Papers

Baryon-meson sum rules enable cross-checks among exclusive mesonic and baryonic measurements. Unlike their heavy-to-heavy counterparts, analogous heavy-to-light relations lack an explicit heavy-quark-symmetry origin. We investigate their origin in the $b\to s\nu\bar\nu$ system by studying the relevant helicity amplitudes at the two kinematic endpoints. Although the sum rule follows algebraically from the simple short-distance structure, its coefficient depends nontrivially on the hadronic dynamics. At maximum recoil, the coefficient for the daughter baryons ${\cal B}=\Lambda,\Xi$ is consistent with the approximate value $1/2$ within current form-factor uncertainties. At zero recoil, by contrast, a kinematic helicity projection enforces its exact vanishing. The fully integrated coefficients are numerically close to $1/4$. However, unlike the one-quarter coefficient in the heavy-to-heavy system, they are not local symmetry coefficients but integrated quantities shaped by the behavior between the two endpoints. This understanding may guide the construction of baryon-meson sum rules in more general heavy-to-light decays.

Here we report on the status of the first on-orbit technology demonstration of the Little UV Camera (LUVCam1). LUVCam1 is a 0.4U payload aboard the 2U cubesat GRBBeta that was launched in July 2024. The primary objective of the mission was to qualify the GSENSE4040 CMOS sensor and its readout electronics in preparation for the Quick UltraVIolet Kilonova Surveyor (QUVIK; Werner et al. \cite{Werner22, Werner24}) satellite. LUVCam will serve as the primary scientific camera for this mission. We report on the performance of the GSENSE4040FSI sensor used on LUVCam1, beginning with its in-lab characterization followed by an assessment of its on-orbit performance using astronomical observations made by LUVCam1. The camera remains operational two years later and has taken pictures of the Moon and stars that we show here. Through LUVCam1, we demonstrated an approach leveraging new-space to qualify the latest COTS CMOS sensors for astronomy missions.

Gradient-guided diffusion samplers provide flexible priors for inverse problems and conditional generation, but strong guidance can move the sampling trajectory into regions where the learned score is poorly supported. Existing tangent-projection strategies limit first-order departure from an iso-density surface, yet discard potentially useful normal motion and overlook the second-order departure induced by tangent motion on a curved surface. We introduce curvature-adaptive tubular correction (CAT), a training-free plugin that regulates both effects within a shared, noise-dependent geometric budget. CAT decomposes the guidance gradient into normal and tangent components, charges normal displacement at first order and tangent displacement according to directional curvature, and obtains their jointly optimal magnitudes from a one-dimensional dual equation. Armijo backtracking calibrates the resulting finite step against the actual guidance objective, while matrix-free directional derivatives avoid constructing the full score Jacobian. We establish local guarantees for the tubular approximation, uniqueness of the correction, and sufficient objective decrease. Across seven inverse problems on FFHQ and ImageNet, CAT improves the evaluated pixel- and latent-space host samplers, with particularly consistent gains in perceptual metrics. It also improves black hole reconstruction on InverseBench and yields the lowest FID among the compared methods at every tested classifier-free guidance scale, while maintaining stable saturation and contrast. These results support curvature-aware tubular control as a reusable mechanism for stabilizing diffusion guidance.

For $N\ge2$, $0<\beta<N$ and $q>1$, we study maximizers of the critical singular anisotropic Moser–Trudinger integral \[ \int_{\mathbb{R}^N} \frac{\Phi_{N,q,\beta} (\lambda_N(1-\beta/N)|u|^{N/(N-1)})} {F^o(x)^\beta}\,\mathrm{d}x, \qquad \|F(\nabla u)\|_N^a+\|u\|_q^b\le 1. \] where $a>0$, $0<b\le N$ and $\Phi_{N,q,\beta}$ is the integrable Taylor remainder. The supremum is attained for every $a>0$ when $b<N$. For $b=N$ and $1<q<q_+$, the first retained Taylor term separates two regimes, with \[ q_-:=\frac{N^2(N-2)}{(N-1)(N-\beta)},\qquad q_+:=\frac{N^2}{N-\beta}. \] Attainment holds for every $a>0$ if $1<q<q_-$, while for $q>1$, $q_-\le q<q_+$, there is a finite threshold $a_c>N$ and attainment holds if and only if $0<a\le a_c$. An exact Euclidean reduction shows that the threshold is independent of the anisotropy. The proof combines critical–subcritical scaling with a nonlinear Green-function concentration bound. Radial flux and Pohozaev identities determine the first correction to the subcritical supremum, and refined Green tests give the strict comparison needed for attainment at the finite threshold, including in dimension two.

We show how the Pinnacle architecture can be adapted to be compatible with superconducting qubits, where the connectivity between qubits must be fixed at fabrication. Specifically, we present a modified instantiation of the architecture that has fixed connectivity degree of eight. With this instantiation, we show that a 2048-bit RSA integer can be factored in one month with approximately 120 000 physical qubits, given a physical error rate of $10^{-3}$, code cycle time of 1 microsecond and reaction time of 10 microseconds.

Polarizability predicts how an object responds to an incident electromagnetic field, the interactions between small particles, or the optical forces exerted upon them. Polarizability is responsible for the effective-medium properties of artificial materials or metasurfaces. Despite significant progress in all these areas, it is unclear what the limits of the strength of such interactions are or, more specifically, what the upper bounds on the polarizability of a given spatial region that an unknown and designed particle would occupy are. This work connects the electromagnetic field description via an integral equation with a dual formulation of quadratic programming to derive fundamental bounds on components of all four polarizability tensors or on their specific combinations. In particular, the work establishes an intuitive visualization of what strong polarizability means and how strong it can be. The developed fundamental bound also answers which materials and domains are best for the given demands on polarizability. These findings establish a versatile platform that can accommodate a wide range of demands on polarizable bodies, providing an absolute measure of their performance against which the results of human-powered or automated design procedures can be compared.

Large Reasoning Models increasingly use intermediate traces for machine translation, but it remains unclear when such reasoning helps or hurts. We analyze reasoning traces across models, languages, domains, and datasets, focusing on reasoning language, length, and structure. We find that the best reasoning language is model-specific, reasoning length has a non-monotonic relationship with quality, and traces exhibit recurring functional patterns. To uncover these patterns, we introduce Hierarchical Meta-Summarization (HMS), a scalable framework that induces coarse- and fine-grained reasoning structures without predefined taxonomies. HMS reveals a shared organization–understanding/planning, translating/drafting, and refining/verifying–alongside domain-specific variation. Our results suggest that MT reasoning should be controlled in a model-aware, length-aware, and pattern-aware manner rather than uniformly encouraged.

Vision-language-action (VLA) models map visual observations and natural-language instructions to robotic actions, but distribution shifts can compromise their reliability. Because these models may still succeed under out-of-distribution (OOD) conditions, detecting OOD inputs alone is insufficient to predict execution failure. In this paper, we introduce VLA-Scope, a two-stage framework that combines input-shift characterization with execution history to predict failure during OOD rollouts. The first stage uses pooled image and language representations to detect OOD inputs and classify their shift categories. For inputs flagged as OOD, the second stage combines the predicted category, action-prefix features, and execution progress features. A logistic regression model shared across shift categories updates failure risk as execution proceeds. We evaluate the framework with OpenVLA on ten LIBERO-Spatial tasks using leave-one-group-out cross-validation. OOD detection achieves a ROC-AUC of 0.9454, and shift classification achieves 91% accuracy. Evaluated independently of the OOD gate on all 1,400 OOD rollouts, the failure predictor achieves a ROC-AUC of 0.8497 after 60 executed actions, compared with 0.7906 without execution progress features. It also achieves a higher ROC-AUC than the evaluated ActProbe and SAFE-MLP baselines. These results suggest that combining action features with temporally aggregated execution step representations improves failure prediction under input shifts.

We study the problem of computing class probabilities in block-independent disjoint (BID) probabilistic databases. Given the probability with which each block in the database realizes each feasible tuple type, the goal is to compute the probability of a class of worlds specified by a given tuple multiplicity vector, thus grouping together worlds with the same bag (multiset) of realized tuple types. For this problem, we prove $\#\mathsf{P}$-hardness even for very restricted and structured inputs. On the other hand, we show that it admits an FPRAS, as well as $\mathsf{XP}$-time algorithms parameterized by the number of tuple types and the treewidth of an incidence graph modeling the connections between blocks and tuples. Finally, we show that augmenting the problem with certain compatibility constraints between block realizations renders it $\#\mathsf{XLP}$- and $\#\mathsf{XALP}$-hard parameterized by pathwidth and treewidth respectively, ruling out $\mathsf{FPT}$ algorithms under standard assumptions. We leave as an open question whether this also holds in the absence of compatibility constraints.

We consider the initial value problem for the Euler–Korteweg equations in the class of irrotational flows. In every space dimension $d \geqslant 2$, we establish a quantitative lower bound for the lifespan of solutions that explicitly exhibits its dependence on the Weber number, the Mach number, and the Sobolev norm of the initial perturbation. In particular, this lower bound can be taken arbitrarily large in a low-Weber-number regime under a suitable algebraic relation between the Mach and Weber numbers.

Barren plateau diagnostics characterize whether gradient signal remains available for training, but surviving signal need not translate into successful optimization. We study this trainability–optimization gap at the level of optimizer steps. Treating coefficient-weighted Hamiltonian-term gradients as task-like components, we introduce step-level diagnostics and derive an exact bridge between signed termwise organization, directional activity, and first-order descent. Resolving this bridge into standard first-order geometry shows that the apparent organization–activity factors are not independent optimization axes and that, at fixed state and update norm, the raw gradient maximizes first-order descent of the summed objective. We compare vanilla gradient descent, a deterministic Hamiltonian-term PCGrad variant, and probe-gated LSO-PCGrad on transverse-field Ising model instances with hardware-efficient and Hamiltonian variational ansatzes, together with matched controls for update norm and probe budget. Blind projection can improve an organization diagnostic while worsening final energy and first-order predictability. After conditioning on standard first-order geometry, residual term-space composition shows no reproducible material incremental association with realized descent, while optimizer-relative update norm shows positive material associations in some settings without cross-regime reproducibility. Matched controls provide no resolved final-energy benefit attributable to the projected direction, and the improvement of LSO-PCGrad is more consistent with probe-based search and step-norm adaptation than with Hamiltonian-term projection itself. These results show that gradient-structure diagnostics can characterize trainability and update geometry without serving as standalone evidence of optimization benefit, which requires controls matched on update norm and search budget.

Reference-guided diffusion stylization aims to transfer visual style from a reference image while preserving the semantics specified by a text prompt. However, image conditioning often entangles transferable style cues with reference-specific content, leading to an inherent trade-off: stronger conditioning improves style fidelity but increases content leakage, whereas aggressive suppression reduces leakage at the cost of style expression. This challenge is further complicated by the distinct spatial organization of texture- and geometry-dominant styles. To address these issues, we propose SafeStyle, a training-free framework for calibrated style residual injection in frozen diffusion models. SafeStyle first estimates style-supported and content-associated subspaces from compact calibration sets, preserving their informative overlap while suppressing useless content variations. It then transports the purified style evidence over adaptive spatial granularity and constrains its effective influence through an explicit residual-norm budget. Experiments across texture- and geometry-dominant styles show that SafeStyle achieves a DINO style similarity of 0.432 while maintaining competitive text alignment. On a semantically disjoint leakage-stress benchmark, it further achieves a DINO style similarity of 0.474 with only 0.8% semantic leakage, demonstrating an effective balance between style fidelity and reference-content suppression.

Producing accurate annotations for deep learning based image segmentation is both costly and labor intensive. This challenge is especially evident in wildland fire applications, where accurately labeled datasets are scarce due to the difficulty of collecting and annotating dynamic fire scenes. To address this problem, our previous work introduced the Centralized Copy-Paste Data Augmentation (CCPDA) method for semantic segmentation of wildland fire imagery, which generates artificial training samples by randomly pasting fire clusters from source images onto target images. However, random placement can produce contextually unrealistic scenes, such as fire burning on asphalt. In this paper, we present a context-aware strategy designed specifically to improve data quality and realism in small multiclass wildland fire datasets, ensuring that augmented samples remain contextually meaningful. The proposed method restricts fire placement to semantically valid target regions and selects the location whose Ash-Vegetation composition most closely matches the source context. This approach preserves existing fire regions in the target image, prevents unrealistic placements, and maintains contextual accuracy by generating images that resemble real wildland fire scenes. We evaluate the Context-Aware CCPDA strategy through numerical analysis and comparisons with other augmentation methods by a weighted sum-based multi-objective optimization (MOO) approach. The results confirm that the context-aware data augmentation strategy leads to improved segmentation performance and contextual realism, outperforming other augmentation procedures.

Discrete audio tokenization has become the critical interface between raw waveforms and autoregressive modeling in recent music generation. As a result, music tokenizers must simultaneously support high-fidelity reconstruction and produce discrete sequences that remain amenable to language modeling. Existing reconstruction-oriented tokenizers often mix musical structure with fine acoustic details, producing high-entropy tokens that are hard to model. In contrast, semantics-guided alternatives are designed for speech and do not fit music well, often hurting reconstruction quality. We address these trade-offs by rethinking music tokenization around a measurable notion of music semantic content grounded in downstream Music Information Retrieval tasks. Guided by this definition, we propose MuSeC, a music semantic codec that factorizes semantic and acoustic content directly from mixed signals without source separation. MuSeC preserves information required for high-fidelity reconstruction while producing more LM-friendly discrete units. Empirically, it improves reconstruction quality and yields more predictable token sequences, providing a practical foundation toward high-fidelity LLM music generation. Demos are available at https://longwaytog0.github.io/MuSeC/.

Technology increasingly supports self-care for understanding and improving one's own mental health. HCI is at the center of the turn towards self-care technology, yet we lack an account of who these interventions serve, what practices they support, how technology mediates those practices, and assumptions underlying design for self-care. In order to characterize the current landscape and inform future research, we analyzed 91 SIGCHI papers that contribute HCI interventions for mental health self-care from the ACM Digital Library from 2015 through June 2026. Then, we conducted an interpretive synthesis to surface six orientations of self-care, which describe how HCI self-care interventions constitute care through shared assumptions regarding self, care, and technology. Overall, our work provides an interconnected vocabulary for positioning HCI mental health self-care, highlights changing responsibilities of care towards users, and discusses implications for providing a more situated account of HCI self-care technology in addressing the 'general' user.

The outage probability in a network of cooperative unmanned airborne vehicles (UAVs) over generalized fading channels is studied analytically using finite mixture with expectation maximization technique. A relay-based topology with one ground control unit (GCU) is considered, where the cooperative UAVs can communicate with the GCU directly or through relay. The application the UAV assigned for specifies the minimum required transmission rate the UAV should achieve. The outage probability of the system is defined as the probability that either the transmission rate over any of the links drops below a predefined minimum threshold for that link or the Relay-GCU link is not able to transmit the aggregate data from all relayed UAVs and the minimum rate required by the relay UAV itself. Throughout the paper, expressions for the outage probability and the average achievable bit rate of a cooperative multi-carrier system are derived over generalized fading channels. Finite Mixture with Expectation-Maximization algorithm is utilized to derive a simple approximate expression for the probability density function (pdf) of the achievable bit rate assuming adaptive M-ary quadrature amplitude modulation (M-QAM). This pdf is used to derive closed-form expressions for the outage probability and the average bit rate.

We introduce a relation problem constructed from the Clauser–Horne–Shimony–Holt (CHSH) game, which we call the two-round one-dimensional CHSH problem. Its two-round structure ensures that the CHSH questions are supplied only after the relevant Pauli-frame data have been fixed, thereby ruling out a simple classical strategy that solves the corresponding problem perfectly when all inputs are supplied simultaneously. We construct a quantum circuit on $2N$ qubits that uses only adjacent two-qubit gates, has operational depth at most eight, and achieves the optimal quantum success probability of CHSH, which is strictly smaller than one. We prove that, for every fixed $0\leq\delta<(\sqrt{2}-1)/4$, any randomized classical circuit with fixed wiring and bounded gate fan-in that achieves an average success probability of at least $(2+\sqrt{2})/4-\delta$ requires depth $\Omega(\log N)$ after the questions of the second round are supplied. This yields an unconditional separation even though the quantum circuit is restricted to a one-dimensional geometry, whereas the classical circuit has no geometric locality restriction. The result shows that perfect quantum success is not necessary for unconditional quantum advantage with shallow circuits.

A search tree on trees (STT) is a data structure for performing a search for a target vertex in a reference tree. A standard binary search tree is a special case of an STT, where the reference tree is a path of totally ordered elements. In this paper, we study the problem of succinct representation of STTs. We consider two cases: (1) general search trees on trees, and (2) Steiner-closed search trees on trees [Bose et al. TALG 2023]. For both cases, we present representations that can be constructed in polynomial time and achieve optimal space up to the lower-order additive terms. We also present data structures for supporting fast traversals of both general and Steiner-closed STTs. For general STTs our data structure still takes optimal space up to lower-order additive terms.

Seasonal succession and human intervention profoundly influence dengue fever transmission, and both humans and mosquito vectors can disperse over long distances. This paper proposes a nonlocal reaction-diffusion dengue model with moving boundaries that incorporates dry-wet seasonality and impulsive intervention. We first present the existence and uniqueness of the global solution to the model, then introduce the definition of the generalized principal eigenvalue, prove its uniqueness when the kernel functions coincide via the method of separation of variables, and further discuss its associated properties. Using this eigenvalue as an index, we obtain a spreading-vanishing dichotomy and derive two criteria that characterize the spreading and vanishing states, respectively. Our results extend both the nonlocal diffusion model without impulsive intervention and the model with impulsive intervention but without seasonal succession. Finally, we validate our theoretical findings and investigate how various factors affect dengue transmission through numerical simulations. The numerical results indicate that a shorter dry season makes disease containment more difficult, whereas more intensive impulsive intervention enhances control efficacy.

At high Peclet number, the classical Taylor-Aris dispersion model becomes inadequate for early-time contrast-agent transport in arteries, while an explicit closure model and a clear physical interpretation of this regime remain lacking. In this study, we develop a novel explicit-closure one-dimensional (1-D) effective dispersion model for this regime, with its functional structures identified through symbolic regression. Analysis of the resulting model reveals that, in the high-Peclet-number regime, axial transport is redistributed between the effective convection flux and the dispersive flux, resulting in a reduction of the effective convective transport velocity in the dispersion model. This redistribution gives rise to a transition from the classical quadratic scaling to a linear scaling of the effective diffusivity with radial Peclet number. Numerical validation demonstrates close agreement with the convection-diffusion model over the investigated high-Peclet-number conditions, while the classical Taylor-Aris model exhibits substantial deviations. Application of the proposed model to averaged flow velocity inversion further demonstrates improved velocity estimation, particularly in the high-Peclet-number regime. These results highlight the importance of accounting for non-classical dispersion for reliable contrast-agent-based arterial blood flow velocimetry and provide new insight into high-Peclet-number mass transport.

We establish a complete characterization of local $C^1$ linearizability for planar diffeomorphisms. For every prescribed hyperbolic real Jordan form, we obtain necessary and sufficient integrability conditions on the modulus of continuity of the derivative for local $C^1$ linearizability. These criteria reduce to three canonical thresholds: the classical, polynomially weighted, and squared-logarithmically weighted Dini conditions. Each threshold is optimal: whenever the corresponding condition fails, we construct a diffeomorphism with the identical linear part that is not locally $C^1$ linearizable. For every non-hyperbolic linear part, explicit polynomial counterexamples show that smoothness alone cannot guarantee even local topological linearization. Beyond $C^1$ existence, we determine the optimal regularity for the derivative of the linearizing conjugacy in every hyperbolic case, with the optimality established by counterexamples.

A substantial body of empirical evidence suggests that stochastic mortality models ignoring long range dependence tend to underestimate life expectancy, which may lead to profound implications for pension schemes and funding arrangements. This paper addresses the modelling of stochastic mortality via a mixture of a fractional Lévy process and standard Brownian motion. Our stochastic mortality model exhibits nice analytical tractability in actuarial valuations and flexibility in the choice of underlying Lévy specifications. The long range dependence feature embedded in our stochastic mortality model is well reflected in our empirical studies on the mortality shocks during World War II and COVID-19. For efficient numerical pricing of longevity derivatives, we construct an effective singular value decomposition approximation scheme to overcome the computational challenges arising from the non-Markovian nature of the fractional Lévy process. Truncation errors in singular value decomposition approximation can be reduced by an effective residual correction scheme.

Reference-based metrics for Grammatical Error Correction (GEC) such as M$^2$ and ERRANT assume that the reference set enumerates all valid edits, and therefore often penalize corrections that are grammatical and meaning-preserving but phrased differently. We introduce RM-EVAL, a reward model trained on human preference data from SEEDA, as a reference-free meta-evaluator that predicts human-like quality judgments at both full-sequence and partial-sequence levels. Beyond evaluation, we show that the same reward model can be used as a learning signal to improve GEC generation via Reward-Guided Text Generation (RGTG), which keeps a base GEC model frozen and performs online, reward-driven decoding. Across SEEDA, RM-EVAL achieves strong agreement with human rankings, and RGTG yields consistent gains in reward and external validation, demonstrating a unified framework for both assessing and enhancing GEC systems without relying on gold references.

We study in-market uniform pricing and out-of-market bid cost recovery (BCR) payments in rolling-window dispatch for real-time power system operations with energy storage resources (ESRs). Due to intertemporal state-of-charge (SOC) constraints, ESR operations are temporally coupled, and existing in-market locational marginal pricing (LMP) may fail to compensate ESR's intertemporal opportunity costs, thereby triggering out-of-market BCR payments. We show that positive BCR is unavoidable when dispatched generators or ESRs have supply-side bids higher than the demand-side bid. We further identify an intertemporal coupling indicator associated with binding SOC constraints and demonstrate empirically that positive BCR arises only when this indicator is active, revealing that BCR is fundamentally driven by intertemporal coupling. In the simulation, we compare a BCR-minimizing uniform pricing scheme (UP-BCR) with existing real-time pricing methods under forecast uncertainty and show that UP-BCR substantially reduces BCR and demand payments relative to LMP while maintaining zero merchandising surplus in a copper-plate model.

Learning robot manipulation policies typically requires substantial demonstration data, which are costly to collect on real robots. Recent methods generate robot demonstrations from human videos by adapting recovered motion and validating the resulting trajectories in simulation. However, methods centered on motion-reference adaptation can limit behavioral diversity by retaining the demonstrated contact strategies and subtask orders, while insufficient understanding of task requirements and scene relations can reduce demonstration generation efficiency by generating invalid candidates. To address these limitations, we propose KnowDemo, a framework that uses structured manipulation knowledge from human videos to generate diverse robot demonstrations for a target workspace. To distinguish task requirements from demonstration-specific choices, we develop a knowledge extraction and reasoning module based on a vision-language model (VLM) that associates object and action descriptions with inferred task conditions, demonstration references, and permissible execution variations. To translate this knowledge into executable demonstrations, we resolve the descriptions against target-scene entities and geometry to guide candidate generation and screening before motion planning and simulation. The resulting demonstrations exhibit multimodal behavior through alternative contact strategies and valid subtask orders, with structured execution labels. Experiments demonstrate additional verified execution modes beyond a reference-only configuration and improved candidate planning success through task-guided grasp sampling. To validate the generated data for policy learning, we fine-tune the pretrained $\pi_{0.5}$ model on simulation data, achieving sim-to-real transfer across three tasks. Project page: https://zhiyuan-gao.github.io/knowdemo/

Vision-language-action (VLA) models built on pretrained vision-language models have demonstrated strong performance across diverse robotic manipulation tasks. However, VLA models that directly map current 2D observations to actions often lack sufficient spatial and temporal understanding, limiting their performance in precise and long-horizon manipulation. Recent methods enhance VLA models through geometric supervision and future-state prediction across the entire scene. However, these methods can suffer from redundant scene information, distracting the model from learning the geometry and dynamics relevant to the current interaction. To address this issue, we propose FOCAL-VLA, a framework that combines subtask-guided geometry distillation with implicit world modeling to learn representations of current spatial structure and future interaction dynamics. To focus geometric learning on the current subtask, we transfer geometric knowledge from VGGT to the VLA model by aligning geometry latents with features from subtask-relevant image regions. To capture the future 3D evolution of the current interaction, we incorporate implicit world modeling using Track4World features from current and future demonstration frames. The two complementary representations jointly guide action generation without running VGGT or Track4World at inference time. Experiments show that FOCAL-VLA outperforms baselines on both simulation benchmarks and real-world manipulation tasks. Project website: https://zhiyuan-gao.github.io/FOCAL-VLA/.

Factual hallucination is commonly defined by incorrect factual outputs. We study a paraphrase-induced hallucination setting, where a model answers a factual question correctly in its original form but generates an incorrect answer under a semantically equivalent paraphrase. Such inconsistencies expose latent factual instability under semantic invariance. However, general-purpose paraphrases are often insufficient as robustness-oriented supervision: near-copy paraphrases provide weak signals, while overly diverse paraphrases may break semantic equivalence. In this paper, we propose HALLUCINATION-R1, a robustness-oriented paraphrase generation framework that learns to produce semantically faithful yet robustness-challenging paraphrases for factual consistency. Through two-stage optimization, it first stabilizes meaning-preserving and diverse paraphrasing, then rewards paraphrases that reveal factual consistency degradation in downstream QA models. Experiments on SimpleQuestions, PopQA, and TruthfulQA show that HALLUCINATION-R1 achieves a strong consistency–diversity trade-off and exposes robustness failures across multiple model families and datasets. Further analyses indicate that these failures are not reducible to surface-level artifacts or semantic drift, but reveal non-trivial factual instability under meaning-preserving variation. A lightweight fine-tuning study also shows that HALLUCINATION-R1-generated data improves robust accuracy under paraphrase variations, suggesting its utility for robustness-oriented training. Our code and models are publicly available at https://github.com/yuwenhan07/Hallucination-R1.

Quadrotors are increasingly deployed in applications such as agriculture, infrastructure inspection, and maintenance. In each of these applications, the robot must navigate complex scene geometry while remaining strictly collision-free. Unlike in ground domains, even minor collisions for aerial vehicles can result in the loss of the robot. This safety requirement induces a pair of technical challenges. First, the environment must be represented with sufficient fidelity to encode complex structure, even when no ground-truth obstacle data is available. Second, a motion planner must leverage this representation to determine a collision-free path to the goal. This paper proposes a system that addresses these complementary challenges. The proposed method, AirSplan, adopts a normalized variant of 3D Gaussian Splatting that encodes high-fidelity scene geometry. It then applies a novel reachability-based motion planner that leverages the differential flatness of quadrotors to compute continuous-time collision constraints that tightly overapproximate the robot's occupancy. Experiments demonstrate that AirSplan successfully finds a path in 81.2% of challenging test cases, a significant improvement over the nearest baseline method's 51.2%.

Parametric CAD reconstruction requires recovering both precise geometry and editable modeling operations from visual observations, making it challenging under limited and ambiguous views. Existing methods mainly rely on 2D appearance cues and lack strong multi-view geometric priors. In this work, we present VGGT-CAD, a geometry-aware framework for parametric CAD reconstruction from single- and multi-view observations. We transfer pretrained 3D geometric priors into CAD reconstruction by encoding camera parameters as condition tokens and jointly modeling them with image tokens. To handle varying numbers of viewpoints, we introduce a variable-view cross-view context aggregation module that adaptively fuses multi-view features. We further develop a training-free geometry-aware view selection strategy to select complementary and reliable frames during inference. The resulting representation is decoded into CAD command sequences using a non-autoregressive decoder. We also develop VideoCAD, a large-scale multi-view video benchmark derived from existing CAD data through multi-view re-rendering. Extensive experiments demonstrate the effectiveness of VGGT-CAD for visual CAD reconstruction under different observation configurations.

We give new conditions on allowable powers of a prime $p$ dividing an integer group determinant for the group $\mathbb{Z}_p^n$, and show these conditions are sharp for $n\leq 5$. The values coprime to $p$ for these groups are already known; determining which multiples of allowable powers of $p$ occur is much more complicated. We show that all multiples of sufficiently large powers of $p$ occur as integer group determinants of $\mathbb{Z}_p^n$. We also provide a complete characterization for the group $\mathbb{Z}_3^3$, where particular arithmetic conditions are required for multiples of certain powers of $3$.