arXiv subjects

Jingzhi Li

Publications and source records attributed to Jingzhi Li.

At least 19 recordsLinked to original sources

arXiv2026

Polarimetric Low-Rank Imaging of Anisotropic Maxwell Media

We consider three-dimensional imaging of compactly supported anisotropic electric media from fixed-frequency polarimetric Maxwell far-field data. Maxwell transversality creates an obstruction absent from scalar Born inversion: each measurement determines only a projected action of the tensor-valued Fourier transform. We first resolve this obstruction by a finite-dimensional polarimetric inversion. For a general complex $3\times3$ contrast, three incidence--observation configurations are necessary, and we give an explicit three-configuration design that is sufficient at every nonzero interior Fourier point. Its Gram determinant yields quantitative conditioning information and exhibits the loss of recoverability at the boundary of the accessible Fourier ball. After tensor demixing, the inverse problem reduces componentwise to restricted Fourier inversion on the unit ball, which we regularize by spectral cutoff in three-dimensional ball generalized prolate spheroidal wave functions. For discrete acquisition, a combined reconstruction error estimate separates the effects of measurement noise, polarimetric amplification, off-grid Fourier mismatch, quadrature error, Born modeling error, and spectral truncation. Numerical tests examine polarimetric conditioning and use analytically generated Born data to compare three- and six-configuration recovery and assess off-grid sensitivity. Reconstructions from full-Maxwell volume-integral data assess the effects of noise, wavenumber, and basis choice, as well as the recovery of different tensor components.

math.NA↗

arXiv2026

Parameters Robust Parallelizable Iterative Decoupled Algorithms for Thermo-Poroelasticity with Nonlinear Convective Transport

This paper presents several parallel iterative algorithms for the nonlinear thermo-poroelasticity. We introduce an auxiliary variable to transform the original model into a four-field formulation to overcome Poisson locking. The iterative idea is extended to linearize and decouple the four-field model. Different coupling strategies are employed among these three subproblems, combined with appropriately designed iteration settings, yielding distinct iterative parallel algorithms. Stabilization terms are incorporated into these algorithms to ensure parameter robustness in extreme situations. We derive error estimates and prove the convergence of these parallel iterative decoupled algorithms. Finally, numerical experiments are presented to compare the performance of the different parallel algorithms in extreme parameter settings, thereby validating their efficiency and robustness.

math.NA↗

arXiv2026

Less is More: Efficient Black-box Attribution via Minimal Interpretable Subset Selection

To develop a trustworthy AI system, it is essential to understand its behavior using attribution methods, which aim to identify the input regions that most influence the model's decisions. For discrete inputs such as images, however, accurately identifying input-prediction interactions is particularly challenging because of combinatorial explosion. We formulate black-box attribution as an ordered interpretable subset-selection problem. Inspired by the marginal-gain principle of submodular optimization, the formulation permits redundancy, positive complementarity, and negative interference among input sub-regions. We propose LiMA (Less input is More faithful for Attribution), which ranks sub-regions by their contributions along a sequence of selected subsets. LiMA employs a composite objective that evaluates subsets through semantic consistency, collaboration, prediction confidence, and semantic effectiveness. We further design a bidirectional greedy search to efficiently identify important and non-critical sub-regions. Experiments on eight foundation models (CLIP, ImageBind, LanguageBind, QuiltNet, etc.) and six datasets (ImageNet, VGG-Sound, CUB-200-2011, etc.) demonstrate strong generalization and faithful interpretations with fewer sub-regions. LiMA achieves state-of-the-art Insertion, Deletion, and average highest confidence, with average improvements of 36.3% in Insertion and 39.6% in Deletion; it is also 1.6 times faster than naive greedy search. For failure attribution on incorrect predictions, LiMA improves average highest confidence by 86.1% over state-of-the-art methods. The code is available at https://github.com/RuoyuChen10/LIMA.

cs.LG↗

arXiv2026

SaTPO: Text-to-Image Safety Alignment via Transition Preference Optimization

Safety alignment of text-to-image diffusion models aims to suppress harmful content without compromising useful generation capabilities. However, preferences over completed images compress multidimensional generation factors into a coarse signal, potentially driving changes beyond those required for safety. To address this, we propose Safety Transition Preference Optimization (SaTPO), which enforces step-wise alignment during denoising. SaTPO leverages the insight that an unsafe prompt and its safe rewrite naturally form a tightly coupled preference pair when conditioned on a shared parent state and noise realization. By anchoring optimization on identical parent states, SaTPO eliminates historical trajectory divergence, confining safety adaptation to an incremental alignment while preserving task-relevant semantics. Multi-scale drift constraints and benign replay further limit behavioral deviation and preserve ordinary generation. We additionally construct CoProPV, a refined dataset ensuring visually verified contrasts. Experiments on Stable Diffusion v1.5 and SDXL demonstrate improved safety-quality trade-offs. Compared with AlignGuard, PerspectiveVision unsafe-detection rates on Inappropriate Image Prompts decrease from 12.70% to 6.00% and from 15.04% to 9.30%, respectively, while FID improves from 32.28 to 25.95 and from 36.50 to 27.51. Warning: this paper includes potentially offensive content.

cs.CV↗

arXiv2026

Pressure Monotonicity for a Rotation-Based Biot Discretization with Circumcentric Mass Lumping

We establish cellwise pressure monotonicity for a mixed finite element discretization of the rotation-based Biot system. The spatial discretization is based on compatible discrete de Rham complexes, using standard lowest-order elements for rotation, displacement, Darcy flux, and pressure. For the temporal discretization, we employ the backward Euler method. Exactness of the discrete complexes reduces the mechanics contribution to the pressure Schur complement to a scaled pressure mass matrix, yielding a positive diagonal mechanics capacity. For the Darcy part, positive circumcentric facet weights yield a weighted cell graph Laplacian after flux elimination, while the mass-lumped product remains uniformly equivalent to the standard Darcy product. The diagonal mechanics capacity and the weighted cell graph Laplacian make the condensed pressure matrix Stieltjes. Consequently, the pressure propagator is entrywise nonnegative, which yields a cellwise discrete maximum principle. Numerical experiments confirm the predicted convergence rates and show that the proposed discretization suppresses spurious cellwise pressure oscillations.

math.NA↗

arXiv2026

Off-Grid Point-Scatterer Localization from Sparse Limited-Aperture Data via Hankel Completion

We study the localization of $s$ distinct planar point scatterers from sparsely sampled single-incidence, single-frequency acoustic far-field data over a limited receiver aperture. Under the first Born approximation, the coherent data form a two-dimensional off-grid exponential sum and admit a low-rank Hankel representation. A limited aperture generally admits multiple aperture-admissible Hankel pencils with different lifted dimensions, sampling multiplicities, and Vandermonde conditioning. Hence, the choice of the Hankel pencil affects both data completion and subsequent localization. In this work, we introduce a unified framework for structured completion and off-grid localization based on general aperture admissible Hankel pencils. We establish exact recovery in the noiseless case and stable recovery under bounded noise from a number of random aperture samples that is linear in $s$, up to factors determined by the pencil geometry, source conditioning, and logarithmic terms, together with an explicit localization bound in terms of the completion error. The analysis separates the contribution of the pencil geometry from the conditioning induced by the source configuration and provides verifiable sufficient conditions for stable completion and MUSIC resolution. These results yield quantitative criteria for selecting sample efficient Hankel pencils under a prescribed physical aperture. Numerical experiments on connected and disconnected apertures demonstrate the effects of pencil geometry, sampling, and noise.

math.NA↗

arXiv2026

SMA: Who Said That? Auditing Membership Leakage in Semi-Black-box RAG Controlling

Retrieval-Augmented Generation (RAG) and its Multimodal Retrieval-Augmented Generation (MRAG) significantly improve the knowledge coverage and contextual understanding of Large Language Models (LLMs) by introducing external knowledge sources. However, retrieval and multimodal fusion obscure content provenance, rendering existing membership inference methods unable to reliably attribute generated outputs to pre-training, external retrieval, or user input, thus undermining privacy leakage accountability To address these challenges, we propose the first Source-aware Membership Audit (SMA) that enables fine-grained source attribution of generated content in a semi-black-box setting with retrieval control capabilities. To address the environmental constraints of semi-black-box auditing, we further design an attribution estimation mechanism based on zero-order optimization, which robustly approximates the true influence of input tokens on the output through large-scale perturbation sampling and ridge regression modeling. In addition, SMA introduces a cross-modal attribution technique that projects image inputs into textual descriptions via MLLMs, enabling token-level attribution in the text modality, which for the first time facilitates membership inference on image retrieval traces in MRAG systems. This work shifts the focus of membership inference from 'whether the data has been memorized' to 'where the content is sourced from', offering a novel perspective for auditing data provenance in complex generative systems.

cs.AI↗

arXiv2026

ColluSkill: Adversarial Cross-Skill Composition for Evading Agent Skill Scanners

Agent skills are emerging as an important attack surface in LLM-based agent systems. Through an empirical study of existing skill scanners, we find that current defenses mainly inspect individual skills, leaving risks from cross-skill composition insufficiently examined. This creates a practical blind spot: multiple locally plausible skills may pass security checks while collectively forming a harmful workflow during agent execution. To investigate this threat, we propose ColluSkill, a collusive multi-skill-chain attack framework that decomposes a complete malicious intent into interdependent sub-payloads embedded in independently packaged skills. The attack does not rely on any single malicious skill, but emerges from the ordered composition of locally plausible behaviors through contextual dependencies, artifact passing, and execution handoffs. ColluSkill further employs LLM-based chain planning and scanner-feedback refinement to preserve chain-level attack semantics while reducing suspicious signals in individual sub-skills. To defend against such attacks, we propose ChainGuard, a context-aware skill-chain scanner that jointly analyzes a candidate skill and the skills already installed in the agent environment. ChainGuard reconstructs cross-skill dependencies, artifact flows, capability compositions, and downstream behaviors to identify risks that emerge only at the workflow level. Experiments on six representative skill scanners show that ColluSkill achieves an average attack success rate of 96.0% and consistently outperforms the evaluated single-skill and multi-skill attack baselines. Meanwhile, ChainGuard reduces the attack success rate to 22.5% while allowing 99.5% of benign workflows to pass, highlighting the importance of chain-level security analysis for agent skill ecosystems.

cs.CR↗

arXiv2026

Iterative Decoupling Methods for a Total-Pressure Formulation of Quasi-Static Electroporoelasticity

Quasi-static electroporoelasticity couples Maxwell's equations with Biot's poroelasticity through electrokinetic coupling between the electric field and the pressure gradient. By introducing the total pressure, the electroporoelasticity equations are reformulated as a five-field system to address poroelastic locking in the nearly incompressible regime. For the resulting five-field system, a monolithic weak formulation is derived, together with a continuous stability estimate. A second-order backward differentiation formula (BDF2) time discretization and a mixed finite- element spatial discretization are then introduced, yieling to a fully discrete monolithic scheme. Building on this scheme, we develop an iterative decoupling method that alternates between an electromagnetic subproblem and a poroelastic subproblem, and prove its geometric convergence to the monolithic solution with an explicit mesh-independent contraction factor under the physical coupling condition. An algebraically equivalent reduced form is also presented, in which the electromagnetic block is solved only once per time step, while the poroelastic block is solved iteratively with electric-field correction updates obtained from the pressure-gradient feedback. Numerical experiments verify the theoretical predictions and demonstrate the locking-free performance.

math.NA↗

arXiv2026

AlloSpatial: Agentic Harness Framework for Spatial Reasoning in Foundation Models

Multimodal Foundation Models (MFMs) have made substantial progress, yet remain fragile in spatial reasoning over the physical world. A key bottleneck lies in their inability to transform local egocentric observations into a global allocentric spatial representation. To address this, we propose AlloSpatial, an agentic framework for allocentric spatial cognition in foundation models. AlloSpatial introduces World2Mind, a plug-and-play cognitive mapping sandbox that converts egocentric observations into structured allocentric priors, including Allocentric-Spatial Trees and route maps that support querying object topology, geometric relations, passability, and trajectories. To utilize these priors reliably under noisy reconstruction and ambiguous visual evidence, AlloSpatial introduces a Spatial Reasoning Harness for tool-use judgment, modality-decoupled cue collection, and geometry-semantic arbitration. We further internalize this process in Qwen3-VL through cold-start reinforcement learning with a harness-gated trajectory-level reward. Experiments on VSI-Bench and MindCube show that AlloSpatial improves proprietary models by 5%-18% in a training-free setting, while ASTs alone support strong spatial reasoning even when visual inputs are removed. The trained AlloSpatial agents further outperform larger general-purpose models and competitive spatial baselines, suggesting that structured allocentric representations, active tool use, and verifiable reasoning offer a promising route toward spatially capable foundation models.

cs.AI↗

arXiv2026

Post-hoc Provider Fairness Adaptation via Hierarchical Exposure Alignment

Provider exposure fairness is crucial for sustaining a healthy content ecosystem and preventing monopolization in recommender systems. Yet, most existing methods either incorporate fairness constraints during model training, requiring expensive retraining when fairness objectives change, or rely on post-hoc reranking with fixed criteria, which lacks adaptability to diverse fairness requirements. To overcome these limitations, we propose Post-hoc Fairness Adaptation (PFA), a lightweight framework that equips a frozen recommender with a fairness adapter, enabling flexible fairness control without retraining the backbone model. Specifically, the fairness adapter learns personalized additive score adjustments from user-item embeddings, which are injected into the original ranking scores to steer provider exposure toward fairness. To train the adapter, we minimize the KL divergence between the actual and the target fair exposure distributions. However, this global objective implicitly treats all providers equally, ignoring structural disparities such as imbalanced provider group sizes and heterogeneous exposure within groups. Consequently, fairness may appear satisfied at an aggregate level while severe inter-group and intra-group exposure imbalances persist, undermining practical fairness. To address this, we design Hierarchical Exposure Fairness Alignment (HEFA), which explicitly balances inter- and intra-group provider exposure disparities, enabling flexible adaptation to diverse fairness requirements. To mitigate potential accuracy degradation, PFA jointly optimizes HEFA with a differentiable NDCG loss, enabling end-to-end fairness optimization while preserving ranking quality. Extensive experiments on three public datasets demonstrate that PFA achieves substantial fairness gains with negligible accuracy loss, consistently outperforming strong baselines.

cs.IR↗

arXiv2026

A Unified Model for Thermo- and Multiple-Network Poroelasticity with a Global-in-Time Iterative Decoupling Scheme

This paper introduces a unified model for thermo-poroelasticity and multiple-network poroelasticity, reformulated into a total-pressure-based system. We first establish the well-posedness of the problem via a Galerkin-based argument and subsequently introduce a robust space-time finite element approximation. To efficiently solve the fully coupled system, we propose a global-in-time iterative algorithm that sequentially decouples the mechanics from the transport equations, while incorporating necessary stabilization terms. We explicitly analyze the convergence rate and provide a rigorous proof that the proposed scheme constitutes a contraction mapping under physically relevant conditions, thereby ensuring its unconditional convergence. Numerical experiments confirm the theoretical stability bounds and demonstrate optimal convergence rates in both space and time, yielding solutions free of non-physical pressure oscillations.

math.NA↗

arXiv2026

Global Convergence and Uniqueness for an Inverse Problem Posed by Gelfand

The first globally convergent numerical method is developed for a coefficient inverse problem (CIP) for the $n-$d, $n\geq 2$ wave equation with the unknown potential in the most challenging case when the $δ-$ function is present in the initial condition with a single location of the point source. In fact, an approximate mathematical model for that CIP is derived. That globally convergent numerical method is developed for this model. This is a new version of the so-called convexification numerical method. Uniqueness theorem is proven as well within the framework of that approximate mathematical model. The question about uniqueness of this CIP was first posed by a famous mathematician I. M. Gelfand in 1954 as an $n-$d ($n=2,3$) extension of the fundamental theorem of V.A. Marchenko in the 1-d case (1950). Based on a Carleman estimate, convergence analysis is carried out. This analysis ensures the global convergence of the proposed numerical method, i.e. it is not necessary to have a good first guess for the solution. Exhaustive computational experiments with noisy data demonstrate a high reconstruction accuracy of complicated structures. In particular, this accuracy points towards a high adequacy of that approximate mathematical model.

math.NA↗

arXiv2025

Parameter-Robust Preconditioners for A Four-Field Thermo-Poroelasticity Model

We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The model involves several parameters that can vary significantly in practical applications, posing a challenge for developing discretization techniques and solution algorithms that handle such variations effectively. We propose a four-field formulation and apply a conforming finite element discretization. The primary focus is on constructing and analyzing preconditioners for the resulting linear system. Two preconditioners are proposed: one involves regrouping variables and treating the 4-by-4 system as a 2-by-2 block form, while the other is directly constructed from the 4-by-4 coupled operator. Both preconditioners are demonstrated to be robust with respect to variations in parameters and mesh refinement. Numerical experiments are presented to demonstrate the effectiveness of the proposed preconditioners and validate their theoretical performance under varying parameter settings.

math.NA↗

arXiv2025

Convexification Numerical Method for Imaging of Moving Targets

The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running along a straight line is used. Lateral Cauchy data are known for each position of the point source. A truncated Fourier series with respect to a special orthonormal basis is used. First, Lipschitz stability estimate is obtained. Next, a globally convergent numerical method, the so-called convexification method, is developed and its convergence analysis is carried out. The convexification method is based on a Carleman estimate. Results of numerical experiments are presented.

math.NA↗

arXiv2025

Some semi-decoupled algorithms with optimal convergence for a four-field linear thermo-poroelastic model

We propose three semi-decoupled algorithms for efficiently solving a four-field thermoporoelastic model. The first two algorithms adopt a sequential strategy: at the initial time step, all variables are computed simultaneously using a monolithic solver; thereafter, the system is split into a mixed linear elasticity subproblem and a coupled pressure-temperature reaction-diffusion subproblem. The two variants differ in the order in which these subproblems are solved. To further improve computational efficiency, we introduce a parallel semidecoupled algorithm. In this approach, the four-field system is solved monolithically only at the first time step, and the two subproblems are then solved in parallel at subsequent time levels. None of the three algorithms requires iterative procedures at each time step, and are free from stabilization. Rigorous analysis confirms their unconditional stability, optimal convergence rates, and robustness under a wide range of physical parameter settings. These theoretical results are further validated by numerical experiments.

math.NA↗

arXiv2025

POD-based reduced order modeling of global-in-time iterative decoupled algorithms for Biot's consolidation model

This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate the backward differentiation formulas for time discretization. In each iteration, these algorithms involve solving a diffusion subproblem over the entire temporal domain, followed by solving a generalized Stokes subproblem over the same time interval. To accelerate the global-in-time iterative process, we present a reduced order modeling approach based on proper orthogonal decomposition, aimed at reducing the primary computational cost from the generalized Stokes subproblem. The effectiveness of this novel method is validated both theoretically and through numerical experiments.

math.NA↗

arXiv2025

An Efficient Iterative Decoupling Method for Thermo-Poroelasticity Based on a Four-Field Formulation

This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element method and a decoupled iterative finite element method. We prove the stability and optimal convergence of the coupled finite element method. Furthermore, we establish the convergence of the decoupled iterative method. This paper focuses primarily on analyzing the iterative decoupled algorithm. It demonstrates that the algorithm's convergence does not require any additional assumptions about physical parameters or stabilization parameters. Numerical results are provided to demonstrate the effectiveness and theoretical validity of these new methods.

math.NA↗