arXiv subjects

Michael K. Ng

Publications and source records attributed to Michael K. Ng.

At least 19 recordsLinked to original sources

arXiv2026

HoloAegis: Frozen Representation, Topological Inference --- Minimally Parametric Safety Manifolds and Their Capability Boundaries for LLM Guardrails

Current LLM safety guardrails face a fundamental tension: fine-tuning distorts pre-trained representations while generative judges incur prohibitive inference costs. We ask a complementary question: how far can safety be achieved through pure geometric reasoning over frozen representations, and where does it fail? We present HoloAegis, a minimally parametric topological inference framework that decouples representation from reasoning: an un-fine-tuned encoder maps text to the unit sphere S^{d-1}, and all decisions reduce to Gibbs-Boltzmann free-energy differences over pre-computed anchor centroids. We contribute a boundary-mapping study rather than a leaderboard claim. On a frozen three-benchmark protocol, HoloAegis (3.2 MB) statistically matches WildGuard-7B (14 GB) on toxicity (0.96 vs. 0.96), exceeds it on harmful behaviors (0.99 vs. 0.79), and cedes oversafety detection (0.62 vs. 0.98) -- while ShieldGemma-2B fails on indirect harms (0.34). These failure modes are complementary and mechanistically traceable: potential-difference scoring senses manifold clustering, whereas policy-conditioned LLM judging requires explicit taxonomy matching. We restate our Topological Boundary Stability conjecture in ratio form and validate it via reference-set bootstrap: anchor banks reduce score variance 4-15x and boundary displacement to approximately 0.44 + 0.23 sqrt(k/K) of the full-space estimator. Per-domain analysis further reveals that geometric separability tracks within-domain semantic homogeneity. Our results chart where geometric guardrails substitute for, and where they must defer to, LLM judges.

cs.AI↗

arXiv2026

Tensor Orthogonal Subspace Split: Theory and Applications

Tensor representations have emerged as a fundamental paradigm for modeling multidimensional data by preserving intrinsic correlations across multiple modes. This paper proposes a novel theoretical framework, termed Tensor Orthogonal Subspace Split (TOSS), which explicitly splits a tensor, along a prescribed mode, into two orthogonal components: a dominant component lying in a prescribed subspace and a residual component lying in the corresponding orthogonal complement. We first present the general formulation of TOSS and systematically investigate its fundamental properties. As an important and practically meaningful special case, we further introduce the rank-one TOSS, which imposes a separable rank-one structure along the splitting mode and admits a clear geometric interpretation. This formulation naturally captures dominant consistent patterns while effectively isolating orthogonal residual component. The proposed framework establishes a unified theoretical foundation for tensor-domain orthogonal split and opens new avenues for structured tensor modeling across diverse applications. Building upon the developed TOSS theory, hyperspectral image restoration and color video background modeling are considered as two representative tasks, for which corresponding optimization models are formulated. Efficient algorithms are developed to solve the resulting problems. Extensive experimental results validate the effectiveness and superiority of the proposed approaches.

math.NA↗

arXiv2026

GeoThreat: Transferable Targeted Adversarial Attacks on Large Vision-Language Models for Remote Sensing Image Interpretation

Adversarial attacks against large vision-language models (LVLMs) serve as an effective means of assessing their robustness in cross-modal semantic understanding. Existing studies mainly focus on corrupting visual inputs to induce predefined erroneous responses in general vision-language tasks, whereas corresponding investigations in remote sensing fields remain largely underexplored. Compared with natural image understanding, remote sensing image interpretation requires joint reasoning over local discriminative cues and global scene context. This poses additional challenges to achieving transferable semantic manipulation toward specified responses under black-box settings. To tackle these challenges, we propose GeoThreat, a transferable targeted adversarial attack method against LVLMs for remote sensing image interpretation. Specifically, GeoThreat modulates adversarial representations in accordance with the target content at both conceptual and perceptual levels. The class tokens from surrogate image encoders are employed as conceptual representations, while perceptual representations are distilled from patch tokens of the adversarial example through collaborative importance estimation. Beyond merely rolling out attention scores across layers, we incorporate adversarial-target similarity gradients to more faithfully characterize the relevance of local visual cues to the intended semantic manipulation. The perceptual representations are then dynamically aligned with target patch tokens in a cross-attentive manner, facilitating the adaptation of local cues toward designated semantic details. Finally, adversarial perturbations are iteratively updated via ensemble-based joint optimization of conceptual calibration and perceptual adaptation. Extensive experiments across diverse LVLMs demonstrate the superiority of GeoThreat in both transferability and controllability.

cs.CV↗

arXiv2026

Hermitian Quaternion Toeplitz Matrices by Quaternion-valued Generating Functions

In this paper, we study Hermitian quaternion Toeplitz matrices generated by quaternion-valued functions. We show that such generating function must be the sum of a real-valued function and an odd function with imaginary component. This setting is different from the case of Hermitian complex Toeplitz matrices generated by real-valued functions only. By using of 2-by-2 block complex representation of quaternion matrices, we give a quaternion version of Grenander-Szegö theorem stating the distribution of eigenvalues of Hermitian quaternion Toeplitz matrices in terms of its generating function. As an application, we investigate Strang's circulant preconditioners for Hermitian quaternion Toeplitz linear systems arising from quaternion signal processing. We show that Strang's circulant preconditioners can be diagonalized by discrete quaternion Fourier transform matrices whereas general quaternion circulant matrices cannot be diagonalized by them. Also we verify the theoretical andnumerical convergence results of Strang's circulant preconditioned conjugate gradient method for solving Hermitian quaternion Toeplitz systems.

math.NA↗

arXiv2026

Operator Inequalities in $Φ$-Product Tensor Algebras: Invariance and Transform Sensitivity

We study classical operator inequalities in $Φ$-product tensor algebras (a transformation $Φ$-based generalization of the $t$-product framework) for third-order tensors. Although these algebras are algebraically isomorphic under different unitary transforms $Φ$, we show that their quantitative behavior is not invariant. We prove that fundamental inequalities, including Golden--Thompson, Jensen, Klein, and Lieb, extend to the $Φ$-product setting with the same constants as in the matrix case. However, the associated defect -- the slack between the two sides of the inequality -- depends explicitly on transform-domain noncommutativity. In particular, we establish a sharp characterization of the defect in terms of slice-wise commutators, revealing that inequality tightness is governed by transform-induced noncommutativity. We further demonstrate strong transform sensitivity by constructing explicit tensor pairs for which the defect vanishes under one transform (e.g., discrete Fourier transform) but grows linearly with the tensor depth under another transform (e.g., discrete Cosine transform), yielding an $Ω(p)$ separation where $p$ is the matrix dimension of $Φ$. Moreover, we prove that no transform is universally optimal: for any pair of transforms, there exist tensors for which each is strictly better than the other. These results show that the choice of transform defines a coordinate system in which commutativity is measured, inducing a nontrivial geometry of inequality tightness. Consequently, optimal transform selection is inherently data-dependent and can be formulated as an optimization problem over the unitary group.

math.FA↗

arXiv2026

Beyond Homophily: Towards Generalized Graph Reconstruction Attack and Defense

Graph neural networks (GNNs) are widely deployed on relational data, yet they can leak sensitive or proprietary information about the training graph adjacency, e.g., social ties, transactions, and interactions. This work studies graph reconstruction attacks (GRA), a form of model inversion that reconstructs the training adjacency from a trained GNN, given different levels of attacker-side information. We first provide a systematic characterization of when and why adjacency becomes recoverable through features, labels, embeddings, and predictions, with leakage modulated by graph homophily, heterophily, and the model's inductive bias. Motivated by these findings, we view GNN inference through a Markov chain approximation lens, treating the layered forward computation as a chain of topology-dependent representations. Building on this view, we develop complementary attack and defense methods. On the attack side, we propose MC-GRA (+), which reconstructs the adjacency by optimizing a surrogate adjacency whose GNN-induced representations align with those of the target model at each layer. On the defense side, we propose MC-GPB (+), which suppresses adjacency-dependent information throughout the representation chain while aiming to preserve classification accuracy under a privacy-utility trade-off. Experiments across homophilic/heterophilic graph benchmarks and GNNs show that our attacks improve reconstruction fidelity over prior methods, while our defenses reduce reconstruction success with only minor accuracy loss.

cs.LG↗

arXiv2026

Truncated Huber Penalty for Sparse Signal Recovery with Convergence Analysis

Sparse signal recovery from under-determined systems presents significant challenges when using conventional L_0 and L_1 penalties, primarily due to computational complexity and estimation bias. This paper introduces a truncated Huber penalty, a non-convex metric that effectively bridges the gap between unbiased sparse recovery and differentiable optimization. The proposed penalty applies quadratic regularization to small entries while truncating large magnitudes, avoiding non-differentiable points at optima. Theoretical analysis demonstrates that, for an appropriately chosen threshold, any s-sparse solution recoverable via conventional penalties remains a local optimum under the truncated Huber function. This property allows the exact and robust recovery theories developed for other penalty regularization functions to be directly extended to the truncated Huber function. To solve the optimization problem, we develop a block coordinate descent (BCD) algorithm with finite-step convergence guarantees under spark conditions. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed approach. Furthermore, we extend the truncated Huber-penalized model to the gradient domain, illustrating its applicability in signal denoising and image smoothing.

math.NA↗

arXiv2026

Complex Diffusion Maps with $ω$-Parameterized Kernels Revealing Inherent Harmonic Representations

In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and the nonlocal Schrödinger kernel relevant to the Schrödinger equation, we propose a unified family of $ω$-parameterized complex-valued kernels for the trade-off between local and nonlocal connections. We establish the theoretical foundation based on the operator spectrum theory, where the corresponding diffusion operator, diffusion distance, and complex harmonic maps are well-defined. An optimization-based interpretation of the maps is also developed, aiming to preserve angular structure in the complex diffusion space rather than relying solely on real-valued magnitude. We extensively evaluate CDM on both synthetic and real-world datasets. The complex-valued kernel amplifies differences among easily confusable samples, improving discriminative power over both linear and nonlinear methods based on real-valued kernels. CDM remains robust in high-noise settings, yielding a clearer eigengap that enhances spectral separation. For resting-state fMRI data, CDM captures more strongly correlated and nonlocal spatiotemporal dynamics. Without task-specific tuning, CDM achieves competitive performance on a public EEG sleep dataset, while maintaining high computational efficiency compared with both traditional machine learning and deep neural network approaches, highlighting its generality and practical value.

cs.LG↗

arXiv2026

A Layer Separation Optimization Framework for Cross-Entropy Training in Deep Learning

This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encountered during training deep networks. For cross-entropy models with fully connected and convolutional neural networks, we introduce auxiliary variables associated with hidden layer outputs and construct corresponding layer separation models, which decompose the original deeply nested optimization problem into a sequence of more manageable subproblems. We also conduct theoretical analyses, proving that the new layer separation loss provides an upper bound for the original cross-entropy loss. Moreover, we design alternating minimization algorithms and prove that, under appropriate conditions, these algorithms exhibit decreasing properties of the loss function. Numerical experiments validate the effectiveness of the proposed methods and indicate improved optimization behavior, especially for fully connected and convolutional neural networks.

cs.LG↗

arXiv2026

Robust Instance Optimal Phase-Only Compressed Sensing

Phase-only compressed sensing (PO-CS) concerns the recovery of sparse signals from the phases of complex measurements. Recent results show that sparse signals in the standard sphere $\mathbb{S}^{n-1}$ can be exactly recovered from complex Gaussian phases by a linearization procedure, which recasts PO-CS as linear compressed sensing and then applies (quadratically constrained) basis pursuit to obtain $\mathbf{x}^\sharp$. This paper focuses on the instance optimality and robustness of $\mathbf{x}^{\sharp}$. First, we strengthen the nonuniform instance optimality of Jacques and Feuillen (2021) to a uniform one over the entire signal space. We show the existence of some universal constant $C$ such that $\|\mathbf{x}^\sharp-\mathbf{x}\|_2\le Cs^{-1/2}σ_{\ell_1}(\mathbf{x},Σ^n_s)$ holds for all $\mathbf{x}$ in the unit Euclidean sphere, where $σ_{\ell_1}(\mathbf{x},Σ^n_s)$ is the $\ell_1$ distance of $\mathbf{x}$ to its closest $s$-sparse signal. This is achieved by showing the new sensing matrices corresponding to all approximately sparse signals simultaneously satisfy RIP. Second, we investigate the estimator's robustness to noise and corruption. We show that dense noise with entries bounded by some small $τ_0$, appearing either prior or posterior to retaining the phases, increments $\|\mathbf{x}^\sharp-\mathbf{x}\|_2$ by $O(τ_0)$. This is near-optimal (up to log factors) for any algorithm. On the other hand, adversarial corruption, which changes an arbitrary $ζ_0$-fraction of the measurements to any phase-only values, increments $\|\mathbf{x}^\sharp-\mathbf{x}\|_2$ by $O(\sqrt{ζ_0\log(1/ζ_0)})$. The developments are then combined to yield a robust instance optimal guarantee that resembles the standard one in linear compressed sensing.

cs.IT↗

arXiv2026

Rethinking Representations for Cross-Domain Infrared Small Target Detection: A Generalizable Perspective from the Frequency Domain

The accurate target-background separation in infrared small target detection (IRSTD) highly depends on the discriminability of extracted representations. However, most existing methods are confined to domain-consistent settings, while overlooking whether such discriminability can generalize to unseen domains. In practice, distribution shifts between training and testing data are inevitable due to variations in observational conditions and environmental factors. Meanwhile, the intrinsic indistinctiveness of infrared small targets aggravates overfitting to domain-specific patterns. Consequently, the detection performance of models trained on source domains can be severely degraded when deployed in unseen domains. To address this challenge, we propose a spatial-spectral collaborative perception network (S$^2$CPNet) for cross-domain IRSTD. Moving beyond conventional spatial learning pipelines, we rethink IRSTD representations from a frequency perspective and reveal inconsistencies in spectral phase as the primary manifestation of domain discrepancies. Based on this insight, we develop a phase rectification module (PRM) to derive generalizable target awareness. Then, we employ an orthogonal attention mechanism (OAM) in skip connections to preserve positional information while refining informative representations. Moreover, the bias toward domain-specific patterns is further mitigated through selective style recomposition (SSR). Extensive experiments have been conducted on three IRSTD datasets, and the proposed method consistently achieves state-of-the-art performance under diverse cross-domain settings.

cs.CV↗

arXiv2026

Blind Hyperspectral and Multispectral Images Fusion: A Unified Tensor Fusion Framework from Coupled Inverse Problem Perspective

Hyperspectral and multispectral images fusion aims at integrating a low-resolution hyperspectral image (LR-HSI) and a high-resolution multispectral image (HR-MSI) to construct a high-resolution hyperspectral image (HR-HSI). It is generally assumed that spatial blurring operator and spectral response operator are prior-known. However, such an assumption is extremely restrictive in practice. To overcome this limitation, this paper formulates blind fusion as a coupled inverse problem, integrating blind deconvolution in the spatial domain with blind unmixing in the spectral domain. From this novel perspective, we propose a unified tensor fusion framework capable of flexible self-adjustment and real-time fusion without pre-training. We further introduce an optimization model for the joint estimation of the target HR-HSI, the spatial point spread function, and the spectral response function. To solve this model, we devise a partially linearized alternating direction method of multipliers (ADMM) algorithm with Moreau envelope smoothing, accompanied by the rigorous convergence analysis. An initialization estimator tailored to the specific characteristics of the fusion problem is proposed. Numerical comparisons with state-of-the-art methods on both synthetic and real-world datasets demonstrate the compelling performance of the proposed method.

math.OC↗

arXiv2026

Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications

Recently, continuous tensor functions have attracted increasing attention, because they can unifiedly represent data both on mesh grids and beyond mesh grids. However, since mode-$n$ product is essentially discrete and linear, the potential of current continuous tensor function representations is still locked. To break this bottleneck, we suggest neural operator-grounded mode-$n$ operators as a continuous and nonlinear alternative of discrete and linear mode-$n$ product. Instead of mapping the discrete core tensor to the discrete target tensor, proposed mode-$n$ operator directly maps the continuous core tensor function to the continuous target tensor function, which provides a genuine continuous representation of real-world data and can ameliorate discretization artifacts. Empowering with continuous and nonlinear mode-$n$ operators, we propose a neural operator-grounded continuous tensor function representation (abbreviated as NO-CTR), which can more faithfully represent complex real-world data compared with classic discrete tensor representations and continuous tensor function representations. Theoretically, we also prove that any continuous tensor function can be approximated by NO-CTR. To examine the capability of NO-CTR, we suggest an NO-CTR-based multi-dimensional data completion model. Extensive experiments across various data on regular mesh grids (multi-spectral images and color videos), on mesh girds with different resolutions (Sentinel-2 images) and beyond mesh grids (point clouds) demonstrate the superiority of NO-CTR.

cs.CV↗

arXiv2026

TVWorld: Foundations for Remote-Control TV Agents

Recent large vision-language models (LVLMs) have demonstrated strong potential for device control. However, existing research has primarily focused on point-and-click (PnC) interaction, while remote-control (RC) interaction commonly encountered in everyday TV usage remains largely underexplored. To fill this gap, we introduce \textbf{TVWorld}, an offline graph-based abstraction of real-world TV navigation that enables reproducible and deployment-free evaluation. On this basis, we derive two complementary benchmarks that comprehensively assess TV-use capabilities: \textbf{TVWorld-N} for topology-aware navigation and \textbf{TVWorld-G} for focus-aware grounding. These benchmarks expose a key limitation of existing agents: insufficient topology awareness for focus-based, long-horizon TV navigation. Motivated by this finding, we propose a \emph{Topology-Aware Training} framework that injects topology awareness into LVLMs. Using this framework, we develop \textbf{TVTheseus}, a foundation model specialized for TV navigation. TVTheseus achieves a success rate of $68.3\%$ on TVWorld-N, surpassing strong closed-source baselines such as Gemini 3 Flash and establishing state-of-the-art (SOTA) performance. Additional analyses further provide valuable insights into the development of effective TV-use agents.

cs.CV↗

arXiv2026

Sparse Tucker Decomposition and Graph Regularization for High-Dimensional Time Series Forecasting

Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a sparse Tucker decomposition method with graph regularization for high-dimensional vector autoregressive time series. By stacking the time-series transition matrices into a third-order tensor, the sparse Tucker decomposition is employed to characterize important interactions within the transition third-order tensor and reduce the number of parameters. Moreover, the graph regularization is employed to measure the local consistency of the response, predictor and temporal factor matrices in the vector autoregressive model.The two proposed regularization techniques can be shown to more accurate parameters estimation. A non-asymptotic error bound of the estimator of the proposed method is established, which is lower than those of the existing matrix or tensor based methods. A proximal alternating linearized minimization algorithm is designed to solve the resulting model and its global convergence is established under very mild conditions. Extensive numerical experiments on synthetic data and real-world datasets are carried out to verify the superior performance of the proposed method over existing state-of-the-art methods.

math.ST↗

arXiv2025

NeuMatC: A General Neural Framework for Fast Parametric Matrix Operation

Matrix operations (e.g., inversion and singular value decomposition (SVD)) are fundamental in science and engineering. In many emerging real-world applications (such as wireless communication and signal processing), these operations must be performed repeatedly over matrices with parameters varying continuously. However, conventional methods tackle each matrix operation independently, underexploring the inherent low-rankness and continuity along the parameter dimension, resulting in significantly redundant computation. To address this challenge, we propose \textbf{\textit{Neural Matrix Computation Framework} (NeuMatC)}, which elegantly tackles general parametric matrix operation tasks by leveraging the underlying low-rankness and continuity along the parameter dimension. Specifically, NeuMatC unsupervisedly learns a low-rank and continuous mapping from parameters to their corresponding matrix operation results. Once trained, NeuMatC enables efficient computations at arbitrary parameters using only a few basic operations (e.g., matrix multiplications and nonlinear activations), significantly reducing redundant computations. Experimental results on both synthetic and real-world datasets demonstrate the promising performance of NeuMatC, exemplified by over $3\times$ speedup in parametric inversion and $10\times$ speedup in parametric SVD compared to the widely used NumPy baseline in wireless communication, while maintaining acceptable accuracy.

cs.CV↗

arXiv2025

Online Inference of Constrained Optimization: Primal-Dual Optimality and Sequential Quadratic Programming

We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation, physics-informed models, safe reinforcement learning, and algorithmic fairness. We develop a stochastic sequential quadratic programming (SSQP) method to solve these problems, where the step direction is computed by sequentially performing a quadratic approximation of the objective and a linear approximation of the constraints. Despite having access to unbiased estimates of population gradients, a key challenge in constrained stochastic problems lies in dealing with the bias in the step direction. As such, we apply a momentum-style gradient moving-average technique within SSQP to debias the step. We show that our method achieves global almost-sure convergence and exhibits local asymptotic normality with an optimal primal-dual limiting covariance matrix in the sense of Hájek and Le Cam. In addition, we provide a plug-in covariance matrix estimator for practical inference. To our knowledge, the proposed SSQP method is the first fully online method that attains primal-dual asymptotic minimax optimality without relying on projection operators onto the constraint set, which are generally intractable for nonlinear problems. Through extensive experiments on benchmark nonlinear problems, as well as on constrained generalized linear models and portfolio allocation problems using both synthetic and real data, we demonstrate superior performance of our method, showing that the method and its asymptotic behavior not only solve constrained stochastic problems efficiently but also provide valid and practical online inference in real-world applications.

stat.ML↗

arXiv2025

Data Valuation by Fusing Global and Local Statistical Information

Data valuation has garnered increasing attention in recent years, given the critical role of high-quality data in various applications. Among diverse data valuation approaches, Shapley value-based methods are predominant due to their strong theoretical grounding. However, the exact computation of Shapley values is often computationally prohibitive, prompting the development of numerous approximation techniques. Despite notable advancements, existing methods generally neglect the incorporation of value distribution information and fail to account for dynamic data conditions, thereby compromising their performance and application potential. In this paper, we highlight the crucial role of both global and local statistical properties of value distributions in the context of data valuation for machine learning. First, we conduct a comprehensive analysis of these distributions across various simulated and real-world datasets, uncovering valuable insights and key patterns. Second, we propose an enhanced data valuation method that fuses the explored distribution characteristics into two regularization terms to refine Shapley value estimation. The proposed regularizers can be seamlessly incorporated into various existing data valuation methods. Third, we introduce a novel approach for dynamic data valuation that infers updated data values without recomputing Shapley values, thereby significantly improving computational efficiency. Extensive experiments have been conducted across a range of tasks, including Shapley value estimation, value-based data addition and removal, mislabeled data detection, and dynamic data valuation. The results showcase the consistent effectiveness and efficiency of our proposed methodologies, affirming the significant potential of global and local value distributions in data valuation.

cs.LG↗