arXiv subjects

Yan Wang

Publications and source records attributed to Yan Wang.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Homotopy Perturbation Method to Solve Nonlinear Partial Differential Equations

Solving nonlinear partial differential equations (PDEs) is important in various scientific and engineering applications. Recently, quantum computing was introduced as an alternative computational paradigm for solving nonlinear PDEs. In this paper, a new method called the quantum homotopy perturbation method (QHPM) is proposed to improve the scalability of solving nonlinear PDEs through two aspects. First, the dimension of the Hilbert space remains the same after the nonlinear PDE is linearized through the homotopy perturbation. Second, the solutions are obtained with a variational quantum simulation framework, where the number of qubits is decreased with functional encoding and the depth of parametrized circuits is reduced. The additional contribution of this paper is the introduction of new criteria for selecting the homotopy series truncation order and circuit depth for cost-effective QHPM. The proposed approach is demonstrated with several examples, including the vorticity transport equation and the reduced magnetohydrodynamics equations.

quant-ph↗

arXiv2026

A Robust Watermark-based Fingerprint Framework for GNNs Ownership Verification

The high training cost of Graph Neural Networks (GNNs) has raised growing concerns regarding model ownership infringement, such as model stealing and unauthorized misuse. To verify model ownership and prevent significant economic losses, two groups of GNN Ownership Verification (OV) methods have been proposed: watermark-based methods and fingerprint-based methods. However, these methods typically face three limitations: (1) the performance degradation of protected models caused by out-of-distribution (OOD) watermark graphs with respect to the training set; (2) the unrealistic assumption that surrogate models have been trained on a watermark-containing training set; and (3) over-reliance on specific output levels for fingerprint extraction. In this paper, we propose a Robust watErMArk-based fingeRprint frameworK for GNNs, named REMARK. REMARK first generates carefully crafted in-distribution watermark graphs that maximize output differences between GNN models, thus mitigating OOD-induced performance degradation. REMARK then extracts robust fingerprints from these output differences to verify GNN ownership, thereby removing the assumptions that surrogate models must be trained on a watermark-containing dataset or expose specific output levels. Extensive experiments across widely used real-world datasets and GNN architectures demonstrate that REMARK achieves state-of-the-art OV accuracy and robustness while preserving the utility of protected models.

cs.LG↗

arXiv2026

T2LSC-Bench: Benchmarking Localized Semantic Control in Text-to-Image Generation

Recent text-to-image models have become increasingly capable of rendering explicit text, but reliable localized text control requires more than generating the correct string. In applications such as product labeling, signage, and interface design, target text should be rendered within a designated text-bearing region without altering the predefined subject identity or surrounding scene semantics. We refer to violations of this requirement as target-text-associated semantic leakage, in which target-text semantics are expressed through non-textual visual content beyond the designated anchor. Existing visual-text benchmarks primarily evaluate readability, spelling accuracy, and layout, leaving this form of semantic leakage largely unexamined. We introduce T2LSC-Bench, a controlled diagnostic benchmark comprising 50 seed subjects and 1,200 prompt cases per model, yielding 7,160 evaluated images across six models. Its factorized design varies semantic relation, scene openness, prompt mode, and language. A dual-branch protocol combines OCR-VLM text verification with structured VLM semantic judgments to measure Text-at-Anchor Accuracy (TAA), Semantic Subject Preservation (SSP), Semantic Leakage Rate (SLR), and Conditional Semantic Leakage Rate (cSLR). Under stress-test conditions, SLR increases from 1.2% to 18.1% and cSLR from 1.3% to 18.2%, whereas TAA decreases only from 91.4% to 90.9%. Anti-leakage prompting reduces SLR from 16.6% to 8.4% without degrading rendering accuracy. Human validation on 420 images shows strong agreement between automatic and adjudicated annotations. These results show that accurate text rendering does not guarantee local containment of target-text semantics.

cs.CV↗

arXiv2026

Dynamic-Robust Photometric-Semantic Reconstruction for Open-Vocabulary 3D Scene Understanding

The integration of novel view synthesis (NVS) and open-vocabulary segmentation (OVS) has recently yielded powerful feed-forward 3D foundation models. However, their inherent reliance on static-scene assumptions leads to severe misalignment of spatial features in unconstrained dynamic environments. To bridge this critical gap, we propose SPAR, a novel joint semantic-geometric encoding architecture that explicitly isolates transient dynamic noise prior to latent space aggregation. Furthermore, we introduce a dynamic-region-aware end-to-end training paradigm that structurally couples motion estimation with multi-view visual and semantic learning. This unified approach enables the network to inherently resolve motion conflicts and distill multi-view consistent, temporally stable scene representations from dynamic inputs. Extensive experiments on the challenging D-RE10K benchmark demonstrate that SPAR achieves state-of-the-art performance. Our end-to-end approach achieves exceptional novel view synthesis quality, yielding a PSNR of 22.15 dB and 23.33 dB given only 3 and 4 input views respectively. Despite being trained in a self-supervised manner, our model achieves an mIoU of 88.5% for motion mask prediction. Furthermore, our analysis reveals a strong inter-task synergy between photometric scene reconstruction and semantic understanding, where semantic synthesis learning consistently enhances photometric fidelity in novel view rendering. Code will be available at https://github.com/dmucby/SPAR.

cs.CV↗

arXiv2026

An improved bound on the minimum size of Tur\'an $(r+1,r)$-systems

For positive integers $n\ge s>r$, let $T(n,s,r)$ denote the minimum number of edges in an $r$-uniform hypergraph on $n$ vertices such that every $s$-set of vertices contains at least one edge. A simple averaging argument shows that the ratio $T(n,s,r)/\binom nr$ is non-decreasing in $n$ and we denote its limit as $n\to\infty$ by $t(s,r)$. The case $s=r+1$ has a rich history, with the previously best known asymptotic bounds for $r\to\infty$ being $1\le r\cdot t(r+1,r)\le 4.91...$ . In this paper, we present a simple probabilistic construction which shows that $(r+2)\cdot t(r+1,r)\le 4$ for every $r\ge1$. We also derandomise it and discuss applications to covering codes.

math.CO↗

arXiv2026

Memory Is Not Always Needed: Characterizing Conditional Memory in Scientific Reasoning

Scientific reasoning requires language models to retrieve specialized knowledge and incorporate it reliably into multi-step computation. Conditional memory provides an explicit lookup pathway that complements dense neural representations, but its usefulness is inherently input- and computation-dependent: retrieved information may repair missing scientific associations, yet it may also introduce distracting shortcuts or interfere with reasoning that the base model can already perform correctly. In this work, we systematically investigate when, where, and to what extent conditional memory should participate in scientific reasoning. We characterize the scientific knowledge boundary and controlled interventions on memory-enabled knowledge-circuit nodes. Based on these analyses, we propose a Knowledge Boundary-Aware Router that uses task-specific input proxies available before generation to determine whether memory is activated, which layer-stage nodes receive memory signals, and how strongly these signals contribute. Experiments on biological and chemical reasoning benchmarks, covering two backbone families and six task types, show that memory effects vary substantially across inputs, tasks, and injection locations. Compared with static and activation-rate-matched random routing, our approach more consistently preserves beneficial memory contributions while suppressing memory-induced regressions, establishing selective memory allocation as an important principle for reliable scientific reasoning.

cs.AI↗

arXiv2026

Beyond Dense Adam States: Adaptive Log-Space Quantization for Memory-Efficient Optimizers

Optimizer-state quantization is commonly designed for Adam's dense, parameter-aligned first- and second-moment arrays. This abstraction breaks for memory-efficient optimizers, whose states may be factored, confidence-modulated, or maintained in a projected space, so similar reconstruction error can produce different update error. We formulate optimizer-state quantization as a joint problem over representation, topology, and update semantics. We then introduce Adaptive Log-Space (AL) quantization for non-negative states. AL fits each block's observed nonzero logarithmic interval and reserves a separate code for exact zero, enforcing $q = 0 \Leftrightarrow x = 0$; signed momentum and state precision remain independently selectable. Controlled probes show that adaptive ranges reduce update error and temporal drift, exact-zero reservation preserves dormant states, and state topology constrains useful block granularity. End-to-end language-model training evaluates the resulting policy across dense, factored, confidence, and projected optimizer states. On TinyLlama-1.1B, AL8 with uniform 8-bit momentum reaches 72.90 perplexity versus 73.54 for bitsandbytes 8-bit AdamW, with comparable optimizer-state storage and higher throughput. CAME matches reference-level final perplexity across three seeds when its non-negative states use AL16, while a semantic grouping-and-protection policy closes most of quantized Adafactor's 100K-step late-loss gap. These results make state topology and update semantics first-class design constraints for optimizer quantization.

cs.LG↗

arXiv2026

Pixel-Space Diffusion via Observation Operators

Pixel-space diffusion models directly model image distributions but remain difficult to optimize. Recent methods alleviate this challenge through target reparameterization, while still relying on a fixed clean-image target throughout denoising. Through empirical analysis, we identify a scale-time mismatch: image structures become predictable from coarse to fine as noise decreases, whereas existing models are forced to predict the full image even under high noise, resulting in low-SNR gradients that hinder optimization. To resolve this mismatch, we propose Observation Operator Diffusion, a unified framework that aligns both the supervision trajectory and feature refinement with the intrinsic recovery order of image structures. Specifically, we replace fixed full-image supervision along the standard flow path with a time-indexed observation trajectory that evolves from coarse structures to the full image during denoising. This trajectory is instantiated with a family of Gaussian-Lanczos operators at varying observation scales, yielding a path-consistent training objective. We further introduce GL-CoDA, a decoder that injects scale-specific Gaussian-Lanczos observations across decoding stages for coarse-to-fine feature refinement. Extensive experiments show that the proposed approach converges substantially faster while consistently improving generation quality, achieving an FID of 1.52 on ImageNet-256.

cs.CV↗

arXiv2026

Efficient production of $^{229m,g}$Th via neutron capture in VUV-transparent crystals

The low-lying isomeric state of $^{229m}$Th, owing to its unique nuclear energy structure, has been widely regarded as one of the most promising candidates for the development of a nuclear clock. However, the limited availability of suitable $^{229}$Th sources with sufficiently high activity remains a major challenge for experimental investigations of the $^{229m}$Th isomer. We propose a neutron-capture-based approach for the in-situ production of $^{229m,g}$Th by doping $^{228}$Ra into crystal hosts, where $^{229m,g}$Th is generated through neutron-capture reactions followed by a sequence of radioactive decay processes. We systematically investigate the background contributions associated with the three doped crystal hosts, namely CaF$_2$, SrF$_2$, and LiF, and evaluate their impact on the detection and identification of $^{229m}$Th. Under a neutron flux of $10^{15}\ \mathrm{n/cm^{2}/s}$ and a $^{228}$Ra doping concentration of $10^{19}\ \mathrm{cm^{-3}}$, the proposed method is capable of producing on the order of $10^{12}$ $^{229}$Th and $^{229m}$Th nuclei within only 1 s of irradiation, with a signal-to-noise ratios as high as $10^5$. In addition, the influences of detector wavelength resolution and post-irradiation measurement time on the detectability of the $^{229m}$Th signal are systematically analyzed, and the corresponding optimal measurement conditions are identified. Furthermore, the spatial distribution of neutron-produced $^{229}$Th within the crystal is investigated, providing practical guidance for optimizing crystal geometry and illumination configuration in future continuous-wave VUV absorption spectroscopy experiments. These results suggest that the proposed scheme provides a promising alternative pathway for the production and detection of $^{229\mathrm{m,g}}$Th, which may facilitate future studies toward the realization of nuclear-clock-based technologies.

nucl-ex↗

arXiv2026

A local clique density theorem in $H$-free graphs

In 2016, Reiher's clique density theorem determined the minimum number of copies of $K_t$ in a graph with a prescribed edge density. In this paper, we investigate its local version and prove a local clique density theorem in $H$-free graphs as follows. For integers $r$ and $t$ with $2\leq t\leq r-1$, any $r$-chromatic graph $H$, any real numbers $\gamma$ and $\alpha$ with $\frac{t-2}{2(t-1)}\leq\gamma\leq \frac{r-2}{2(r-1)}$ and $0\leq\alpha\leq 1$, we determine the maximum value $\beta:=\beta(r,t,\alpha,\gamma)$ such that for every $n$-vertex $H$-free graph $G$ with at least $\gamma n^2$ edges, every $\lceil\alpha n\rceil$-vertex subset in $G$ contains at least $(\beta-o(1))n^{t}$ copies of $K_t$. In particular, when $H=K_r$, every $\lceil\alpha n\rceil$-vertex subset contains at least $\lfloor\beta n^t\rfloor$ copies of $K_t$, which is an exact bound. For suitable choices of $\alpha$ and $\gamma$, namely, those for which all part ratios in the corresponding extremal construction are rational, this bound is attained for infinitely many values of $n$.

math.CO↗

arXiv2026

Multi-quantum-channel mediated tunable single-photon skyrmions from metasurfaces

Quantum optical skyrmions, as topologically robust quantum information carriers, hold transformative potential for resilient high-dimensional quantum information networks. However, their practical exploitation was still restricted to a single quantum channel, which precludes the multiplexing essential for practical high-capacity quantum networks. Here, we utilize a metasurface to achieve multi-channel quantum state distribution of the polarization-entangled photon pairs, inducing a two-photon bunching effect in both the spin and spatial dimensions with compact flat optics. At the spatial bunching port, controlled manipulation of the spin-orbit interaction enables the generation of a tunable single-photon skyrmion pair. In contrast to any prior skyrmion generation, the single-photon skyrmions are mediated and topologically controlled by quantum measurement in multiple channels. Concurrently, during the amplitude and phase modulation process, both the skyrmion localization and the texture helicity can be precisely customized. The proposed tunable single-photon skyromions offer multidimensional controllability and topological stability provide a viable path toward noise-resilient high-dimensional quantum information processing.

physics.optics↗

arXiv2026

MedClaw: Heuristic Agent Harness for Long-Horizon Surgical Video Reasoning

Understanding tens-of-minutes surgical videos requires long-horizon temporal reasoning, answering what happens before, after, or across stages of a procedure by grounding the question in visual evidence spread across time. Existing approaches handle this poorly: a one-shot vision-language model (VLM) compresses the whole procedure to fit its context window and loses the detail a "before" or "after" question depends on, while video agents that train the model where to look are data-hungry and transfer poorly to out-of-domain surgery. We build an agent harness that separates reasoning from perception and improves by evolving context rather than optimizing weights. A text-only orchestrator plans which evidence to gather and issues an auditable sequence of tool calls, while frozen vision-language sub-agents execute each call over the pixels, viewing, cropping, inspecting frames, and retrieving external knowledge. We further propose a gradient-free, reward-gated Heuristic Skill Distillation loop that mines the agent's own low-scoring traces and keeps a candidate skill only when it raises a validation reward, yielding reusable retrieval skills, notably directed re-look. Growing an external skill library rather than tuning weights, the loop adapts from only about 100 labeled examples, far fewer than supervised or reinforcement fine-tuning requires. To evaluate this agent, we introduce MedClawBench, a de-leaked, doctor-grounded benchmark of 1,123 questions over self-built long neurosurgery recordings and a held-out public lecture-video test split. Across both datasets and all four evaluation dimensions, our agent consistently outperforms one-shot VLMs and general video-agent frameworks, with the largest gains on the long, out-of-domain neurosurgery videos. Project page: https://fyycs.github.io/medclaw/.

cs.CV↗

arXiv2026

HounsWorld: A Multimodal World Model for Hidden Patient-State Readout, Reconstruction, and Simulation

Clinical intelligence requires estimating a patient's underlying condition from incomplete observations rather than learning isolated mappings from scans to answers. Volumetric medical images provide dense observations of anatomy, attenuation, and lesions, whereas clinical language provides sparse but complementary semantic observations. We formulate CT-centered intelligence as inference over a shared latent patient state, under which readout, reconstruction, and simulation all become state-dependent prediction problems. To operationalize this view, we introduce HounsBench, a computed tomography (CT) centric patient-state benchmark that unifies these three task families with patient-disjoint splits and per-family metrics, and HounsWorld, a 3B multimodal world model that treats volumetric scans and language as observations of the shared state through Joint Understanding-Generation Learning. A shared transformer forms an implicit patient-state estimate and supports three outputs: query-conditioned answers that read out the state, reports and captions that reconstruct it in language, and condition-specific CT volumes for low-dose denoising, virtual contrast enhancement, and anatomy-constrained text-and-mask-to-volume generation. Zero-initialized CT adapters preserve pretrained multimodal mappings, while condition-explicit Hounsfield-unit window sampling exposes clinically meaningful density observations. HounsWorld shows strong performance across all three task families while consistently improving CT understanding through clinically structured completion. Our project is available at https://github.com/byhwhite/HounsWorld.git

cs.CV↗

arXiv2026

Covering the ternary cube by binary subcubes

For an integer $n\ge0$, let $f(n)$ be the minimum number of subcubes of $\mathbb{Z}_3^n$ of the form $A_1\times\cdots\times A_n$, where $|A_i|=2$ for every $i$, whose union covers $\mathbb{Z}_3^n$. A simple counting argument gives $f(n)\ge(3/2)^n$, while $f(n)=O(n(3/2)^n)$ by random construction. We prove that $f(n)\le2(3/2)^n-1$, answering a problem of Imre Leader. We also show that $f(n)/(3/2)^n$ is nondecreasing and there exists a constant $C_3$ such that $f(n)=(C_3+o(1))(3/2)^n$ where $1.62227<C_3\le2$.

math.CO↗

arXiv2026

Every fork-free graph is perfectly weight divisible

A graph $G$ is \emph{perfectly weight divisible} if, for every positive integral weight function on $V(G)$ and every induced subgraph $H$ of $G$ with at least one edge, the vertex set $V(H)$ can be partitioned into two sets $A$ and $B$ such that $H[A]$ is perfect and the maximum weight of a clique in $H[B]$ is smaller than the maximum weight of a clique in $H$. Perfect divisibility and its weighted form provide a natural approach to polynomial $\chi$-boundedness. A \emph{fork}, also known as a \emph{chair}, is the graph obtained from a claw by subdividing one of its edges once. In this paper, we prove that every fork-free graph is perfectly weight divisible. As a consequence, we confirm a conjecture of Sivaraman that every fork-free graph is perfectly divisible.

math.CO↗

arXiv2026

Pair-Centric Graph Rewiring for Over-Squashing via Optimal Transport-Guided Communication Alignment

Message-passing neural networks (MPNNs) often struggle when task-relevant information is distributed across distant regions of a graph, since local propagation must compress remote signals through limited structural interfaces. Graph rewiring provides a structural response to over-squashing. Most existing methods rely on edge-level bottleneck scores or graph-level connectivity surrogates. With a limited rewiring budget, the key question is which pairwise communications most need structural support. This paper proposes PairAlign, a pair-centric graph rewiring framework that makes this question explicit through demand-support shortage. Specifically, PairAlign combines original-graph structural demand with current-graph finite-hop propagation support; their ratio highlights interactions whose communication demand is poorly supported by topology, and our theory shows that this score provides a computable proxy for the corresponding Jacobian-based shortage with a pair-level interpretation of over-squashing. Our theory reveals a two-sided effect of edge insertion: a new edge can create useful walks and simultaneously dilute existing normalized transition mass. Guided by this observation, PairAlign optimizes shortage to favor edge additions that alleviate over-squashing. Beyond selecting useful additions, PairAlign further introduces an Optimal Transport-guided rewiring mechanism to coordinate the finite edge budget for pair-level structural compatibility and shortage-target coverage. It formulates communication alignment between the candidate edge budget and the shortage targets, and the theory shows that this allocation covers shortage targets more broadly and effectively than a greedy-local assignment. Experiments on standard graph benchmarks show PairAlign's improvement across message-passing backbones, validating pair-level repair as an effective route for alleviating over-squashing.

cs.LG↗

arXiv2026

StageWAM: Joint-Embedding Stage Prediction for World-Action Models in Robot Manipulation

Generalist robot policies aim to map multimodal observations and linguistic task instructions to actions across diverse tasks. However, existing methods typically represent the future as a fixed, short video-action chunk. This short-term future captures local scene evolution for action execution, but it does not explicitly describe the stage-level future that specifies how a task should progress from its current stage to the next. We therefore distinguish two complementary futures for robot manipulation: a short-term physical future to capture local scene evolution and a stage-level semantic future to represent task progress. We introduce StageWAM, which augments a Motus-based World Action Model (WAM) with Stage-JEPA, a goal-conditioned Joint-Embedding Predictive Architecture (JEPA) predictor. Given the current observation and task instruction, Stage-JEPA uses a frozen V-JEPA2 encoder to extract the current-state representation and predicts the latent target of the next inferred stage. Across 50 RoboTwin 2.0 tasks in clean and randomized environments, StageWAM achieves 90.25% overall success and reduces the mean number of execution steps in successful rollouts by 5.97% relative to the strongest baseline.

cs.RO↗

arXiv2026

JEPA-WAM: Learning Vision-Language-Action Policies with Joint-Embedding World Modeling

Robust robot control benefits from explicitly modeling state transitions, but video-generation world action models (WAMs) introduce substantial deployment cost. Existing latent WAMs avoid explicit future generation, but often compress predictive representations or separate predictive modeling from the representations used for action generation. We introduce JEPA-WAM, a latent WAM built in a pretrained V-JEPA space, which couples latent transition prediction with continuous action generation through a shared predictor. JEPA-WAM predicts a spatially structured joint current-future target that captures task-shared visual temporal structure between current and future observations, while preserving dense patch-level correspondence. Through the shared predictor, transition supervision directly shapes the backbone, from which dedicated representations are extracted for action prediction. The same design can also be instantiated in pretrained VLA policies while preserving their original perception and action pathways. On LIBERO-Plus, JEPA-WAM achieves 79.2%, the best result without large-scale robot-policy pretraining, while its pretrained $\pi_{0.5}$ instantiation reaches 86.3%, achieving the best overall performance. Experiments on RoboTwin 2.0 and real-world bimanual manipulation further demonstrate strong generalization under visual and spatial shifts.

cs.RO↗