arXiv subjects

Xiang Xu

Publications and source records attributed to Xiang Xu.

At least 19 recordsLinked to original sources

arXiv2026

Increasing stability for the inverse potential problem of the fractional Helmholtz equation

This paper is concerned with the inverse potential scattering problem for the three-dimensional fractional Helmholtz equation. For every $0<α<1$, we establish an increasing stability of determining the potential function from multifrequency exterior measurements of the scattered field. The stability consists of a Lipschitz data discrepancy and a logarithmic remainder that decreases when the upper measured wavenumber increases. The key ingredient in the analysis is to construct appropriate geometric optics solutions, which relate the X-ray transform of the potential to the measured fields. As a consequence, the stability is derived by applying analytic continuation. Two-dimensional numerical examples with noisy near-field data illustrate the benefit of enlarging the measured frequency band for three representative fractional orders.

math.AP↗

arXiv2026

Inverse source problem for the stochastic fractional Helmholtz equation in inhomogeneous media

This paper is concerned with an inverse source problem for the stochastic fractional Helmholtz equation in a three-dimensional inhomogeneous medium. The source is modeled as real Gaussian spatial white noise with an unknown nonnegative strength function. For admissible frequencies, we establish well-posedness of the radiating solution in the distributional sense and show that it has a smooth representation outside the source region. For the inverse problem, by using two-point correlations of the field measured in an exterior open set at a single frequency, we prove a logarithmic stability estimate for recovering the source strength under an a priori Sobolev bound. As a uniform Hölder stability estimate is unavailable for the general admissible class, by assuming the difference between two source strengths has a fixed sign, we improve the stability to Hölder continuity with an optimal Hölder exponent. The analysis combines scattering theory and quantitative continuation for the fractional Laplacian using the Caffarelli-Silvestre extension.

math.AP↗

arXiv2026

An inverse moving point source problem in inhomogeneous acoustic media: uniqueness, stability and reconstruction

This paper is concerned with the simultaneous recovery of the trajectory and intensity of an unknown moving point source in an inhomogeneous acoustic medium. We prove that the whole-boundary measurements over a finite time interval uniquely determine the moving source. Furthermore, under suitable propagation and rank assumptions, Lipschitz stability of determining both the trajectory and intensity is derived using waveforms measured at four fixed receivers outside the source region. A novel Volterra--Euler reconstruction scheme is developed for solving the inverse problem, and the error estimate is derived for the proposed scheme. Numerical experiments are presented to demonstrate the effectiveness of the proposed numerical method.

math.AP↗

arXiv2026

Uniqueness and stability for inverse potential scattering with multiple wavenumbers

This paper is concerned with the inverse scattering problem of determining a real-valued potential for the three-dimensional Schrödinger equation from multi-wavenumber data. Under suitable a priori bounds, we establish local increasing stability from near-field Dirichlet data on a fixed sphere for polynomially decaying potentials, and global increasing stability from full far-field amplitudes for exponentially decaying potentials. The stability estimates consist of a noise term and a remainder term, with the latter decreasing as the upper measured wavenumber increases. We also obtain global uniqueness from exact near-field data under weaker regularity assumptions. The analysis combines analytic continuation, weighted resolvent estimates, and half-ray identities whose differences at chord endpoints cancel the unknown exterior contribution.

math.AP↗

arXiv2026

Enhancing Quasi-Two-Dimensional Electronic Structure in Bi2O2Se via Chlorine Substitution

Bismuth oxyselenide (Bi2O2Se) has emerged as a leading semiconductor candidate for next-generation electronics and quantum phenomena research. However, its strong ionic interlayer bonding of Se layers fundamentally restricts the full potential of this otherwise promising quasi-two-dimensional (2D) material. In this work, we demonstrate chlorine substitution as an effective strategy to introduce van der Waals gaps and modify the electronic structure of the system. Through comprehensive transport and angle-resolved photoemission spectroscopy (ARPES) measurements on Bi6O6Se2Cl2 single crystal, an optimal Cl-doping compound, we show that the key electronic features, including indirect band gap, high electron mobility, and carrier effective mass, are well preserved, while the 2D character of the system is sufficiently enhanced. First-principles calculations attribute this selective tunability to the unique spatial separation between conductive Bi-O layers and dopant Se/Cl layers, which enables independent optimization of interlayer coupling and intralayer transport. Remarkably, our theoretical calculations combined with experimental observations project a broad bandgap engineering across a wide range (0.8 ~ 3.5 eV) within the Bi2O2Se system. Our findings not only expand the application potential of Bi2O2Se-based materials in optoelectronics, nanoelectronics, and fundamental research but also highlight spatial decoupling as a viable strategy for modifying detailed electronic structure of quasi-2D quantum systems.

cond-mat.mtrl-sci↗

arXiv2026

ALoDLM: Adaptively Looped Diffusion Language Models

Diffusion language models (DLMs) enable fast generation by predicting multiple tokens in parallel, but their practical adoption remains limited by a persistent quality gap relative to comparably sized autoregressive (AR) models. We attribute this gap to a computation-difficulty mismatch: within a partially observed sequence, some unknown tokens are easy to predict, while others require substantially more computation. Existing DLMs nevertheless apply uniform computational depth to all unknown positions at each denoising step. We introduce ALoDLM, which replaces uniform computation with token-adaptive latent recurrence. At each denoising step, ALoDLM iteratively refines latent representations and allocates computation according to token difficulty. Tokens ready to commit are fed back as discrete context, while unresolved tokens retain and further refine their latent states through additional recurrent passes. To learn token prediction and computation allocation jointly, we formulate token-wise computation schedules as latent variables and derive a conditional negative evidence lower bound (NELBO). We train ALoDLM at 1.7B and 8B parameter scales. Across eleven benchmarks, ALoDLM outperforms all evaluated DLMs and the corresponding AR baselines in average benchmark score at both scales. ALoDLM also retains fast parallel decoding, yielding a strong quality-efficiency trade-off among evaluated autoregressive and diffusion models under optimized inference engines.

cs.AI↗

arXiv2026

STAR-GRPO: Canonical Anchoring and Reliability-First Advantages against Representation-Dependent Reward Hacking

Reward hacking occurs when policy optimization exploits a brittle reward interface or an overly permissive proxy objective, improving the training score without improving the underlying response quality. This phenomenon is amplified in group-relative policy optimization: an unsupported reward can shift the group baseline and alter the updates of other rollouts, while post-hoc or purely relative weighting cannot represent group-wide uncertainty. We propose \emph{Self-Tuned Anchored Reliability Group-Relative Policy Optimization} (STAR-GRPO), a reliability-first advantage estimator based on paired assessments of the same rollout. STAR separates the quality signal from its learning influence: score disagreement determines rollout reliability, relative reliability enters a self-tuned robust location--scale fit before group normalization, and absolute group reliability attenuates the resulting bounded advantage. The analysis establishes coordinate and second-moment bounds, characterizes exact centering through the weighted location equation, and gives reliability-dependent attenuation guarantees for outlying rewards. We evaluate STAR-GRPO in two complementary reward-hacking regimes. In token-interface exploitation, STAR prevents runaway optimization of the deployed-interface score while improving the canonical quality signal. In rubric-proxy overoptimization for medical reasoning, STAR improves independent semantic evaluation, narrows the proxy--judge discrepancy, and reduces overclaim while optimizing the same task proxy. Together, these results show that reliability-first normalization offers a principled way to limit unsupported reward influence on both group baselines and policy updates, while retaining the task reward as the optimization target.

cs.AI↗

arXiv2026

Dual-Channel Robust Group-Relative Policy Optimization via Advantage and Sequence-Weight Estimation

Group-relative policy optimization relies on reward-derived advantages and sequence-level likelihood weights, both of which can be sensitive to localized outliers. Extreme rewards can collapse the contrast among clean responses after group normalization, while token-level log-ratio perturbations can alter sequence weights and clipping decisions. We introduce RoVR-GSPO, a dual-channel robust optimizer that addresses these failure modes separately. Its reward channel combines robust reference estimation with bounded residual credit, while its ratio channel uses differentiable SoftRoVR aggregation to construct robust sequence weights. We provide stability and efficiency analyses for both channels. Experiments on mathematical reasoning, long-context summarization, and tool-call annotation show consistent improvements over GSPO, while controlled perturbation studies demonstrate stronger robustness to reward contamination and token-ratio anomalies.

cs.AI↗

arXiv2026

FORGE: Form-Optimal Routing of Grounded Evidence for Frozen LLM Agents

In agentic AI systems, frozen foundation models are increasingly deployed as closed-weight API endpoints, making downstream adaptation possible only through the inputs and inference procedures surrounding the model. As a result, for each input query, two coupled decisions largely determine both answer quality and token cost: what evidence to provide and how much reasoning budget to allocate. Fixed defaults along these axes are often suboptimal, misallocating support form or reasoning depth on roughly 80% of queries in our analysis. To address this challenge, we propose FORGE, a unified framework for adapting frozen models through per-query routing over a joint action space that spans both support form and thinking depth. Under an entropy-regularized, cost-aware utility objective, we derive a closed-form Boltzmann routing target and instantiate the policy as a lightweight 269K-parameter factorized router. The routing policy is trained around the frozen host, without any weight access, through a three-stage pipeline: offline arm enumeration, supervised Kullback-Leibler (KL) distillation from the Boltzmann target, and Group Relative Policy Optimization (GRPO) refinement with host feedback. Across 5 knowledge-intensive benchmarks and 8 frozen backbones ranging from 7B to 671B parameters, FORGE improves accuracy at 42-45% lower token cost on both main hosts, transfers zero-shot across hosts at lower token cost, and composes with intrinsic thinking budgets where available.

cs.LG↗

arXiv2026

Rethinking Latent Visual Reasoning: Grounding Latent Reasoning in Visual Evidence

Latent visual reasoning (LVR) enables multimodal large language models (MLLMs) to perform intermediate computation in continuous latent tokens rather than expressing every reasoning step in words. However, unlike textual CoT, latent reasoning is not directly observable, making it difficult to supervise what latent tokens learn. In this work, we first conduct a thorough analysis of latent-token behavior and identify a latent evidence-credit gap: latent tokens respond only weakly to image perturbations that alter the correct answer. We hypothesize that this issue stems from the lack of explicit supervision during GRPO training. These findings suggest that a final-answer reward provides too little guidance on what visual evidence to preserve or how credit should be assigned across latent tokens. To bridge this gap, we propose ReaLVR, which brings visual-evidence supervision to the model's own free-running latent trajectories. ReaLVR contrasts correct and model-generated wrong answers to determine where stronger supervision is needed, and relevant and mismatched visual evidence to specify what to preserve. Across three model families, ReaLVR consistently outperforms evaluated LVR baselines, achieving the highest five-task average of 63.7% on Qwen2.5-VL-7B. Crucially, we are the first to scale visual reasoning in latent space, showing that our framework continues to deliver robust improvements at frontier model scales up to 235B. Further analyses show more question-sensitive latent-token positions, stronger alignment with relevant visual regions, and greater fixed-context dependence on the most attended latent tokens.

cs.CV↗

arXiv2026

SLCA-GRPO: Resolving Cross-Segment Credit Misattribution in Tool-Calling RL

Tool-calling agents produce heterogeneous outputs, interleaving structured tool invocations with user-facing natural language summaries. This output heterogeneity presents a structural failure mode in standard on-policy Reinforcement Learning (RL): algorithms like GRPO indiscriminately broadcast a homogeneous trajectory-level scalar advantage to all tokens. Consequently, gradient noise from summary generation leaks into tool-decision tokens, causing cross-segment credit misattribution and brittle optimization. In this work, we propose SLCA-GRPO, a framework incorporating Segment-Locked Credit Assignment (SLCA). To enable scalable exploration without costly real APIs and stable training, we first construct the Schema-Guided LLM Simulator (SGLS) as foundational training infrastructure. Building on this, SLCA decouples advantage estimation at the structural segment level within a single group of rollouts, without requiring additional rollouts from intermediate states. Supported by Hierarchical Rewards (HierR), SLCA routes execution advantages to tool tokens and preference advantages to summary tokens, eliminating advantage contamination (the dominant cross-segment credit misattribution channel) within each policy update. On a 7B backbone, SLCA-GRPO accelerates convergence and outperforms standard GRPO, ToolPO, and RLTR by +2.53 pp on in-domain evaluation, +1.36 pp on the Berkeley Function-Calling Leaderboard (BFCL), and +9.15 pp on $τ^2$-Bench under the same training budgets, achieving higher accuracy with reduced tool redundancy and costs.

cs.AI↗

arXiv2026

Stability for the inverse source problem of the stochastic fractional Helmholtz equation

This paper is concerned with the inverse source problem for the stochastic fractional Helmholtz equation driven by white noise. For every fractional order $0<α<1$, we prove the existence and uniqueness of the outgoing distributional solution to the direct problem with resolvent estimates at high frequencies, and establish its stochastic representation. For the inverse problem, we demonstrate that the variance of the source can be uniquely determined by the correlated random exterior data at a single frequency. We further establish an increasing stability estimate for the inverse problem by using the multifrequency correlated exterior data. Our stability result shows that as the upper bound of the bandwidth of the utilized frequency increases, the stability will also improve. The analysis employs the construction of geometric optics solutions, which connects the correlated data to the X-ray transform of the variance.

math.AP↗

arXiv2026

Free-Breathing PDFF and R2* Quantification at 0.55T: Reduced Respiratory Motion Sensitivity and a Time-Resolved 4D MRI Approach

Purpose: Free-breathing multi-echo MRI enables hepatic PDFF/R2* quantification without breath-holds, but respiratory motion can affect R2* estimation through motion-induced field variations. We investigated whether respiratory motion sensitivity is reduced at 0.55T versus 3T and developed a time-resolved free-breathing 4D MRI approach without respiratory binning. Methods: A navigator-embedded multi-echo stack-of-stars sequence was implemented. Ten subjects were scanned during free breathing and deliberate bulk motion at both 3T and 0.55T. Data were reconstructed using motion-averaged, motion-resolved, and time-resolved approaches. Quantitative performance was also evaluated in a PDFF/R2* phantom using Cartesian and radial acquisitions. Results: Phantom experiments showed close radial-Cartesian agreement for R2* and PDFF at 3T. At 0.55T, R2* showed good agreement over the low-to-moderate range but higher uncertainty at high R2*, where larger radial-Cartesian PDFF differences were also observed. R2* was substantially less sensitive to respiratory motion at 0.55T than at 3T, whereas PDFF was relatively insensitive at both field strengths. Under bulk motion, time-resolved reconstruction provided robust R2* and PDFF measurements, with particularly high consistency between free-breathing and bulk-motion acquisitions at 0.55T. Conclusion: R2* quantification was less sensitive to respiratory motion at 0.55T than at 3T, while PDFF remained relatively insensitive. Time-resolved reconstruction provided additional robustness to bulk motion. Reduced susceptibility effects at 0.55T and time-resolved reconstruction may provide complementary advantages for motion-robust free-breathing hepatic R2* and PDFF quantification.

physics.med-ph↗

arXiv2026

Understanding In-Context Multimodal Jailbreaks via Posterior Reweighting

In-context learning (ICL) jailbreaks reveal a critical vulnerability in multimodal large language models (MLLMs): harmful demonstrations in the prompt can induce unsafe outputs without modifying model parameters. Despite extensive empirical evidence, existing work lacks a principled understanding of why such jailbreaks reliably succeed or how their effectiveness scales with context composition. We propose a posterior reweighting framework that models a safety-aligned MLLM as implicitly operating over competing behavioral modes, and interprets in-context demonstrations as inference-time evidence that dynamically shifts the model's posterior preference between safe and harmful behaviors. This view formalizes jailbreak as a process of evidence accumulation, yielding predictive scaling laws with respect to demonstration count, harmful ratio, adversarial strength, and semantic diversity. Guided by this framework, we introduce a posterior-aware inference-time defense that adaptively injects benign counter-evidence based on estimated risk, effectively suppressing harmful posterior drift while preserving model utility. Compared to existing in-context defenses, our method achieves a significantly improved robustness-utility trade-off under a fixed intervention budget. Together, our results establish posterior reweighting as a unifying and predictive framework for understanding and mitigating ICL jailbreak in MLLMs.

cs.CR↗

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

On the Plasticity Collapse in Continual Machine Unlearning

Machine unlearning enables deep neural networks to selectively remove the influence of specific data in response to privacy and regulatory requirements. While prior work largely studies single-shot unlearning, real-world systems must accommodate continual unlearning, where multiple unlearning requests occur sequentially over time. In this work, we identify a fundamental limitation of this setting: plasticity collapse, a progressive breakdown in a model's ability to effectively forget. Through theoretical analysis of continual unlearning dynamics, we show that continual unlearning operations accumulate geometric constraints in parameter space, leading to saturated subspaces that restrict future updates. This structural effect induces two distinct failure modes: (1) Forward failure -- diminishing forgetting quality for subsequent tasks, and (2) Backward failure -- spontaneous re-memorization of previously forgotten information. Extensive experiments across multiple architectures, datasets, and methods in image classification confirm that plasticity collapse is not an artifact of specific implementations, but a pervasive phenomenon inherent to continual unlearning. Our findings reveal a critical barrier to the long-term reliability of machine unlearning systems and motivate the development of plasticity-preserving unlearning algorithms. Our code is available at https://github.com/TIML-Group/Continual-Machine-Unlearning-Plasticity-Collapse

cs.LG↗

arXiv2026

PACE: Primitive-Aware Code Evolution for Automated Algorithm Design

Large Language Model (LLM)-based automated algorithm design typically evolves algorithms as complete, indivisible programs. While this whole-program perspective simplifies the search space, it fundamentally couples the useful local logic to its host program. Consequently, valuable code snippets vanish when the overall program is discarded, making it highly difficult to assess the contribution of individual algorithmic components.To address this, we propose Primitive-Aware Code Evolution (PACE), which decouples local logic from complete programs by representing it as persistent units called Executable Algorithmic Primitives (EAPs). To enable code-level transfer, PACE maintains a dynamic set of EAPs. Algorithm evolution is driven by primitive-aware operators that structurally guarantee the retention and cross-program transfer of these components. To evaluate them effectively, PACE leverages Thompson sampling based on parent-relative performance improvements, guiding primitive selection from the set without requiring extra evaluation datasets. Experiments on four tasks demonstrate that PACE effectively discovers competitive algorithms while structurally preserving valuable algorithmic components.

cs.SE↗

arXiv2026

Exponential decay for the 3D Boussinesq equations with Navier boundary conditions

We study the three-dimensional incompressible Boussinesq equations on a bounded domain with smooth boundary and Navier boundary conditions. We construct global weak solutions by a Galerkin approximation and establish the associated Leray--Hopf energy inequalities. For nonnegative boundary friction, the total energy decays exponentially when the friction coefficient is positive on a boundary subset of positive surface measure. In the frictionless case, the scalar field and the velocity component orthogonal to the rigid-motion kernel decay exponentially; when the kernel is trivial, this is exponential decay of the total energy. When the scalar initial datum vanishes, this also proves exponential decay for the Navier--Stokes system on solids of revolution for every friction coefficient $α\in L^\infty(\partialΩ)$ such that $α\ge0$ almost everywhere and $α\not\equiv0$, resolving the corresponding case left open in \cite{Kelliher2025}. The proof uses a weighted Korn--Poincaré inequality and a two-time Gronwall-type inequality with an exponentially decaying forcing term.

math.AP↗