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Teng Zhang

Publications and source records attributed to Teng Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery

Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain poorly understood. This paper establishes that, under deterministic conditions, a variant of IRLS with dynamic smoothing regularization converges linearly to the underlying subspace from any initialization. We extend these guarantees to affine subspace estimation, a setting that lacks prior recovery theory. Additionally, we illustrate the practical benefits of IRLS through an application to low-dimensional neural network training. Our results provide the first global convergence guarantees for IRLS in robust subspace recovery and, more broadly, for nonconvex IRLS on a Riemannian manifold.

stat.ML↗
arXiv2026

Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator

We study the subspace-constrained Tyler's estimator (STE) for recovering a low-dimensional linear subspace from data contaminated by outliers. Under deterministic conditions on inlier spread and outlier alignment, we prove linear convergence to the true subspace from a sufficiently accurate initialization. The guarantee also applies when the dimension-scaled signal-to-noise ratio is below one, where general robust subspace recovery is SSE-hard. When initializing STE from a candidate subspace, we provide a sufficient recovery condition based on the initial angular error and the size of the identity shift applied to the subspace projector. For noisy inliers, we prove a subspace error proportional to the noise level within an explicit iteration bound. Finally, under an asymptotic, anisotropic Gaussian inlier--outlier model, we show that Tyler's M-estimator (TME) provides a successful STE initialization even when TME's own leading eigenspace differs from the target subspace.

math.ST↗
arXiv2026

Clarkson--McCarthy type inequalities, part II: refinements, unitary orbits, unitarily invariant norms and $\ell_s$--$\ell_s$ estimates

In previous work \cite{Zha26a}, the author established Clarkson--McCarthy type inequalities for several classes of operator families, including $\ell_p$--$\ell_p$ estimates and mixed $\ell_q$--$\ell_p$ estimates, by means of operator square-sum identities. The present paper has two main aims. First, using the tracial joint spectral measures recently introduced by O.~Heinävaara \cite{Hei25}, we obtain several refinements of the McCarthy--Clarkson inequalities, one of which confirms a conjecture of Audenaert \cite{AK17}. Second, combining tools from matrix analysis with complex interpolation theory, we establish Clarkson--McCarthy type inequalities for unitary orbits, unitarily invariant norms, and $\ell_s$--$\ell_s$ estimates, again in the framework of operator square-sum identities.

math.FA↗
arXiv2026

On the embedding rigidity problem for uniformly locally finite coarse spaces

In this paper, we construct countable uniformly locally finite metric spaces $X$ and $Y$ such that $C_u^*(X)$ is isomorphic to a hereditary $C^*$-subalgebra of $C_u^*(Y)$, but neither space coarsely embeds into the other. This gives a negative answer to the embedding rigidity problem for uniformly locally finite coarse spaces. On the positive side, we prove that a hereditary embedding $C_u^*(X)\to C_u^*(Y)$ implies an injective coarse embedding $X\to Y$ whenever $C_u^*(Y)$ contains no block-rank-one ghost projection. In particular, this strengthens the coarse embedding theorem of Braga, Farah, and Vignati by obtaining injectivity under the same hypothesis that every sparse subspace of $Y$ yields only compact ghost projections.

math.OA↗
arXiv2026

Hierarchical GTV Estimation: Bridging the Gap between Container-Level Ranking and Item-Level Conversion

Emerging e-commerce platforms, such as live-streaming and Online-to-Offline (O2O) services, inherently operate under a "Container-based" display paradigm. In this setting, a critical granularity mismatch exists: the platform performs ranking and estimation at the container level (e.g., livestream rooms or stores), whereas the actual transactions occur at the item level within these containers. This structural discrepancy complicates Gross Transaction Value (GTV) estimation, introducing unique challenges including high label variance, severe label sparsity, and dynamic item heterogeneity. To address these challenges, we propose a novel framework named Hierarchical GTV Estimation (HGE). HGE employs a Hybrid Set-Aware Encoder (HSAE) to model the dynamic composition of items and feature interactions. To mitigate label variance, we introduce a Proxy-Label Learning (PLL) strategy that decomposes post-click GTV into purchase probability, quantity, and unit price. Furthermore, a Residual Correction and Ensemble Fusion (RCEF) module is designed to handle label sparsity by effectively combining item-level aggregation with container-level inference. Extensive experiments on large-scale industrial datasets demonstrate that HGE significantly outperforms state-of-the-art baselines, achieving a +0.63% lift in XAUC offline and a +1.42% increase in Revenue Per Search (RPS) in online A/B tests. HGE framework has been fully deployed into our main traffic.

cs.IR↗
arXiv2026

Gravitational-Wave Detector for Postmerger Neutron Stars: Beyond the Quantum Loss Limit of the Fabry-Perot-Michelson Interferometer

Advanced gravitational-wave detectors that have made groundbreaking discoveries are Michelson interferometers with resonating optical cavities as their arms. As light travels at finite speed, these cavities are optimal for enhancing signals at frequencies below their bandwidth frequency. A small amount of optical loss will, however, significantly impact the high-frequency signals which are not optimally amplified. We find an elegant interferometer configuration with an "L-resonator" as the core, significantly surpassing the loss limited sensitivity of dual recycled Fabry Perot Michelson interferometers at high frequencies. Following this concept, we provide a broadband design of a 25 km detector with outstanding sensitivity between 2-4 kHz. We have performed Monte-Carlo population studies of binary neutron star mergers, given the most recent merger rate from the GWTC-3 catalog and several representative neutron star equations of state. We find that the new interferometer configuration significantly outperforms other third-generation detectors by a factor of 3 to 7 in the signal-to-noise ratio of the post-merger signal. Assuming a detection threshold with signal-to-noise ratio >5 and for the cases we have explored, the new design is the only detector that confidently achieves a detection rate larger than one per year, with the rate being 1 to 30 events per year.

gr-qc↗
arXiv2026

RocketAgent: A Long-Horizon Engineering Agent for Multidisciplinary Design of Liquid-Rocket Thrust Chambers

Liquid-rocket thrust-chamber design involves interdependent analyses in which downstream constraints can require earlier design decisions to be revisited. Managing these dependencies across heterogeneous tools requires consistent design information and coordinated updates throughout the workflow. We present RocketAgent, a long-horizon engineering agent for multidisciplinary preliminary design of liquid-rocket thrust chambers. A single plan-owning Coding Agent coordinates engineering skills for performance sizing, subsystem optimization, geometry generation, and multiphysics assessment. A provenance-aware knowledge graph supports method selection, while a typed Design Intermediate Representation maintains shared parameters, artifacts, and decisions. Revision-aware checks invalidate affected results and block superseded inputs, with consequential changes subject to engineering approval. In a representative simulation-based design, RocketAgent continued from an infeasible cooling search through an engineer-authorized operating-point revision, identified feasible subsystem designs, and coordinated subsequent geometry generation and multiphysics assessment to support final configuration selection. Separate module tests assessed surrogate predictions and nozzle adaptation. A two-configuration comparison across three controlled scenarios verified the expected dependency invalidations and superseded-input blocking before solver execution. The representative case demonstrates sustained coordination across a multidisciplinary design workflow, while the controlled tests establish the behavior of the revision mechanisms supporting that execution.

cs.AI↗
arXiv2026

Shortcut-Resistant CAM Distillation for Long-Tailed Recognition

Real-world datasets often follow a long-tailed distribution, making generalization to tail classes difficult. We revisit this problem through the lens of shortcut learning, where models prefer the easiest predictive cues (e.g., background or textures) over object-centric semantics, especially under scarce and biased supervision. We find that this tendency is amplified for tail classes: limited examples often share similar contexts, making non-semantic signals highly correlated and thus tempting shortcuts, whereas head classes with diverse appearances and environments encourage more stable object-focused representations. Motivated by this observation, we propose Shortcut-Resistant CAM Distillation (SRCD), a plug-and-play framework that transfers object-focused explanations from head to tail classes. SRCD operates in the Class Activation Map (CAM) space, where a CAM provides a class-specific spatial evidence map for a prediction. SRCD aggregates CAMs from a small set of head-class candidates into a shortcut-resistant teacher using an energy-model weighting based on coherence and concentration, and distills it to the tail-class CAM. We provide a theoretical analysis that quantifies shortcut reliance as shortcut-region evidence mass in CAM space and shows that SRCD suppresses tail shortcuts. Extensive experiments on long-tailed benchmarks consistently improve strong baselines. The code is available at https://github.com/Haifeng3/SRCD.

cs.LG↗
arXiv2026

A Broadband Room-Temperature Design for the Einstein Telescope

The unique underground location of the Einstein Telescope (ET) is expected to substantially suppress seismic and gravity-gradient noise, providing a favorable environment for gravitational-wave detection at low frequencies compared with surface-based observatories. The baseline ET design aims to achieve broadband sensitivity through a xylophone configuration, in which separate cryogenic and room-temperature interferometers are optimised for low- and high-frequency gravitational-wave detection. However, achieving the target low-frequency sensitivity introduces substantial technical complexity caused by vertical suspension thermal noise, vibrations of the cryocooler, and detuned optical configuration. In this paper, we demonstrate an alternative, entirely room-temperature, fully resonant, single-interferometer architecture that addresses these challenges and achieves broadband sensitivity superior to that of the conventional ET xylophone configuration. Using mature fused-silica suspension technology, recent advances in optical coatings, and novel inertial isolation, we show that 4-m-long fused-silica fibres can meet the required suspension thermal-noise performance. We further demonstrate that vibrations, optical rigidity, and quantum back-action noise can be controlled through appropriate design of the interferometer, test mass suspensions, optical seismometers, and quantum states.

gr-qc↗
arXiv2026

When Windowed Anderson Acceleration Converges Faster

Windowed Anderson acceleration AA($m$) combines at most $m+1$ recent iterates by least squares. For a real affine contraction $x\mapsto Wx+b$ with $q=\|W\| \in(0,1)$, we determine exactly when AA($m$) converges from every starting point with an asymptotic factor below $q$. We give a polynomial criterion for this improvement and an equivalent spectral condition: there is no probability distribution on the phases of the eigenvalues of modulus $q$ whose first $m$ cosine moments are $q,q^2,\ldots,q^m$. If such a distribution exists, we construct a starting point from which AA($m$) reproduces fixed-point iteration at every step. Otherwise, over a fixed number of consecutive steps, every run contracts the residual norm by a common factor strictly smaller than the corresponding power of $q$. The polynomial criterion also gives explicit convergence-rate bounds with constants independent of the dimension. When $q$ equals the spectral radius, this characterizes improvement over the asymptotic convergence factor of fixed-point iteration. For general affine contractions, the asymptotic factor never exceeds the numerical radius of $W$, and a related moment condition gives a uniform upper bound strictly below that radius.

math.NA↗
arXiv2026

Matrix Triangle Inequalities: Past, Present, and Future

This survey provides a concise overview of matrix triangle inequalities. Classical topics, such as inequalities for unitarily invariant norms, are revisited from a different perspective, with a particular emphasis on unitary orbit inequalities and various notions of matrix moduli. The exposition progresses from elementary results to much more recent developments, highlighting the evolution of the subject and its ongoing directions of research.

math.FA↗
arXiv2026

Observation and control of polariton noise in a thermal Rydberg atom electrometer

The establishment of metrics and control of fundamental noise sources in quantum sensing is a long-standing goal in quantum science and technology. We report on the observation of polariton-mediated optical noise in a thermal Rydberg atom vapor and demonstrate its active control and suppression using a radio-frequency field in Rydberg electrometry. The noise exhibits structured amplification and reduction across the Rydberg electromagnetically induced transparency resonance. This reveals a nonlinear slow-light feedback mechanism in which the polariton medium stores and releases probe-field energy. We show that the reference radio-frequency field used in Rydberg heterodyne receivers can also tune the medium into an operating regime where high electromagnetic-field responsivity coincides with reduced optical noise. This operating-point control enables optimization of the electric-field sensitivity within the constraints imposed by Rydberg-polariton physics. These results establish polariton noise as a previously unrecognized intrinsic noise source in thermal Rydberg vapors and the corresponding control method as a crucial aspect of continued efforts to achieve fundamental sensitivity limits in Rydberg electrometry.

physics.atom-ph↗
arXiv2026

Geometric Certificates for Deterministic Global Linear Convergence of Overparameterized Projected Gradient Descent

We study projected gradient descent (ProjGD) for the rank-constrained problem $\min\{f(X): \operatorname{rank}(X)\le r\}$ when the unconstrained minimizer $X_*$ has rank $r_*\le r$. Our main contribution is a quantitative geometric certificate relating the normal component of $\nabla f(X)$ to the smallest nonzero singular value of $X$. Under a rank-$(r+r_*)$ restricted curvature condition with constants $0<μ \sqrt{r_*/r}(L-μ)/(2Lμ)$. With an additional rank-$2r$ restricted smoothness assumption, we establish deterministic global linear convergence for $\sqrt{r_*/r}(L-μ)/(2Lμ)<η<1/L$. The result accommodates arbitrary rank overparameterization $r\ge r_*$ and is independent of the singular-value condition number of $X_*$. As a consequence, we obtain an alternative proof of the sharp threshold $δ<(1+\sqrt{r_*/r})^{-1}$ for the absence of spurious local minima in the asymmetric setting, where $δ=(L-μ)/(L+μ)$. This threshold and matching asymmetric examples were established in recent work.

math.OC↗
arXiv2026

Entire solutions of higher order Briot-Bouquet equations

For a meromorphic function $f$ in the complex plane, we determine when $f$ and $f^{(k)}$ are algebraically dependent. This happens precisely when $f$ belongs to the class $W$ of elliptic functions and their degenerates, or satisfies a linear differential equation $f^{(k)} + af + b = 0$ with constant coefficients. The case of functions having a pole was settled previously. We complete the proof by treating entire solutions.

math.CV↗
arXiv2026

Imaging how fluctuations destroy superconductivity in two dimensions

Two-dimensional superconductors test our understanding of quantum phases. Low-temperature "anomalous metal" states are widely observed where conventional theories predict only superconducting or insulating ground states. In model systems based on proximity-coupled Josephson junction arrays, the critical temperature falls far faster with decreasing normal-state conductance than predicted by existing models. Whether these observations indicate a new quantum phase, a need to refine models of disorder and fluctuations, or both remains unresolved. Using scanning magnetic susceptometry, we image the local superfluid phase stiffness $ρ_s$ in gate-tunable Josephson junction arrays consisting of epitaxial Al islands on an InAs quantum well. Across six arrays and more than two orders of magnitude in the zero-temperature phase stiffness $ρ_{s0}$, the diamagnetic critical temperature $T_{c,φ}$ is suppressed more strongly than can be explained solely by thermal phase fluctuations, scaling approximately as $T_{c,φ}\proptoρ_{s0}^{0.3}$. While $ρ_s$ is remarkably uniform at high carrier densities, at low carrier densities we find that anomalous metal transport emerges together with large-scale inhomogeneity that transport alone cannot directly detect. These results are inconsistent with a classical XY description within standard junction models, instead pointing to quantum fluctuations that suppress superconductivity throughout the superconducting phase and amplify inhomogeneity near the superconductor-insulator transition, producing anomalous metal behavior.

cond-mat.supr-con↗
arXiv2026

Dynamic Skill Lifecycle Management for Agentic Reinforcement Learning

Large language model agents increasingly rely on external skills to solve complex tasks, where skills act as modular units that extend their capabilities beyond what parametric memory alone supports. Existing skill-based RL methods assume external skills either accumulate as persistent guidance or internalized into the policy, eventually leading to zero-skill inference. We argue this assumption is overly restrictive, since with limited parametric capacity and uneven marginal contribution across skills, the optimal active skill set is non-monotonic, task- and stage-dependent. In this work, we propose SLIM, a framework of dynamic Skill LIfecycle Management for agentic reinforcement learning (RL), which dynamically updates the active external skill set as the policy evolves.Specifically, SLIM estimates each active skill's marginal external contribution through leave-one-skill-out validation, then applies three lifecycle operations: retaining high-value skills, retiring skills whose contribution becomes negligible after sufficient exposure, and expanding the skill bank when persistent failures reveal missing capability coverage. Experiments show that SLIM outperforms the best baselines by an average of 7.1\% points across ALFWorld and SearchQA. Results further indicate that policy learning and external skill retention are not mutually exclusive: some skills are absorbed into the policy, while others continue to provide external value, supporting SLIM as a more general paradigm for skill-based agentic RL.

cs.LG↗
arXiv2026

Same Reward, Different Skills: When Multimodal RL Learns to Look

Reinforcement learning with verifiable rewards (RLVR) improves vision-language benchmark scores even without visual information during training. With images at test, blind-trained models recover roughly half of the real-image gain at 3B and nearly four fifths at 7B. Prolonged real-image training can erode grounding while benchmark gains persist. Both findings expose the same gap: an image in the prompt is not an image in the learning signal. Our design rule, visual resolvability, asks that visual evidence be necessary for a correct answer and that the task remain learnable. We test it on counterfactual coordinate scenes in which the question stays fixed and the target is never named, so a correct answer requires finding the target in the image. With standard GRPO and correctness-and-format rewards, a 7B model raises its accuracy at finding the target (discovery) from 0.425 to 0.875 on held-out scenes denser than any it trained on, and it improves on question types it never trained on. Two controls locate the source of the gain. Replacing test images with gray canvases drops discovery to zero; training on gray canvases instead, at matched step 30 and in each of four seeds, yields essentially none of the gain even when the model is then tested with real images. The learned skill carries over to grounding tasks built independently of the training corpus. A caption that answers the training question, added to the same images, reward and budget, cuts the gain by nearly two thirds. Changing what reward requires changes what RL learns.

cs.LG↗