arXiv subjects

Yong Wang

Publications and source records attributed to Yong Wang.

At least 37 records · Page 2Linked to original sources

arXiv2026

Asymptotic Stability of Steady Prandtl Equations with Suction

Despite its physical importance, the stability of Prandtl boundary layers under wall suction remains relatively unexplored in rigorous PDE analysis. In this paper, we establish the global-in-$x$ asymptotic stability of a suction profile. For any prescribed algebraic decay rate in $x$, we prove that sufficiently small inflow perturbations with sufficiently rapid spatial decay yield downstream decay at that rate. The von Mises transformation reduces the Prandtl system to a degenerate parabolic equation with a favorably directed convection term. We first identify the downstream decay mechanism in an associated uniformly parabolic problem, then control the boundary degeneracy using a sharp Hardy-type estimate. Together, these arguments yield stability and decay for the original Prandtl system.

math.AP↗

arXiv2026

Robust LLM Unlearning Against Relearning Attacks: The Minor Components in Representations Matter

Large language model (LLM) unlearning aims to remove specific data influences from pre-trained model without costly retraining, addressing privacy, copyright, and safety concerns. However, recent studies reveal a critical vulnerability: unlearned models rapidly recover "forgotten" knowledge through relearning attacks. This fragility raises serious security concerns, especially for open-weight models. In this work, we investigate the fundamental mechanism underlying this fragility from a representation geometry perspective. We discover that existing unlearning methods predominantly optimize along dominant components, leaving minor components largely unchanged. Critically, during relearning attacks, the modifications in these dominant components are easily reversed, enabling rapid knowledge recovery, whereas minor components exhibit stronger resistance to such reversal. We further provide a theoretical analysis that explains both observations from the spectral structure of representations. Building on this insight, we propose Minor Component Unlearning (MCU), a novel unlearning approach that explicitly targets minor components in representations. Extensive experiments on three datasets validate that, by concentrating unlearning effects in these inherently robust directions, our method achieves substantially improved resistance to relearning attacks.

cs.CL↗

arXiv2026

Diffusion-grounded VideoLLM for Entity-aware temoporal grounding

Precise temporal grounding requires distinguishing when a queried event occurs from when its participating entities are merely visible. We propose Diffusion-Grounded VideoLLM, which conditions temporal feature extraction on query-relevant entities before language reasoning. The framework tracks entities named in the query and uses their masks to condition a frozen video diffusion backbone. Intermediate spatiotemporal features are extracted through truncated denoising and combined with entity tokens and timestamp embeddings. The language model uses this evidence together with the full query to generate temporal intervals and answers to grounded questions. On Charades-STA and NExT-GQA, the model obtains 43.5 mIoU and 28.4 Acc@GQA, improving the reported Grounded-VideoLLM reference by 6.7 and 1.7 points, respectively. Component and entity-pathway ablations support the usefulness of conditioning diffusion features on query-relevant entities for temporal grounding.

cs.CV↗

arXiv2026

RepNN: Tackling spectral bias in deep neural networks for regression and PDE problems via parameter reparameterization

Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors. In this study, we investigate this limitation by examining the failure of shallow ReLU neural networks in fitting high-frequency functions. This observation identifies two important factors in resolving rapid oscillations: the initial slope scale and the distribution of partition points induced by the networks. Motivated by this analysis, we propose RepNN, a reparameterized neural network model with ReLU or tanh activations designed for high-frequency and multiscale problems. The key idea is to reparameterize the weights and biases in the first hidden layer, which enables effective control of the initial slope scale and provides an appropriate distribution of the initial partition points. Furthermore, treating the reparameterized weights and biases as trainable parameters allows the DNN to achieve adaptive frequency scaling during training. In addition, we derive quantitative estimates for the output and slope magnitudes of the reparameterized DNN to guide the initialization of the proposed method. Numerical experiments, including multiscale one-, two-, and four-dimensional function approximations, forward and inverse PDE problems in combination with physics-informed neural networks (PINNs), and operator learning for an earthquake problem using real data, demonstrate that RepNN improves the predicted accuracy of vanilla DNNs in capturing highly oscillatory features. These results indicate that RepNN provides an effective and flexible approach for overcoming spectral bias and applying DNNs to multiscale problems.

cs.LG↗

arXiv2026

Noise-adapted Neural Operator for Robust Non-Line-of-Sight Imaging

This work has been submitted for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the extraction of information from obscured or hidden scenes is achieved through the utilization of indirect light signals resulting from multiple reflections or scattering. The inherently weak nature of these signals, coupled with their susceptibility to noise, necessitates the integration of physical processes to ensure accurate reconstruction. This paper presents a parameterized inverse problem framework tailored for large-scale linear problems in 3D imaging reconstruction. Initially, a noise estimation module is employed to adaptively assess the noise levels present in transient data. Subsequently, a parameterized neural operator is developed to approximate the inverse mapping, facilitating end-to-end rapid image reconstruction. Our 3D image reconstruction framework, grounded in operator learning, is constructed through deep algorithm unfolding, which not only provides commendable model interpretability but also enables dynamic adaptation to varying noise levels in the acquired data, thereby ensuring consistently robust and accurate reconstruction outcomes. Furthermore, we introduce a novel method for the fusion of global and local spatiotemporal data features. By integrating structural and detailed information, this method significantly enhances both accuracy and robustness. Comprehensive numerical experiments conducted on both simulated and real datasets substantiate the efficacy of the proposed method. It demonstrates remarkable performance with fast scanning data and sparse illumination point data, offering a viable solution for NLOS imaging in complex scenarios.

cs.CV↗

arXiv2026

EMIR$^2$: Evolution-Aware Memory with Intent-Guided Multi-Round Retrieval

Long-term memory enables large language model (LLM) agents to leverage historical interactions for future tasks. However, existing memory systems struggle to utilize continuously evolving historical information, as they often rely on static memory representations and single-round retrieval strategies, failing to track factual changes or integrate distributed evidence across long-term interactions. To address these challenges, we propose \textsc{EMIR}$^{2}$, an \textbf{E}volution-Aware \textbf{M}emory framework with \textbf{I}ntent-Guided Multi-\textbf{R}ound \textbf{R}etrieval, enabling LLM agents to maintain evolving historical knowledge and adaptively retrieve relevant evidence. Specifically, \textsc{EMIR}$^{2}$ constructs a State-Evolving Memory Graph (SEMG) that represents long-term memory as evolving knowledge states supported by temporal event trajectories and evidential associations. By maintaining semantic states through evidence-based updates, SEMG preserves historical evolution and enables evidence tracing under complex and conflicting scenarios. Building upon this, we introduce an intent-guided multi-round retrieval mechanism that iteratively identifies missing evidence and expands retrieval based on accumulated information. Experiments on LoCoMo and MemConflict demonstrate that \textsc{EMIR}$^{2}$ improves long-term memory utilization, dynamic and static conflict handling, and complex retrieval performance, achieving relative improvements of more than 12\% in certain categories. These results highlight the effectiveness of jointly modeling memory evolution and adaptive evidence acquisition for long-term agent interactions.

cs.AI↗

arXiv2026

Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

Operator learning is an emerging field at the intersection of machine learning and scientific computing. By learning mappings between function spaces, neural operators provide data-driven surrogate models for families of partial differential equations (PDEs). Once trained, these models can evaluate solution operators efficiently, making them suitable for many-query applications such as real-time prediction and parameter sweeps. However, maintaining high approximation accuracy and stable long-term predictions remains challenging for complex forward and inverse problems. To address these challenges, we propose the Starter-Iterator Neural Operator (SINO), which incorporates the initialization and residual-correction structures of classical iterative solvers into neural operator learning. The frequency-domain Starter captures dominant global spectral features and provides an informed initial approximation, while the latent-space Iterator applies successive residual-based corrections to refine local and multiscale solution structures. Experiments on representative time-dependent PDEs, including the Navier-Stokes and acoustic wave equations, together with applications to image super-resolution and weather forecasting, show that SINO achieves competitive accuracy and stable performance across the benchmarks considered in this work.

math.NA↗

arXiv2026

Hamiltonian-Type Spectral Functionals for Time-Dependent Perturbed Hodge--de Rham Operators

Let $g_t$ be a smooth family of Riemannian metrics on an oriented manifold of even dimension $n\geq4$, and let $D_t=d+δ_{g_t}+Ψ_t$ on the fixed exterior bundle, with $Ψ_t$ self-adjoint. We evaluate a scalar-weighted residue functional obtained from the operator expression in Hawkins' Hamiltonian action using the coefficient derivative $\partial_tD_t$. The velocity contribution depends only on $\partial_tg_t$. A direct symbol calculation reduces the lapse correction to a divergence and a Dirichlet term; for a nonconstant test function, integration by parts retains a mixed gradient term. For compact manifolds with a warped collar, we specify compatible factorizations of the weighted KKW term and of the commutator correction. Their boundary residues are computed explicitly. The collar-derivative and perturbation contributions cancel in the weighted KKW factorization, and the remaining boundary terms involve normal derivatives of the scalar weights. The closed formula is recovered when the boundary is empty.

math.DG↗

arXiv2026

Know Your Body: A Harness for Direct and Self-Improving Robot Control with VLMs

A general-purpose vision-language model can understand a task goal without knowing how a particular robot's motion and functional parts produce the intended effect. We introduce KnowBody, a harness that makes these action-relevant body relations explicit, queryable, and revisable while keeping the model weights frozen. Initialized from one off-task trajectory, a partial body model guides action selection and the interpretation of past interactions. New evidence refines the model, and knowledge dependent on revised body estimates is rechecked before reuse. Across 32 fixed-budget trials on four real-robot tasks, initialized KnowBody achieves 75% completion versus 25% for the native harness and requires fewer planner rounds on successful trials in tasks completed by both. With persistent updates enabled, planner rounds decrease by 29-53% from the first to the fifth recorded success.

cs.RO↗

arXiv2026

One-forms, spectral Einstein functionals and the noncommutative residue

For two one-forms and the Dirac operator, Dabrowski etc. recovered the spectral Einstein functionals by computing their noncommutative residue in Theorem 4.1 \cite{DL}. In this paper, we generalize the results of Dabrowski etc. to the cases of four dimensional spin manifolds with boundary.

math.DG↗

arXiv2026

CellRFT: Reinforcement Fine-Tuning for Single-Cell Perturbation Modeling

Predicting cellular responses to perturbations supports the study of gene function, disease mechanisms, and therapeutic strategies. Despite advances in single-cell perturbation modeling, existing models typically optimize surrogate losses that do not directly reflect the biological criteria used for evaluation, so better data fitting need not yield better biological predictions. To address this mismatch, we introduce \textbf{CellRFT}, a reinforcement fine-tuning framework that uses biological evaluation as direct training feedback. CellRFT uses policy-gradient optimization to learn from non-differentiable evaluations of generated cell populations and integrates multiple biological rewards through hierarchical reward aggregation. Comprehensive experiments demonstrate CellRFT's applicability across different pretrained models and effectiveness in improving perturbation prediction, reveal that optimizing one biological criterion can help or hinder others, and show that complementary rewards can improve criteria beyond those directly optimized, offering a way to probe how biological metrics shape model behavior, with the potential to inform evaluation design. Code will be made available.

cs.LG↗

arXiv2026

Validity of Prandtl Expansion for Steady Compressible Navier-Stokes-Fourier Flows

Assume no-slip boundary conditions for the velocity field and either insulated or Dirichlet boundary conditions for the temperature field in a steady compressible fluid. In the inviscid limit $\v \rightarrow 0$, we develop a mathematical framework for the uniform-in-$\v$ remainder estimate for the linear steady compressible Navier-Stokes-Fourier equations around a Prandtl layer profile with both velocity and thermal layers, which leads to the validity of the Prandtl layer expansion.

math.AP↗

arXiv2026

Steady Prandtl Layer for Compressible Fluids

Despite its importance, there have been few PDE results to investigate Prandtl layers for compressible fluids, in which the thermal boundary layer for the temperature field interacts with the classical velocity Prandtl boundary layer in a strong nonlinear fashion. We establish local-in-$x$ well-posedness of Prandtl layers for steady compressible fluids and construct Prandtl layer expansion in strong Sobolev norms, a foundation for the validity of Prandtl layer theory \cite{Guo-Wang}. Our method is based on a combination of the recent quotient estimate for the velocity field and an introduction of a pseudo entropy estimate for the temperature field.

math.AP↗

arXiv2026

Efficient quantum state tomography with two complementary projective measurements

Quantum state tomography (QST) is of fundamental importance to characterize quantum systems in quantum information processing, but its practical implementation is severely hindered by the exponential scaling of measurement and computational costs. In this paper, we present a novel QST protocol that utilizes Kirkwood-Dirac (KD) quasiprobability to reconstruct quantum states. First, it enables state reconstruction with only two complementary rank-one projective measurements, thus significantly reducing the measurement cost. Then, a complex logistic regression estimator is proposed to process collected KD data, together with a projected gradient algorithm to mitigate numerical instability and to accelerate convergence. The product-operator structure of KD quasiprobability is further exploited to reduce the computational cost. Finally, extensive experiments are implemented to confirm the validity of our protocol. Notably, the full reconstruction of randomly generated 15-qubit mixed-state instances can be accomplished within 20 minutes under the GPU implementation. These results suggest a promising route toward scalable QST and benchmarking large-scale quantum systems.

quant-ph↗

arXiv2026

Debiasing as a Measurement Intervention: Calibrated Ties and Resolution Loss in LLM-as-a-Judge Evaluation

LLM-as-a-judge protocols are commonly debiased by instructing judges to ignore presentation cues such as citation formatting, source labels, and evidence-display style. We show that this intervention can suppress bias while damaging the resolution of the measurement instrument. We introduce TraceJudgeBench, a diagnostic benchmark for auditing citation-like artifacts in RAG and agent-workflow evaluation, covering content-equivalent pairs, citation ablations, correctness conflicts, human-validated soft and moderate quality gaps, prompt-strength ladders, decoupled judging, and a controlled workflow-ranking probe. Across GPT-5.5, Claude Sonnet 4.6, and DeepSeek V4-Flash, stronger anti-citation prompts reduce worse-cited wins from up to 50.5% to 0%; yet some operating points already convert validated moderate-gap decisions into Tie before the strict stress-test endpoint, while correctness-conflict accuracy remains at or above 93.0%. A second, 50-pair FinQA moderate-gap construction reproduces the qualitative frontier, and open-weight Qwen2.5-14B-Instruct-AWQ and Gemma-3-12B-IT runs reproduce the central HotpotQA frontier. TRACE-style decoupling recovers 96.5-100.0% better-plain resolution across the reported settings. Human validation separates three meanings of Tie: correct equivalence Tie, calibrated soft-boundary Tie, and resolution-destroying Tie on validated quality gaps. We frame debiasing as a measurement intervention whose bias suppression, resolution retention, Tie cost, and protocol cost must be reported jointly. The supplementary artifact contains benchmark splits, prompts, raw judge outputs, validation summaries, and analysis.

cs.DL↗

arXiv2026

The Bimetric generalization of Kastler--Kalau--Walze Type Theorems

Let $M^n$ be a closed oriented manifold of even dimension $n=2m\ge2$, equipped with a smooth metric $g_1$ and a Riemannian metric $g_2$. We compute the Wodzicki residue of $D_{g_1}^2D_{g_2}^{-n}$ on the common exterior bundle, where $D_{g_r}=d+δ_{g_r}$. This is the noncommutative integral of $D_{g_1}^2$ relative to the reference operator $D_{g_2}$. Its local density involves the curvatures of the two metrics and the difference of their Levi--Civita connections. Integration by parts gives a closed-manifold formula without explicit derivatives of the connection difference. For compact manifolds with boundary and $n\ge4$, we assume that both metrics are Riemannian and satisfy $g_r=h_r(x_n)^{-1}g^{\partial M}+dx_n^2$ near the boundary, with $h_r(0)=1$. We compute the noncommutative residues of two factorizations involving even and odd powers of $D_{g_2}$. Their interior contributions coincide, whereas their boundary terms are explicit multiples of the integral of $K_{g_1}-K_{g_2}$, with the coefficient for the even factorization twice that for the odd one. Here $K_{g_r}$ is the trace of the second fundamental form with respect to the inward unit normal. The calculation uses a second-order residue formula and direct boundary symbol expansions. When the metrics coincide, the formulas reduce to the Hodge--de Rham Kastler--Kalau--Walze identity.

math.DG↗

arXiv2026

Merging Modal Clusters via Significance Assessment

To deal with superfluous clusters and to reduce the number of clusters as often desired in practice, a modal cluster merging procedure is proposed. Based on some new properties established in this paper for Morse functions, the procedure merges clusters in a sequential manner without causing unnecessary density distortion. Each cluster is evaluated for its significance relative to the other clusters, using the Kullback-Leibler divergence or its log-likelihood approximation, by truncating the density for the cluster at an appropriate level. The least significant cluster is then merged into one of its adjacent clusters, using the novel concept of cluster adjacency defined in this paper. The resulting hierarchical clustering tree is useful for determining the number of clusters, as may be preferred by a specific user or in a general, meaningful manner. Numerical studies show that the new procedure deals well with difficult clustering problems and often produces intuitively appealing and numerically more accurate clustering results, as compared with several other popular clustering methods in the literature.

stat.ME↗

arXiv2026

Learning Human Health and Diseases from 24-hour Wrist Movement

Much of human health and function unfolds beyond the clinic, through the movements of everyday life. Wrist-worn accelerometers capture these movements continuously, yet their rich signals are often reduced to a small set of predefined behavioural summary measures. Here, we present Sensori, a self-supervised foundation model that learns general-purpose health representations directly from 24 hours of raw tri-axial wrist movement. We developed and evaluated the model across four population-based cohorts from the United Kingdom, China and the United States, comprising 122,640 participants contributing 683,617 person-days of free-living recordings. Sensori condensed each day of movement into a representation that captured diverse movement behaviours, demographic characteristics, health axes and physical function. Evaluation in independent cohorts showed that these representations generalised across populations and measurement settings without retraining. When added to common clinical covariates, Sensori significantly improved prevalent disease classification for 52 of 102 eligible conditions (median delta AUROC, 0.060; range, 0.012-0.242) and incident disease risk prediction for 26 of 87 eligible conditions (median delta Uno's C-index, 0.064; range, 0.025-0.172), with the largest gains for neurological and psychiatric disorders. These findings establish 24-hour wrist movement as a rich and scalable source of health information, with the potential to support passive health monitoring and disease prediction at population scale.

cs.LG↗