arXiv subjects

Yupeng Wang

Publications and source records attributed to Yupeng Wang.

At least 19 recordsLinked to original sources

arXiv2026

Sharp embeddings between quasi-Banach Besov spaces and shallow ReLU variation spaces

Let $\mathcal D$ be the normalized ridge dictionary generated by $\operatorname{ReLU}^k$ on a bounded Lipschitz domain $Ω\subset\mathbb R^d$. We establish sharp embeddings between isotropic Besov spaces and the associated variation space $\mathcal L_1(\mathcal D)$ in the quasi-Banach range $0 k+d/p$ for $1<q\le\infty$. A rescaled-bump construction shows that this smoothness threshold is sharp. Conversely, for $0<p<1$, \[ \mathcal L_1(\mathcal D)\hookrightarrow B^{k+1}_{p,2}(Ω), \] and both the smoothness $k+1$ and the fine index $2$ are optimal. The forward embedding converts known Besov regularity, in particular for solutions of partial differential equations, into controlled approximation error bounds and convergence of greedy algorithms based on shallow $\text{ReLU}^k$ neural networks. The proofs combine Littlewood--Paley localization, Fourier--Radon representations, measure-valued derivatives, and vector-valued singular-integral estimates.

math.FA↗

arXiv2026

Chronological stability for nonstationary matrix refinement

A matrix cascade is an iterative refinement process in which vector-valued data are repeatedly filtered by matrix-valued masks across successively finer scales. Such cascades arise in multichannel subdivision, Hermite refinement, multiresolution synthesis, and exponential-spline constructions, and in nonstationary schemes the masks may vary with scale. We develop a chronological stability framework for this setting, allowing both the transition operators and the associated matching spaces to change from level to level. If the chronological radius satisfies $ρ_{\rm ch}<1$ and the matching defects are summable, then the cascade converges uniformly and, for every $q\in(ρ_{\rm ch},1)$, \[ \|F_n-Φ\|_\infty \lesssim q^n+\sum_{j=1}^nδ_j q^{\,n-j} +\sum_{j>n}δ_j . \] The time-weighted defect term records the level at which each perturbation is inserted, and the matching spaces need not converge; they may even alternate indefinitely. For compact piecewise-linear seeds, every finite ordered matrix cascade admits an exact fixed-width ReLU realization with $O(n)$ depth and parameters, and this linear depth order is worst-case optimal at fixed width. Consequently, exponentially decaying defects yield certified approximants of size $O(\log\varepsilon^{-1})$. We further construct stable two-channel classes in which the chronological radius and the leading metric-entropy coefficient are independent invariants, showing that stability does not determine finite-accuracy description complexity. The framework therefore provides tolerance-controlled finite representations for nonstationary multiresolution and exponential-spline refinement.

math.NA↗

arXiv2026

Sharp approximation rates for shallow ReLU neuralnetworks on critical Besov classes

Let $\mathbb D$ be the normalized ridge dictionary generated by $\operatorname{ReLU}^k$ on a bounded Lipschitz domain $Ω\subset\mathbb R^d$. We determine the sharp algebraic rate of finite $n$-term approximation from $\mathbb D$ when the outer $\ell^1$ coefficient budget is independent of $n$. More precisely, let $d\ge3$, $k\in\mathbb N_+$, $0\le m\le k$, $0<p<1$, and $0<q\le1$. For the unit ball of the critical Besov space $B_{p,q}^{k+d/p}(Ω)$, measured in $H^m(Ω)$, the optimal algebraic exponent is \[ \min\left\{\frac{k-m+d/2}{d-1}, \frac{k-m+d/2+1/p-1/2}{d}\right\}. \] We prove two-sided estimates in the three regimes determined by the two branches of this minimum and give the corresponding logarithmic factors at and beyond the transition. The estimates coincide without logarithmic loss in the strict angular regime and at the transition when $q\le[1/2+(k-m+d/2)/(d-1)]^{-1}$. The upper estimate combines critical wavelet sparsity, localized Fourier--Radon representations, and a stable allocation of directions and biases. The lower estimates arise from two distinct obstructions, namely radial ridge approximation on the direction sphere and Gevrey localization in the joint direction--bias space. The critical smoothness is exactly the endpoint at which Besov regularity provides a uniform shallow-network variation bound without additional scale decay. The resulting representation exponent is strictly larger than the degree-limited exponent for fixed-degree isotropic finite elements under a parameter-count comparison. This last statement concerns best approximation, not training or computational complexity.

math.NA↗

arXiv2026

Quantum fluctuations in a quartet superfluid of two-dimensional Fermi mixture

We study quantum fluctuations in a quartet superfluid (QSF) of two-dimensional (2D) fermion mixtures with mass imbalance. Here QSF is a high-order superfluid that corresponds to the condensation of ($1+3$) clusters, each consisting of a light fermion and three heavy ones. By incorporating the Gaussian fluctuations respecting dominant four-body correlations in this system, our theory successfully recovers the leading universal logarithmic contribution to the 2D equation of state in the deep binding regime, thereby offering a correct physical picture of quartet clusters behaving as composite bosons. By extending the Gaussian fluctuation theory from pairing to quartet superfluids, our results shed light on quantum fluctuations in general fermion superfluids with arbitrarily high-order correlations.

cond-mat.quant-gas↗

arXiv2026

Self-calibrated multiparameter measurement of three-dimensional microwave fields

Rydberg atoms are promising for microwave (MW) sensing and control, but full local MW characterization remains difficult. Existing methods generally do not provide self-calibrated reconstruction of the three-dimensional vector field, which is valuable for both atom-based sensing and in-situ field characterization in complex electromagnetic environments. We propose and implement multi-level, Zeeman-resolved Rydberg electromagnetically induced transparency (EIT) spectroscopy in a laser-cooled atomic ensemble. We extract the three polarization amplitudes from a single spectrum and show that the MW polarization components give rise to closed interferometric loops within the atoms' internal Hilbert space, enabling extraction of their relative phases. Moreover, it is self-calibrated and requires no external reference MW fields, with MW parameters largely separable from one another and from other experimental parameters. These features make it broadly applicable to dedicated sensing platforms as well as quantum optics and quantum information experiments.

physics.atom-ph↗

arXiv2026

Galois representations over convergent de Rham period ring

Let $\mathbf{B}_{\mathrm{dR}}^{+, \dagger} \subset \mathbf{B}_{\mathrm{dR}}^{+}$ be the ``convergent" de Rham period ring which is the (un-completed) stalk at the de Rham point of the Fargues--Fontaine curve. We develop a Tate--Sen formalism to relate Galois representations over $\mathbf{B}_{\mathrm{dR}}^{+, \dagger}$ to regular connections over convergent functions. As a consequence, when the Sen weights (of the mod $t$ reduction) satisfy a $p$-adic non-Liouville condition, Galois cohomology of a $\mathbf{B}_{\mathrm{dR}}^{+, \dagger}$-representation compares to that of its $\mathbf{B}_{\mathrm{dR}}^{+}$-base change, and hence is finite. In addition, restricted to objects whose Sen weights are algebraic numbers, the categories of $\mathbf{B}_{\mathrm{dR}}^{+, \dagger}$-representations and $\mathbf{B}_{\mathrm{dR}}^{+}$-representations are equivalent.

math.NT↗

arXiv2026

ViTac-Tracing: Visual-Tactile Imitation Learning of Deformable Object Tracing

Deformable objects often appear in unstructured configurations. Tracing deformable objects helps bringing them into extended states and facilitating the downstream manipulation tasks. Due to the requirements for object-specific modeling or sim-to-real transfer, existing tracing methods either lack generalizability across different categories of deformable objects or struggle to complete tasks reliably in the real world. To address this, we propose a novel visual-tactile imitation learning method to achieve one-dimensional (1D) and two-dimensional (2D) deformable object tracing with a unified model. Our method is designed from both local and global perspectives based on visual and tactile sensing. Locally, we introduce a weighted loss that emphasizes actions maintaining contact near the center of the tactile image, improving fine-grained adjustment. Globally, we propose a tracing task loss that helps the policy to regulate task progression. On the hardware side, to compensate for the limited features extracted from visual information, we integrate tactile sensing into a low-cost teleoperation system considering both the teleoperator and the robot. Extensive ablation and comparative experiments on diverse 1D and 2D deformable objects demonstrate the effectiveness of our approach, achieving an average success rate of 80% on seen objects and 65% on unseen objects.

cs.RO↗

arXiv2026

TMR-VLA:Vision-Language-Action Model for Magnetic Motion Control of Tri-leg Silicone-based Soft Robot

In-vivo environments, magnetically actuated soft robots offer advantages such as wireless operation and precise control, showing promising potential for painless detection and therapeutic procedures. We developed a trileg magnetically driven soft robot (TMR) whose multi-legged design enables more flexible gaits and diverse motion patterns. For the silicone made of reconfigurable soft robots, its navigation ability can be separated into sequential motions, namely squatting, rotation, lifting a leg, walking and so on. Its motion and behavior depend on its bending shapes. To bridge motion type description and specific low-level voltage control, we introduced TMR-VLA, an end-to-end multi-modal system for a trileg magnetic soft robot capable of performing hybrid motion types, which is promising for developing a navigation ability by adapting its shape to language-constrained motion types. The TMR-VLA deploys embodied endoluminal localization ability from EndoVLA, and fuses sequential frames and natural language commands as input. Low-level voltage output is generated based on the current observation state and specific motion type description. The result shows the TMR-VLA can predict how the voltage applied to TMR will change the dynamics of a silicon-made soft robot. The TMR-VLA reached a 74% average success rate.

cs.RO↗

arXiv2026

Nonlinear optical spectra from Rydberg-mediated photon-photon interactions

While Rydberg-Rydberg interactions are essential for quantum nonlinear optics and quantum information processing, their role in microwave and radio-frequency sensing remains poorly understood. Here we experimentally investigate Rydberg interaction-induced nonlinearity in cold-atom Rydberg electromagnetically induced transparency (EIT). In a three-level EIT system, increasing photon-photon interactions produces nonlinear spectral broadening accompanied by resonance shifts, while a microwave-dressed four-level system exhibits pronounced nonlinear broadening without detectable spectral shifts. Our three-level data can be explained by a conditional superatom model, whereas our four-level observations are surprisingly captured by a simple dephasing model. Comparisons with three representative models provide key insights to the role of many-body interactions in Rydberg EIT spectroscopy. Furthermore, our results clarify the conditions under which microwave field characterization can be performed in the nonlinear regime without introducing systematic bias. Our study advances both fundamental understanding of many-body physics and practical development of atomic sensors.

physics.atom-ph↗

arXiv2026

Integrable Stochastic Processes Associated with the $D_2$ Algebra

We introduce an integrable stochastic process associated with the $D_2$ quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the model under three types of boundary conditions (periodic, twisted, and open boundaries), and present its exact solution, including the spectrum, eigenstates, and some observables. This integrable model can be generalized to the asymmetric case, decomposing into two asymmetric simple exclusion processes, and its exact solutions are also studied.

math-ph↗

arXiv2025

Prismatic crystals for smooth schemes in characteristic $p$ with Frobenius lifting mod $p^2$

Let $(A,(p))$ be a crystalline prism with $A_n = A/p^{n+1}A$ for all $n\geq 0$. Let $\frakX_0$ be a smooth scheme over $A_0$. Suppose that $\frakX_0$ admits a lifting $\frakX_n$ over $A_n$ and the absolute Frobenius $\rF_{\frakX_0}:\frakX_0\to \frakX_0$ admits a lifting over $A_1$. Then we show that there is an equivalence between the category of the prismatic crystals of truncation $n$ on $(\frakX_0/A)_{\Prism}$ and the category of $p$-connections over $\frakX_n$, which is compatible with cohomologies. This generalises a previous work of Ogus. We also give some remarks on trivializing the Hodge--Tate gerbe $π_{\frakX_0}^{\rm HT}:\frakX_0^{\rm HT}\to\frakX_0$ introduced by Bhatt--Lurie.

math.AG↗

arXiv2025

Robust Rydberg facilitation via rapid adiabatic passage

We propose and analyze a robust implementation of Rydberg antiblockade based on rapid adiabatic passage. Although Rydberg antiblockade offers key opportunities in quantum information processing and sensing, its sensitivity to position disorder and parameter imperfections has posed a central roadblock. By adiabatically sweeping across the interaction-shifted resonance, our approach is unaffected by realistic levels of disorder and parameter variations. As a straightforward application case, we show that it naturally gives rise to avalanche excitation growth in both one- and two-dimensional arrays. This avalanche process yields high gain with exceptionally low background, making it promising for rare-event detection. These results establish a practical route to robust Rydberg antiblockade dynamics, paving the way for future experimental and technological applications.

quant-ph↗

arXiv2025

Training Tactile Sensors to Learn Force Sensing from Each Other

Humans achieve stable and dexterous object manipulation by coordinating grasp forces across multiple fingers and palms, facilitated by a unified tactile memory system in the somatosensory cortex. This system encodes and stores tactile experiences across skin regions, enabling the flexible reuse and transfer of touch information. Inspired by this biological capability, we present GenForce, the first framework that enables transferable force sensing across tactile sensors in robotic hands. GenForce unifies tactile signals into shared marker representations, analogous to cortical sensory encoding, allowing force prediction models trained on one sensor to be transferred to others without the need for exhaustive force data collection. We demonstrate that GenForce generalizes across both homogeneous sensors with varying configurations and heterogeneous sensors with distinct sensing modalities and material properties. This transferable force sensing is also demonstrated with high performance in robot force control including daily object grasping, slip detection and avoidance. Our results highlight a scalable paradigm for cross-sensor robotic tactile learning, offering new pathways toward adaptable and tactile memory-driven manipulation in unstructured environments.

cs.RO↗

arXiv2025

An integrable Anderson-impurity problem embedded in the one-dimensional Hubbard model

An exactly solvable one-dimensional Hubbard model with a single Anderson impurity embedded at the boundary is constructed in the framework of the quantum inverse scattering method. The model is solved exactly by the nested Bethe ansatz method. We identify the boundary bound states and determine the ground state phase diagram. By deriving the impurity contribution to the magnetic susceptibility, we show that in the dilute electron limit, a nearly free local moment forms at the impurity site, while at finite electron densities, the impurity spin is screened by the host electrons, consistent with Kondo physics.

math-ph↗

arXiv2025

Unlocking Mixed Reality for Medical Education: A See-Through Perspective on Head Anatomy

Extended reality (XR), encompassing Virtual Reality (VR), Augmented Reality (AR), and Mixed Reality (MR), is emerging as a transformative platform for medical education. Traditional methods such as textbooks, physical models, and cadaveric dissections often lack interactivity and fail to convey complex spatial relationships effectively. The emerging MR technology addresses these limitations by providing immersive environments that blend virtual elements with real-world contexts. This study presents an MR application for head anatomy education, enabling learners to intuitively interact with see-through 3D anatomical structures via hand gestures and controllers. Our hierarchical information design supports progressive learning, guiding users from basic anatomical labels to detailed structural insights. Additionally, the system incorporates an automatic calibration module that aligns virtual anatomical models with a real human head, thereby facilitating realistic human-model interactions. Experiments show that the system can effectively match the anatomical model with real-time scenes, thus enhancing the interactivity and immersion of medical education, providing an innovative tool for teaching anatomy.

cs.HC↗

arXiv2025

Pressure-Driven Moiré Potential Enhancement and Tertiary Gap Opening in Graphene/h-BN Heterostructure

Moiré superlattices enable engineering of correlated quantum states through tunable periodic potentials, where twist angle controls periodicity but dynamic potential strength modulation remains challenging. Here, we develop a high-pressure quantum transport technique for van der Waals heterostructures, achieving the ultimate pressure limit (~9 GPa) in encapsulated moiré devices. In aligned graphene/h-BN, we demonstrate that pressure induces a substantial enhancement of the moiré potential strength, evidenced by the suppression of the first valence bandwidth and the near-doubling of the primary band gap. Moreover, we report the first observation of a tertiary gap emerging above 6.4 GPa, verifying theoretical predictions. Our results establish hydrostatic pressure as a universal parameter to reshape moiré band structures. By enabling quantum transport studies at previously inaccessible pressure regimes, this Letter expands the accessible parameter space for exploring correlated phases in moiré systems.

cond-mat.str-el↗

arXiv2025

CellCLAT: Preserving Topology and Trimming Redundancy in Self-Supervised Cellular Contrastive Learning

Self-supervised topological deep learning (TDL) represents a nascent but underexplored area with significant potential for modeling higher-order interactions in simplicial complexes and cellular complexes to derive representations of unlabeled graphs. Compared to simplicial complexes, cellular complexes exhibit greater expressive power. However, the advancement in self-supervised learning for cellular TDL is largely hindered by two core challenges: \textit{extrinsic structural constraints} inherent to cellular complexes, and intrinsic semantic redundancy in cellular representations. The first challenge highlights that traditional graph augmentation techniques may compromise the integrity of higher-order cellular interactions, while the second underscores that topological redundancy in cellular complexes potentially diminish task-relevant information. To address these issues, we introduce Cellular Complex Contrastive Learning with Adaptive Trimming (CellCLAT), a twofold framework designed to adhere to the combinatorial constraints of cellular complexes while mitigating informational redundancy. Specifically, we propose a parameter perturbation-based augmentation method that injects controlled noise into cellular interactions without altering the underlying cellular structures, thereby preserving cellular topology during contrastive learning. Additionally, a cellular trimming scheduler is employed to mask gradient contributions from task-irrelevant cells through a bi-level meta-learning approach, effectively removing redundant topological elements while maintaining critical higher-order semantics. We provide theoretical justification and empirical validation to demonstrate that CellCLAT achieves substantial improvements over existing self-supervised graph learning methods, marking a significant attempt in this domain.

cs.LG↗

arXiv2025

EndoVLA: Dual-Phase Vision-Language-Action Model for Autonomous Tracking in Endoscopy

In endoscopic procedures, autonomous tracking of abnormal regions and following circumferential cutting markers can significantly reduce the cognitive burden on endoscopists. However, conventional model-based pipelines are fragile for each component (e.g., detection, motion planning) requires manual tuning and struggles to incorporate high-level endoscopic intent, leading to poor generalization across diverse scenes. Vision-Language-Action (VLA) models, which integrate visual perception, language grounding, and motion planning within an end-to-end framework, offer a promising alternative by semantically adapting to surgeon prompts without manual recalibration. Despite their potential, applying VLA models to robotic endoscopy presents unique challenges due to the complex and dynamic anatomical environments of the gastrointestinal (GI) tract. To address this, we introduce EndoVLA, designed specifically for continuum robots in GI interventions. Given endoscopic images and surgeon-issued tracking prompts, EndoVLA performs three core tasks: (1) polyp tracking, (2) delineation and following of abnormal mucosal regions, and (3) adherence to circular markers during circumferential cutting. To tackle data scarcity and domain shifts, we propose a dual-phase strategy comprising supervised fine-tuning on our EndoVLA-Motion dataset and reinforcement fine-tuning with task-aware rewards. Our approach significantly improves tracking performance in endoscopy and enables zero-shot generalization in diverse scenes and complex sequential tasks.

cs.RO↗