arXiv subjects

Hui Xu

Publications and source records attributed to Hui Xu.

At least 19 recordsLinked to original sources

arXiv2026

A Discretely Entropy Conserving/Stable Flux Reconstruction Scheme via Hybridized Split Form Differential Operator and Generalized Entropy Projection

This paper proposes a novel discretely entropy conserving/stable flux reconstruction (FR) scheme for nonlinear conservation laws. The scheme combines a hybridized split-form differential operator with a generalized entropy projection, enabling discrete entropy conservation for arbitrary nodal distributions and arbitrary correction functions without modifying the original quadrature weights. The formulation is built directly upon the classical FR framework and is shown to preserve conservation properties while achieving entropy conservation in the semi-discrete sense. Numerical experiments using the isentropic vortex problem confirm the theoretically predicted accuracy and demonstrate robust entropy behavior with entropy-dissipative interface fluxes.

math.NA↗

arXiv2026

A subcell-refined entropy-residual-driven limiting strategy for high-order discontinuous Galerkin methods

Fine-grained, subcell-level dissipation control is essential for achieving robust high-order discontinuous Galerkin (DG) simulations of nonlinear hyperbolic systems in under-resolved regimes while preserving accuracy. This paper proposes a subcell-refined entropy-residual-driven limiting strategy for DG on Legendre-Gauss-Lobatto nodes. The limiter introduces only nearest-neighbor pairwise dissipation within each element, with closed-form coefficients that supply the minimal dissipation required to restore the element entropy inequality. The strategy is a diagonal, locally stable approximation of classical entropy-stable methods, and a generalized subcell framework reveals split-form DG and residual-distribution-based entropy correction schemes as particular choices of the limiting coefficients. For the Euler equations, a physically consistent jump operator separately models thermal and shear entropy production while preserving velocity and pressure equilibrium; a subcell refinement of the Zhang-Shu positivity limiter ensures pointwise positivity. Extensive numerical tests confirm that the scheme maintains optimal high-order accuracy, strictly enforces entropy dissipation, and significantly reduces the difficulty of a posteriori positivity-preserving procedures.

physics.comp-ph↗

arXiv2026

Cognitive Link-Flexible FTN-OTFS Design for High-Mobility LEO Satellite Communications

Low Earth orbit (LEO) satellite links are challenged by pronounced signal-to-noise ratio (SNR) variation and severe Doppler shifts. Although mobility robustness is provided by orthogonal time frequency space (OTFS) modulation, the rate-reliability tradeoff of faster-than-Nyquist (FTN) signaling is constrained by fixed packing. In this paper, an SNR-aware flexible FTN-OTFS framework is proposed, in which the packing factor is adapted to changing link conditions under a prescribed reliability requirement. Link-state perception and packing decisions are supported by estimated SNR and offline reliability thresholds, with constant decision complexity achieved through a fixed-mode lookup table. Elevation-dependent propagation, fractional Doppler, and FTN-induced interference are incorporated into the signal model, while colored noise is accommodated by covariance-aware linear minimum mean-square error detection. Throughput and bit error rate are analytically characterized, and energy efficiency and peak-to-average power ratio are evaluated. Simulation results show that conservative packing preserves reliability under unfavorable conditions, while denser signaling improves throughput as the link strengthens. These findings highlight the potential of cognitive FTN adaptation for efficient future LEO wireless communications.

cs.IT↗

arXiv2026

Cayley-tree pseudo-orbit tracing: period subgroups and relative geometry

We introduce Cayley-tree POTP, obtained by imposing the pseudo-orbit equations of a finitely generated group action only along a spanning tree of a Cayley graph. For zero-dimensional actions, we characterize this property by equicontinuity along normalized replacement paths; for subshifts, the criterion is expressed in the right-coset space of the common left-period subgroup. These criteria characterize virtual freeness and, for commensurated subgroup pairs, identifies Cayley-tree POTP of the coset full shift with relative quasi-tree geometry and a finite Bass--Serre decomposition. For infinite-index VFP pairs, Cayley-tree POTP of the coset full shift is equivalent to virtual cohomological codimension one, although ordinary POTP holds for every such shift. Finally, we prove that the strong topological Rokhlin property passes to finite-index overgroups. Consequently every finitely generated virtually free group has this property, answering the virtually cyclic case posed by Doucha, and Cayley-tree POTP is generic for its Cantor actions.

math.DS↗

arXiv2026

Training Documents Reranker with Search Rubrics for Deep Research Agent

Retrieval systems help deep research agents generate high-quality answers by providing relevant documents. However, existing retrievers typically select documents through relevance matching, while individually well-matched top-$k$ documents may not form a \textit{set} that satisfies the complex information needs of an agent query (\eg, diverse, concise and authoritative documents). In this paper, we propose search-oriented rubrics that \textit{explicitly} define the requirements that high-quality document sets should satisfy for each agent query. Our search rubrics are organized into a hierarchical structure and synthesized using a powerful LLM. Based on these search rubrics, we further train a document reranker \textbf{RubricRanker} to select a high-quality subset from retrieved documents. We design a two-stage training framework that consists of rubrics-guided supervised fine-tuning and rubric-based reinforcement learning. Extensive experiments demonstrate that RubricRanker outperforms the strongest baseline by 2.6 points on four deep research benchmarks and generalizes well to five RAG benchmarks.

cs.IR↗

arXiv2026

SEER: A Self-Grounded Evidence Interface for Controlled Spatial Relation Classification

Spatial relation questions require a model to identify the queried subject and object before comparing their layout. Yet a VLM can recognize both entities and still answer from the wrong instance or an ambiguous global view. We ask whether making query-specific evidence explicit can mitigate this failure and propose SEER (Self-grounded Evidence for Entity-Relation Reasoning), a training-free inference-time evidence interface for frozen VLMs. SEER hides candidate relations during pair localization, constructs a query-specific view with explicit subject/object roles, and retains the full image and sparse box geometry as complementary evidence. For relation-choice protocols with exact inverse support, an optional refinement swaps the entity roles and changes the forward decision only when exactly one visual state obeys the corresponding inverse relation. On an image-disjoint GQA-Train900 test frozen before model scoring, SEER pools to +3.94 [2.17,5.72] over Full; the gain remains positive under label-independent grounding-order counterbalancing and on the 535 rows whose entity names are unique. The unchanged protocol yields +4.35 to +11.79 on all 2,434 filtered EmbSpatial pair-relation questions across three models. Matched controls separate local refocus from role-explicit conditioning. These results establish query-specific evidence construction as the principal intervention, with reciprocal consistency as a smaller protocol-specific refinement.

cs.CV↗

arXiv2026

RECAP: Relation Evidence Calibration for Detecting Spatial Relation Hallucinations in Vision-Language Models

Vision-language models can answer spatial relation questions confidently even when the image supports an incompatible relation. We formulate relation-grounded selective prediction: accept or reject an already-produced yes/no answer by auditing its visual support, rather than treating uncertainty as evidence. RECAP, our relation-evidence calibration framework, compares image-conditioned likelihoods for a claim, its semantic contradictions, and optional one-sided supports, then converts these witnesses into an answer-conditioned rejection risk. A calibration-only gate preserves confidence as a veto when confidence is demonstrably informative and otherwise deploys relation evidence alone. Across 20 group/image-disjoint splits, RECAP lowers H-FPR@80 over confidence by between 2.0 and 17.9 points on VSR and raises Acc@80 by 3.0, 8.6, and 12.6 points on What'sUp for Qwen3-VL-8B, InternVL3.5-8B, and LLaVA-1.5-7B. It outperforms matched VCD-style visual contrast on all four primary metrics in all six settings. Full-pool VSR fallback, target-ranked GSR-Bench transfer, equal-budget supervised controls, and two additional checkpoints show a consistent operating principle: structured counterevidence complements certainty when confidence is misaligned, while the gate retains confidence when it is already useful.

cs.CV↗

arXiv2026

Rigid Functions, IP-Systems, and Topological Mild Mixing

We study uniform rigidity and topological mild mixing through continuous observables. For a fixed sequence of times, the observables rigid along that sequence form a closed unital $T^{\pm1}$-invariant algebra and determine the maximal factor uniformly rigid along the prescribed sequence. We then give functional forms of the classical ${\rm SIP}^{*}$- and ${\rm IP}^{*}$-return-time criteria: a topological dynamical system is mildly mixing exactly when it has no nonconstant locally SIP-rigid observable, and in the minimal category the same property is equivalent to the absence of nonconstant locally IP-rigid observables. Finally, a locally IP-rigid observable yields a canonical orbit-name factor carrying marked local data. For fixed local data, the $T^{\pm 1}$-invariant core of the local rigidity algebra determines a uniformly rigid factor whenever the core is nontrivial.

math.DS↗

arXiv2026

Adherence Semigroups and Density Finite-Sums Configurations

In this paper, we use the adherence semigroup to describe finite-sums configurations in topological dynamical systems. We establish a correspondence between exact finite sumsets and powers of adherence elements. As applications, we give dynamical formulations of density finite-sums results, characterize total minimality through the density of adherence-power orbits, and give a positive answer to the ultrafilter question in [Question~8.9, 6]. We also characterize the sets that belong to the common sum of two commuting nonprincipal ultrafilters.

math.DS↗

arXiv2026

Beyond Relevance-Centric Retrieval: Rubric-Oriented Document Set Selection and Ranking

As large language models and AI agents become the primary consumers of search results, document set quality determines the upper bound of downstream generation. Yet existing evaluation systems remain confined to scoring documents independently and aggregating via nDCG, ignoring inter-document interactions (redundancy, conflict, complementarity) and unable to answer what makes one document set better than another. To address these issues, we propose a complete evaluate-diagnose-optimize framework. We design SetwiseEvalKit, a three-level, nine-dimension document set evaluation benchmark covering both short-form and long-form scenarios, comprising approximately 28K high-quality evaluation rubrics. We systematically evaluate 12 rerankers: even the best method achieves no more than 45% coverage, cross-document coordination dimensions are universally weak, and no single method maintains top performance across both settings. Building on this, we propose Rubric4Setwise, a training-free method that converts rubric-based evaluation criteria into document set selection signals, achieving the best downstream generation performance with fewer documents and search rounds. It is the only method that maintains state-of-the-art results across both scenarios, validating the effectiveness of closing the loop from evaluation to optimization.

cs.CL↗

arXiv2026

Asymptotics of randomly weighted sums without moment conditions of random weights

In the paper, we investigate the asymptotics of randomly weighted sums with upper tail asymptotically independent and quasi-upper tail asymptotically independent primary random variables without requiring moment assumptions on random weights. For the case of primary random variables with regularly varying tails, we obtain more explicit results via an extension of Breiman's theorem. Then an application of the obtained results is established to asymptotically estimate for the finite-time and infinite-time ruin probabilities in a discrete-time risk model.

math.PR↗

arXiv2026

EgoAERO: Learning Dexterous Manipulation from a Single Egocentric Video without Object Assets

Egocentric RGB-D videos offer a natural source of human dexterous manipulation demonstrations, but existing data is difficult to use for robot learning because object pose, geometry, and contact information are often missing or require pre-scanned object assets. We present EgoAERO, the first framework that learns dexterous manipulation from a single egocentric RGB-D human demonstration without object assets. EgoAERO reconstructs contact-consistent hand-object trajectories through asset-free object tracking and reconstruction, ego motion compensation, and adaptive contact optimization, then converts them into robot policies using two-stage residual learning. We further introduce an online quality assessment mechanism and construct EgoDex-R, a large-scale egocentric dataset with 4.3M RGB-D frames for dexterous policy learning. Simulation and real-world experiments show that EgoAERO enables single-demonstration dexterous manipulation and achieves downstream performance close to CAD-based reconstructions on HOI4D.

cs.RO↗

arXiv2026

Identifying sensitivity-dominant parameters via active subspaces in reduced-order modeling of fluid dynamics

Reduced-order models (ROMs) are widely employed to describe complex system dynamics when simulations with full-order models (FOMs) are computationally prohibitive. This study presents POD-AS-PRS, a novel model-reduction framework based on the active subspaces (AS) technique, which performs dimensionality reduction in both the state and parameter spaces, enabling efficient and high-fidelity approximations of quantities of interest (QoI). The approach employs proper orthogonal decomposition (POD) to extract low-dimensional coefficients from CFD snapshots, which are inputs to a residual neural network (ResNet) with linear layers to learn their nonlinear mapping to QoI. Reverse-mode automatic differentiation (AD) is utilized to compute gradients with respect to the coefficients, enabling AS analysis to identify influential modes by shifting the analysis to the POD coefficient space, thereby achieving a dual-stage dimensionality reduction driven by QoI sensitivity rather than modal energy. A surrogate model is subsequently constructed using a polynomial response surface (PRS) based on AS-derived active variables, retaining only the highly influential POD coefficients to ensure accurate and efficient QoI reconstruction. The framework is validated on periodic and chaotic bluff-body flows, demonstrating high accuracy with few influential parameters, while AD-based gradients achieve a two-order-of-magnitude speed-up over finite-difference approximations. Sensitivity analysis further reveals that the influential coefficients are not necessarily proportional to modal energy, highlighting the critical flow structures. Consequently, POD-AS-PRS identifies a low-dimensional manifold of sensitivity-dominant parameters that govern the QoI, elucidating the essential flow structures and their coupling with control parameters, thereby enabling efficient and accurate QoI reconstruction.

physics.flu-dyn↗

arXiv2026

Quasi-disjointness in topological dynamics

Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is preserved under taking factors, proximal extensions, and group extensions. As a consequence, we establish that every minimal {\bf PI} system is quasi-disjoint from all minimal systems. In addition, some variant of quasi-disjointness, namely strong quasi-disjointness is also introduced and examined. Particularly, we prove that each {\bf AI} system is strongly quasi-disjoint from all minimal systems.

math.DS↗

arXiv2026

RIS-Empowered OTFS Modulation With Faster-than-Nyquist Signaling in High-Mobility Wireless Communications

High-mobility wireless communication systems suffer from severe Doppler spread and multi-path delay, which degrade the reliability and spectral efficiency of conventional modulation schemes. Orthogonal time frequency space (OTFS) modulation offers strong robustness in such environments by representing symbols in the delay-Doppler (DD) domain, while faster-than-Nyquist (FTN) signaling can further enhance spectral efficiency through intentional symbol packing. Meanwhile, reconfigurable intelligent surfaces (RIS) provide a promising means to improve link quality via passive beamforming. Motivated by these advantages, we propose a novel RIS-empowered OTFS modulation with FTN signaling (RIS-OTFS-FTN) scheme. First, we establish a unified DD-domain input-output relationship that jointly accounts for RIS passive beamforming, FTN-induced inter-symbol interference, and DD-domain channel characteristics. Based on this model, we provide comprehensive analytical performance for the frame error rate, spectral efficiency, and peak-to-average power ratio (PAPR), etc. Furthermore, a practical RIS phase adjustment strategy with quantized phase selection is designed to maximize the effective channel gain. Extensive Monte Carlo simulations under a standardized extended vehicular A (EVA) channel model validate the theoretical results and provide key insights into the trade-offs among spectral efficiency, PAPR, input back-off (IBO), and error performance, with some interesting insights.The proposed RIS-OTFS-FTN scheme demonstrates notable performance gains in both reliability and spectral efficiency, offering a viable solution for future high-mobility and spectrum-constrained wireless systems.

cs.IT↗

arXiv2026

Unique continuation inequalities for the Dunkl-Schrödinger equation via uncertainty principles

In this paper, we establish unique continuation inequalities at two time points for the Dunkl--Schrödinger equation. The proof is based on quantitative uncertainty principles for the Dunkl transform. In particular, we prove that pairs of (\varepsilon,k)-thin sets form strong annihilating pairs for the Dunkl transform, which yields quantitative unique continuation properties for solutions to the Dunkl--Schrödinger equation.

math.AP↗

arXiv2026

Ada-MK: Adaptive MegaKernel Optimization via Automated DAG-based Search for LLM Inference

When large language models (LLMs) serve real-time inference in commercial online advertising systems, end-to-end latency must be strictly bounded to the millisecond range. Yet every token generated during the decode phase triggers thousands of kernel launches, and kernel launch overhead alone can account for 14.6% of end-to-end inference time. MegaKernel eliminates launch overhead and inter-operator HBM round-trips by fusing multiple operators into a single persistent kernel. However, existing MegaKernel implementations face a fundamental tension between portability and efficiency on resource-constrained GPUs such as NVIDIA Ada: hand-tuned solutions are tightly coupled to specific architectures and lack portability, while auto-compiled approaches introduce runtime dynamic scheduling whose branch penalties are unacceptable in latency-critical settings. We observe that under a fixed deployment configuration, the optimal execution path of a MegaKernel is uniquely determined, and runtime dynamic decision-making can be entirely hoisted to compile time. Building on this insight, we propose Ada-MK: (1) a three-dimensional shared-memory constraint model combined with K-dimension splitting that reduces peak shared memory usage by 50%; (2) MLIR-based fine-grained DAG offline search that solidifies the optimal execution path, completely eliminating runtime branching; and (3) a heterogeneous hybrid inference engine that embeds MegaKernel as a plugin into TensorRT-LLM, combining high-throughput Prefill with low-latency Decode. On an NVIDIA L20, Ada-MK improves single-batch throughput by up to 23.6% over vanilla TensorRT-LLM and 50.2% over vLLM, achieving positive gains across all tested scenarios--the first industrial deployment of MegaKernel in a commercial online advertising system.

cs.CL↗

arXiv2026

Efficient LLM-based Advertising via Model Compression and Parallel Verification

Large language models (LLMs) have shown remarkable potential in advertising scenarios such as ad creative generation and targeted advertising. However, deploying LLMs in real-time advertising systems poses significant challenges due to their high inference latency and computational cost. In this paper, we propose an Efficient Generative Targeting framework that integrates adaptive group quantization, layer-adaptive hierarchical sparsification, and prefix-tree parallel verification to accelerate LLM inference while preserving generation quality. Extensive experiments on two real-world advertising scenarios demonstrate that our framework achieves significant speedup with acceptable quality degradation, making it operationally viable for practical deployments.

cs.CL↗