polarization video reconstruction architecture. The method jointly models polarization directions in space and time and uses a polarization-aware implicit neural representation for continuous, high-fidelity upsampling. By analyzing temporal variations in polarization parameters, we further introduce a flow-guided polarization variation loss to supervise polarization dynamics. We also establish the first large-scale color DoFP polarization video benchmark to support this research direction. Extensive experiments on this benchmark demonstrate the effectiveness of the method.

cs.CV↗

arXiv2026

PolarAPP: Beyond Polarization Demosaicking for Polarimetric Applications

Polarimetric imaging enables advanced vision applications such as normal estimation and de-reflection by capturing unique surface-material interactions. However, existing applications (alternatively called downstream tasks) rely on datasets constructed by naively regrouping raw measurements from division-of-focal-plane sensors, where pixels of the same polarization angle are extracted and aligned into sparse images without proper demosaicking. This reconstruction strategy results in suboptimal, incomplete targets that limit downstream performance. Moreover, current demosaicking methods are task-agnostic, optimizing only for photometric fidelity rather than utility in downstream tasks. Towards this end, we propose PolarAPP, the first framework to jointly optimize demosaicking and its downstream tasks. PolarAPP introduces a feature alignment mechanism that semantically aligns the representations of demosaicking and downstream networks via meta-learning, guiding the reconstruction to be task-aware. It further employs an equivalent imaging constraint for demosaicking training, enabling direct regression to physically meaningful outputs without relying on rearranged data. Finally, a task-refinement stage fine-tunes the task network using the stable demosaicking front-end to further enhance accuracy. Extensive experimental results demonstrate that PolarAPP outperforms existing methods in both demosaicking quality and downstream performance. Code is available upon acceptance.

cs.CV↗

arXiv2026

Polarization Uncertainty-Guided Diffusion Model for Color Polarization Image Demosaicking

Color polarization demosaicking (CPDM) aims to reconstruct full-resolution polarization images of four directions from the color-polarization filter array (CPFA) raw image. Due to the challenge of predicting numerous missing pixels and the scarcity of high-quality training data, existing network-based methods, despite effectively recovering scene intensity information, still exhibit significant errors in reconstructing polarization characteristics (degree of polarization, DOP, and angle of polarization, AOP). To address this problem, we introduce the image diffusion prior from text-to-image (T2I) models to overcome the performance bottleneck of network-based methods, with the additional diffusion prior compensating for limited representational capacity caused by restricted data distribution. To effectively leverage the diffusion prior, we explicitly model the polarization uncertainty during reconstruction and use uncertainty to guide the diffusion model in recovering high error regions. Extensive experiments demonstrate that the proposed method accurately recovers scene polarization characteristics with both high fidelity and strong visual perception.

eess.IV↗

arXiv2025

Are Your Generated Instances Truly Useful? GenBench-MILP: A Benchmark Suite for MILP Instance Generation

The proliferation of machine learning-based methods for Mixed-Integer Linear Programming (MILP) instance generation has surged, driven by the need for diverse training datasets. However, a critical question remains: Are these generated instances truly useful and realistic? Current evaluation protocols often rely on superficial structural metrics or simple solvability checks, which frequently fail to capture the true computational complexity of real-world problems. To bridge this gap, we introduce GenBench-MILP, a comprehensive benchmark suite designed for the standardized and objective evaluation of MILP generators. Our framework assesses instance quality across four key dimensions: mathematical validity, structural similarity, computational hardness, and utility in downstream tasks. A distinctive innovation of GenBench-MILP is the analysis of solver-internal features -- including root node gaps, heuristic success rates, and cut plane usage. By treating the solver's dynamic behavior as an expert assessment, we reveal nuanced computational discrepancies that static graph features miss. Our experiments on instance generative models demonstrate that instances with high structural similarity scores can still exhibit drastically divergent solver interactions and difficulty levels. By providing this multifaceted evaluation toolkit, GenBench-MILP aims to facilitate rigorous comparisons and guide the development of high-fidelity instance generators.

cs.LG↗

arXiv2025

Rethinking the Unsolvable: When In-Context Search Meets Test-Time Scaling

Recent research has highlighted that Large Language Models (LLMs), even when trained to generate extended long reasoning steps, still face significant challenges on hard reasoning problems. However, much of the existing literature relies on direct prompting with simple in-context learning examples for evaluation, which largely overlooks advanced techniques to elicit LLMs' deliberate reasoning before drawing conclusions that LLMs hit a performance ceiling. In this paper, we systematically explore the combined potential of in-context search and test-time scaling on super hard reasoning tasks. We find that by employing advanced in-context search prompting to LLMs augmented with internal scaling, one can achieve transformative performance breakthroughs on tasks previously deemed "unsolvable" (e.g., reported success rates below 5%). We provide both empirical results and theoretical analysis of how this combination can unleash LLM reasoning capabilities: i) Empirically, on controlled NP-hard tasks and complex real-world planning benchmarks, our approach achieves up to a 30x improvement in success rates compared to previously reported results without any external mechanisms; ii) Theoretically, we show that in-context search prompting, when combined with internal scaling, significantly extends the complexity class of solvable reasoning problems. These findings challenge prevailing assumptions about the limitations of LLMs on complex tasks, indicating that current evaluation paradigms systematically underestimate their true potential. Our work calls for a critical reassessment of how LLM reasoning is benchmarked and a more robust evaluation strategy that fully captures the true capabilities of contemporary LLMs, which can lead to a better understanding of their operational reasoning boundaries in real-world deployments.

cs.AI↗

arXiv2020

Numerical analysis on boundary integral equation to exterior Dirichlet problem of Laplace equation

This paper investigate on numerical analysis on modified Single-layer approach to exterior Dirichlet problem of Laplace equation. We complete the convergence and error analysis of Petrov-Galerkin and Galerkin-Collocation methods with trigonometric basis for the induced modified Symm's integral equation of the first kind on analytic boundary. Besides, utilizing the composite trapezial quadrature formula and trigonometric interpolation to handle the singularity in modified logarithmic kernel, we establish the numerical procedure for implementation. On these numerical examples, we compare the effect and efficiency of different Petrov-Galerkin and Galerkin-Collocation methods.

math.NA↗

arXiv2020

A non-conditional divergence criteria of Petrov-Galerkin method for bounded linear operator equation

Petrov-Galerkin methods are always considered in numerical solutions of differential and integral equations $ Ax=b $. It is common to consider the convergence and error analysis when $ b \in \mathcal{R}(A) $ which make the equation solvable. However, the case when $ b \notin \mathcal{R}(A) $ is always ignored. In this paper, we consider the numerical behavior of Petrov-Galerkin methods when $ b \notin \mathcal{R}(A) $. It is a natural guess that when $ b \in \mathcal{R}(A) $, the corresponding approximate solution constructed by Petrov-Galerkin methods with arbitrary basis will diverge to infinity. We prove this conjecture for bounded linear operator equation with dense range $ \mathcal{R}(A) $ and give a more general divergence result for bounded linear operator equation with not necessarily dense range $ \mathcal{R}(A) $. Several applications show its power.

math.NA↗

arXiv2020

Unified analysis on Petrov-Galerkin method into Symm's integral of the first kind

On bounded and simply connected planar analytic domain $ Ω$, by $ 2π$ periodic parametric representation of boundary curve $ \partial Ω$, Symm's integral equation of the first kind takes form $ K Ψ= g $, where $ K $ is seen as an operator mapping from $ L^2(0,2π) $ to itself. The classical result show complete convergence and error analysis in $ L^2 $ setting for least squares, dual least squares, Bubnov-Galerkin methods with Fourier basis when $ g \in H^r(0,2π), \ r \geq 1 $. In this paper, weakening the boundary $ \partial Ω$ from analytic to $ C^3 $ class, we maintain the convergence and error analysis from analytic case. Besides, it is proven that, when $ g \in H^r(0,2π), \ 0 \leq r < 1 $, the least squares, dual least squares, Bubnov-Galerkin methods with Fourier basis will uniformly diverge to infinity at first order. The divergence effect and optimality of first order rate are confirmed in an example.

math.NA↗

arXiv2019

Generalization of Lax Equivalence Theorem on Unbounded Self-adjoint Operators with Applications to Schrödinger Operators

Define $ A $ a unbounded self-adjoint operator on Hilbert space $ X $. Let $ \{ A_n \} $ be its resolvent approximation sequence with closed range $ \mathcal{R}(A_n) (n \in \mathrm{N}) $, that is, $ A_n (n \in \mathrm{N}) $ are all self-adjoint on Hilbert space $ X $ and \begin{equation*} \hbox{ \raise-2mm\hbox{$\textstyle s-\lim \atop \scriptstyle {n \to \infty}$}} R_λ(A_n) = R_λ(A)\quad (λ\in \mathrm{C} \setminus \mathrm{R}), \ \textrm{where} \ R_ λ(A) := (λI-A)^{-1}. \end{equation*} The Moore-Penrose inverse $ A^\dagger_n \in \mathcal{B}(X) $ is a natural approximation to the Moore-Penrose inverse $ A^\dagger $. This paper shows that: $ A^\dagger $ is continuous and strongly converged by $ \{ A^\dagger_n \} $ if and only if $ \sup\limits_n \Vert A^\dagger_n \Vert < +\infty $. On the other hand, this result tells that arbitrary bounded computational scheme $ \{ A^\dagger_n \} $ induced by resolvent approximation $ \{ A_n \} $ is naturally instable (that is, $ \sup_n \Vert A^\dagger_n \Vert = \infty $) for any self-adjoint operator equation with non-closed range, for example, free Schrödinger operator, Schrödinger operator with Coulumb potential and Schrödinger operator in model of many particles. This implies the infeasibility to globally and approximately solve non-closed range self-ajoint operator equation by resolvent approximation.

math.FA↗

arXiv2019

Galerkin Method with Trigonometric Basis on Stable Numerical Differentiation

This paper considers the $ p $ ($ p=1,2,3 $) order numerical differentiation on function $ y $ in $ (0,2π) $. They are transformed into corresponding Fredholm integral equation of the first kind. Computational schemes with analytic solution formulas are designed using Galerkin method on trigonometric basis. Convergence and divergence are all analysed in Corollaries 5.1, 5.2, and a-priori error estimate is uniformly obtained in Theorem 6.1, 7.1, 7.2. Therefore, the algorithm achieves the optimal convergence rate $ O( δ^{\frac{2μ}{2μ+1}} ) \ (μ= \frac{1}{2} \ \textrm{or} \ 1)$ with periodic Sobolev source condition of order $ 2μp $. Besides, we indicate a noise-independent a-priori parameter choice when the function $ y $ possesses the form of \begin{equation*} \sum^{p-1}_{k=0} a_k t^k + \sum^{N_1}_{k=1} b_k \cos k t + \sum^{N_2}_{k=1} c_k \sin k t, \ b_{N_1}, c_{N_2} \neq 0, \end{equation*} In particular, in numerical differentiations for functions above, good filtering effect (error approaches 0) is displayed with corresponding parameter choice. In addition, several numerical examples are given to show that even derivatives with discontinuity can be recovered well.

math.NA↗