Papers

Language model APIs can expose token-specific biases while withholding logits and token probabilities. Existing bias-based extraction recovers relative logits, leaving a common additive component undetermined in ideal arithmetic. We identify a numerical side channel in floating-point bias addition that exposes information about this component through token identities alone. The channel distinguishes score vectors with identical complete unperturbed log probabilities. Our method exploits changes in representable spacing at binary exponent boundaries. Under the stated binary32 arithmetic assumptions and a known reachable score interval, it recovers a logit pair and its unknown tie-breaking priority exactly in at most 52 token queries. Given complete relative logits, one recovered anchor determines the original logit vector. We evaluate recovery across 11 public checkpoints from seven model families and extend the local method with adaptive interval search and anchor selection. In end-to-end experiments with vLLM, SGLang, and llama.cpp, adaptive recovery succeeds on all 128 Qwen3-0.6B inputs per system, including 64 held-out inputs. A separate token-only experiment extracts a pretrained small model's complete output-head representation up to an invertible hidden-basis transformation. We also establish a sufficient condition for suppressing common-shift disclosure by subtracting the maximum before bias addition. In controlled experiments, this mitigation eliminates all observed distinctions between common-shift variants and preserves token decisions under the tested random biases.

Selecting weights and projection directions from the observations used for testing can invalidate a reference distribution. We develop a framework for exact conditional inference under rotation symmetry. A maximal invariant permits adaptation while leaving a uniform common phase for calibration. This yields explicit Cauchy references for invariantly selected weights and projections. Under separate block rotations, the same principle gives exact normal-score combinations with coefficients selected from all blockwise invariants. The calibration results require neither densities nor moments. To illustrate the framework, we study direction learning and power in spherical Gaussian location models, identifying a regime in which consistent detection is possible without consistent direction recovery. For heterogeneous functional data, a matched mean–residual construction produces the required null symmetry under a conditional Gaussian model. Simulations compare Radius and Blend, two representative procedures, with sample splitting, and an electrocardiogram analysis illustrates their application.

We study the nonequilibrium dynamics of a bosonic Mott insulator following a sudden quench from a periodic to a quasiperiodic lattice. Using ab initio multiconfigurational (MCTDHB) continuum many-body dynamics, we characterize the evolution through momentum distributions, fragmenta- tion, correlation functions, and information entropy. We find that melting of Mott correlations does not necessarily imply relaxation of the many-body state. In the weakly interacting regime, the initial Mott-like correlation undergo recurrent melting and partial recovery, while the information entropy displays large, intermittent fluctuations within the simulated time window. In contrast, a strongly interacting and fully fragmented Mott insulator retains its characteristic Mott correla- tions, up to partial distortions, while the many-body information entropy approaches a well-defined stationary regime plateau with comparatively small fluctuations. These results indicate that Mott- correlation dynamics and many-body relaxation can be dissociated in this finite system and support the use of information entropy, evaluated in the multiconfigurational representation, as a sensitive complementary diagnostic of nonequilibrium relaxation.

We present new algorithms for approximate shortest path computation in weighted undirected graphs within the Massively Parallel Computation (MPC) model. Specifically, we construct an $a$-approximate Single-Source Shortest Path (SSSP) oracle: Given a query consisting of a source vertex $u \in V$, the oracle returns $a$-approximate distances $\delta(u,v)$ for all $v \in V$. Fix an $n$-vertex weighted undirected graph. We consider two regimes of the MPC model: the near-linear regime, where each machine has $\tilde{\Theta}(n)$ memory, and the heterogeneous regime, where all machines have $\Theta(n^\gamma)$ memory for some constant $\gamma\in (0,1]$, except for a single machine with $\tilde{\Theta}(n)$ memory. We develop randomised algorithms that construct $O(1)$-approximate SSSP oracles in $O(\log\log n)$ rounds in the near-linear regime and in $O(\log^2\log n)$ rounds in the heterogeneous regime. These oracles answer distance queries in $O(1)$ rounds. Our results improve upon the recent work of Dory and Matar (SPAA 2024) which, for the same total memory, requires $\left(\log\log n\right)^{2+O(1/\gamma)}$ rounds and applies only to unweighted graphs in the heterogeneous setting. We say that $\tilde N_k(u)$ is the approximate $k$-nearest neighbourhood of a vertex $u$ if there exists an approximate distance estimate $\delta$ such that $\tilde N_k(u)$ consists of the $k$ vertices closest to $u$ according to $\delta$, breaking ties by vertex ID. The main technical ingredient is a new method for efficiently computing approximate $n^{O(\gamma)}$-nearest neighbourhoods in the heterogeneous MPC model in $O(\log^2\log n)$ rounds.

Over the past decade, femtoscopic measurements using Lévy-stable source functions have been carried out in collision systems ranging from small to large at SPS, RHIC, and LHC energies. In recent years, these have been accompanied by a number of phenomenological studies of the same systems and energies. We contribute to this line of work by investigating the shape of two-pion pair-source distributions in central $^7$Be+$^9$Be and $^{129}$Xe+$^{139}$La collisions simulated with the UrQMD model in cascade mode. To make the comparison with measurements meaningful, kinematic selections similar to the experimental ones are applied to the simulated events and particles. One-dimensional Lévy fits are performed, and the resulting source parameters are studied as functions of pair transverse mass, collision energy, and system size. We find that the simulated sources are well described by Lévy distributions in all systems considered, which offers a common phenomenological picture of the space-time structure of pion emission. Finally, we compare our findings with results from an intermediate system, Ar+Sc. The results serve as a purely hadronic reference for past and upcoming femtoscopic measurements of the NA61/SHINE experiment.

Submodular maximization arises in a wide range of combinatorial optimization problems and has been extensively studied from the perspective of approximation algorithms. For maximizing nonnegative, non-monotone submodular functions subject to a matroid constraint, randomized algorithms achieve a $0.401$-approximation, whereas obtaining comparable deterministic guarantees remains challenging. In this paper, we present a deterministic $0.401$-approximation algorithm in the exact value and independence oracle model, improving upon the previous deterministic guarantee of $(0.385-\varepsilon)$ \cite{ChenGLSZ2026}. Our algorithm builds on the extended multilinear extension and provides a deterministic implementation of the recursive guided framework underlying the randomized $0.401$-approximation algorithm. The main technical ingredient is a direction oracle supported on at most two partitioned matroid bases. This oracle simultaneously satisfies the growth condition required by the extended-multilinear update and an approximate stationarity condition needed to construct the recursive guides. The resulting finite-support representation enables exact evaluation of the relevant expectations and marginal values without random sampling. The algorithm uses polynomially many value- and independence-oracle queries.

Generating and editing presentation slides requires models to combine accurate text rendering, instruction following, visual grounding, aesthetic design, and precise editing within one canvas. Existing work covers only subsets of these capabilities and lacks large-scale slide-native supervision and diagnostic evaluation. We formulate four slide-centric tasks and build a scalable data engine with over 13M continual-pretraining records and 1.9M supervised fine-tuning records. We also introduce VisSlideBench, a benchmark of 1,527 manually screened instances that covers all four tasks with task-specific, multidimensional evaluation. Its automatic rankings agree with blinded, dimension-wise human rankings. Using these resources, we train InfoVis, a unified 9B slide generation and editing model. On VisSlideBench, InfoVis leads every evaluated open-source model on all eleven metrics and scores 7.94 overall against 7.99 for Nano-Banana-2. Starting from FLUX.2-klein-base-9B, slide-specific post-training adds 1.6 points overall, with the largest generation gains in content faithfulness; the remaining gap to proprietary models is smallest in content faithfulness and largest in aesthetic quality. Built on InfoVis, our document-to-slide workflow achieves the second-highest Aesthetics score on the external SlidesGen-Bench. We will release the model, code, data, and benchmark.

This note proves that the Kuznetsov component of a quartic double solid or a special Gushel-Mukai threefold does not have non-trivial admissible subcategories.

Industrial manipulation in flexible manufacturing, e.g., high-mix, low-volume (HMLV) electronics assembly, requires robot policies to adapt to changing products and production conditions. Such settings impose industrial process constraints, including product variants, moving material flows, finite execution windows, and tight geometric tolerances. However, existing evaluation frameworks do not systematically capture these constraints when assessing generalist robot policies. To address this gap, we introduce LIBERO-Industry, a novel benchmark built on the widely used robot learning benchmark LIBERO, that translates the aforementioned industrial constraints into controllable task conditions and measurable success criteria. Specifically, LIBERO-Industry comprises three classic task scenarios: Static-to-Dynamic (S2D) loading, Dynamic-to-Static (D2S) unloading, and Dynamic-to-Dynamic (D2D) transfer. The suites contain 216 tasks in total that systematically vary object geometry, conveyor speed, interaction-window duration, and geometric acceptance region size. Extensive experiments across five generalist robot policies (including vision-language-action models and world-action models) show that performance progressively degrades as industrial constraints are introduced and combined. Under a shared fine-tuning and evaluation protocol, the LIBERO-Industry co-training condition achieved higher observed target-transfer completion than the original-LIBERO condition.

Parallel token proposals need a joint law, not merely accurate token marginals. We construct coordinate-Bethe-ansatz laws from the periodic XXZ chain and compare them with their maximum-entropy pairwise projections at identical one- and two-site moments. In an eight-site, three-excitation sector, symmetry makes the full probability-law difference one-dimensional, determined by a contiguous three-site moment $\delta$. Along the Bethe branch, this gap changes sign and vanishes exactly at $\Delta=(3+\sqrt3)/2$, where the eigenstate law becomes pairwise. A nonlinear two-token readout preserves separate token marginals yet exposes a distance $2|\delta|$; a direct three-token readout preserves all one- and two-token marginals yet exposes $4|\delta|$. At $\Delta=1.5$ these deterministic binary distances are $0.02654573$ and $0.05309145$. We give an exact target-alignment formula and prove a strict speculative accepted-prefix advantage throughout an unrestricted open neighborhood of a constructed target. These are finite-law existence results, not measured language-model or wall-clock gains.

Generative models offer a powerful route to scientific simulation and discovery by enabling the study of complex populations and rare phenomena. Flow matching can generate realistic samples, yet inaccurate occurrence frequencies can distort population statistics and compromise inferences about rare events. Here we developed generalized mass-preserving coupled flow matching (G-MPCF), which matches the probability masses of Gaussian source regions to those of weighted data regions. This construction encodes the desired regional frequencies in the correspondence between noise and observations, shaping the learned dynamics while preserving the prescribed target distribution. On a rare-mode benchmark, G-MPCF reduces relative score error by 95.0% and numerical integration error by 89.9% compared with independent flow matching. On CIFAR-10 with a 100:1 class-probability ratio, it reduces corrected class-mass error by 44.6% compared with minibatch optimal transport, while improving mean image fidelity with matched computational budgets. We envision that incorporating regional probability calibration into generative modelling will support more reliable scientific simulation and inference, enabling the study of systems in which rare events and their occurrence frequencies are central to understanding the underlying mechanisms.

We study several function-theoretic aspects of the domains $G_{E(3;3;1,1,1)}$ and $G_{E(3;2;1,2)}$. We introduce and investigate the notions of $\Gamma_{E(3;3;1,1,1)}$-inner functions and $\Gamma_{E(3;2;1,2)}$-inner functions, and establish their relationships with $\Gamma_{E(2;2;1,1)}$-inner functions and $\Gamma_{E(2;1;2)}$-inner functions. We provide explicit constructions and representations of rational $\Gamma_{E(3;3;1,1,1)}$-inner functions and rational $\Gamma_{E(3;2;1,2)}$-inner functions. As an application of these results, we obtain partial solutions to the associated interpolation problems and construct explicit rational inner interpolants for interpolation data lying in suitable subsets of $G_{E(3;3;1,1,1)}$ and $G_{E(3;2;1,2)}$, respectively.

Cloud graphical user interface (GUI) agents send instructions and screenshots to remote planners, exposing personally identifiable information (PII). Existing placeholder defenses mask detected spans and reuse exact strings. Fragmented or changed forms can expose PII or break entity continuity across turns. PrivacyGuard addresses this private reference problem with source-linked sanitization (SAN) and a structured reference lifecycle (REF). SAN reconstructs fragmented or overlapping evidence and rewrites the complete source extent. REF links changed appearances to session entities and supports locally resolvable references without returning raw values to the upload path. In five-turn sessions scored against common gold, PrivacyGuard reduces audited source-value leakage by 33.55%–82.60% relative to the closest prior full-pipeline system in all four reader–language combinations. REF raises strict cross-form continuity from 0.04 under exact-value reuse to 0.81. In reference-required Android tasks, verified completion rises from 8/30 and 7/30 to 17/30 and 20/30. On AndroidLab, PrivacyGuard achieves the highest or tied-highest task-success point estimate among protection pipelines for all four planners. On PrivScreen, it reduces fixed-reader field exposure by 62.72%–62.84% relative to the same baseline. PrivacyGuard lowers upload exposure while preserving a locally resolvable task path.

Transmission switching is an effective approach for restoring operational flexibility and improving the economic performance of AC/multi-terminal DC (MTDC) grids following DC-side faults. Its practical implementation requires that the faulted branch be safely isolated and that the associated switching commands be successfully delivered through the communication network. However, conventional transmission switching models generally represent switching actions using binary variables, without considering the availability of communication resources or whether the corresponding DC circuit breakers (DCCBs) can interrupt the fault current affected by time delay. To address these issues, this paper develops an explicit optimal info–power flow (OIPF) formulation that incorporates information transmission into the post-fault transmission-switching optimization for AC/MTDC grids. The switching status of each DC branch is determined by the availability of its communication path and associated communication resources. In addition, binary switching decisions are supplemented by a DCCB feasibility constraint that limits the estimated delayed-interruption current to the DCCB breaking capability. The resulting problem is formulated as a mixed-integer second-order cone programming (MISOCP) model that can be efficiently solved using off-the-shelf optimization solvers. Numerical results reveal that limited communication capacity and additional routing costs may render electrically beneficial switching actions infeasible or uneconomical, while delay-aware DCCB interruption constraints may favor lower-delay communication routes despite their higher costs.

Game-Creation-Agents (GCA) turns a natural-language request into a runnable Phaser 4 browser game. The pipeline first builds a multimodal game design document that couples mechanics and scene contracts to grounded visual references. It then projects that document into a runtime scaffold, machine-readable contracts, and deterministic tests. Eight specialized agents next carry out production: scenes are implemented serially, assets are produced in parallel, and one reduced manifest joins the two branches into a single build. Build-linked real-UI checks and a code-blind critic then verify that build and decide whether the game may ship. Each blocker returns to the agent that owns the affected artifact for a bounded repair, and the game is released once all the gates pass. We evaluate finished games separately, through their rendered interfaces alone, over prompt-matched tasks run under a common protocol. GCA achieves stronger requirement satisfaction, core mechanics, content depth, and functional visuals than a comparable open pipeline. In a side-by-side human study, raters also score GCA's games higher on every dimension and prefer them overall.

We show that every proper variety of distributive $\ell$-pregroups is periodic; as a result, the subvariety lattice of the variety of distributive $\ell$-pregroups decomposes into a disjoint union of bounded intervals each consisting of all properly $n$-periodic varieties, for different $n \in \mathbb{Z}^+$. On the way, we study non-periodic (one-generated) subalgebras of $\mathbf{F}(\mathbb{Z})$ and show that they either contain a non-periodic idempotent or they contain idempotents of arbitrary big periodicity. The same results holds for non-periodic one-generated subalgebras of $\mathbf{F}(\mathbf{J} \overrightarrow{\times} \mathbb{Z})$, where $\mathbf{J}$ is a chain, generated by a composite element and the resulting idempotents can be taken to be local in the associated wreath product.

We investigate quantum criticality in the transverse-field Ising model on finite Cayley trees and demonstrate that their extensive boundary fundamentally changes the nature of the quantum phase transition compared with the infinite, boundary-free Bethe lattice. Using tree tensor-network simulations for systems with up to $N=12286$ sites, we identify a boundary-driven continuous transition at $h_x^c\approx1.76$, distinct from the mean-field Bethe-lattice transition at $h_x^c\approx2.23$. We characterize this transition through finite-size scaling of the magnetization and magnetic susceptibility and extract a consistent set of critical exponents. By introducing next-nearest-neighbor interactions, we demonstrate the robustness of the extracted critical exponents, providing numerical argument for the Ising boundary universality class on the Cayley tree. Furthermore, we show that the physics of the boundary-free Bethe lattice can be efficiently recovered on a finite Cayley tree by fine-tuning a local boundary field. The resulting effective Bethe line, whose existence is tied to the mean-field nature of the bulk transition, effectively screens the extensive boundary and restores both the critical point and the mean-field critical scaling of the infinite Bethe lattice.

Since Brill's work of 1959, the conformal factor of finite-amplitude Brill waves, the axisymmetric and time-symmetric vacuum initial data on $\mathbb{R}^3$ that describe pure gravitational radiation, has been obtained only numerically, up to the most recent studies. Here an explicit one-parameter family of such data is constructed: the first explicit real-analytic, non-trivial, asymptotically flat vacuum initial data with trivial topology and a single end. The free metric function is a closed-form combination of elementary functions and a dilogarithm. The data have the toroidal conformal symmetry of Beig and Husa, and a change of variable of Natanzon type reduces every mode equation to the Gauss hypergeometric equation, so that the conformal factor is a series with explicit Gamma-function coefficients. The quantities that have so far required numerical work are thereby obtained exactly. A ground-state identity gives a sharp existence criterion: complete, asymptotically flat data exist precisely for $k<k_c=0.8048016772\ldots$, and the explicit series is identified with the unique variational solution. The ADM mass is an absolutely convergent digamma series, with $m/a=\pi k^2/10+O(k^3)$ for small amplitudes and an explicit residue at its critical divergence. Sufficiently strong waves contain trapped surfaces: it is proved that for $k$ close to $k_c$ the rescaled conformal factor converges to an explicit function and explicit tori and spheres become outer trapped, so that the data contain an apparent horizon. A numerical search, restricted to equatorially symmetric star-shaped surfaces, finds marginally trapped (minimal) spheres, which appear in a fold near $k=0.7670$. No thin-torus or weak-field approximation is used.

Magnetic activity is a result of the interaction between rotation and dynamo processes in cool stars with outer convection zones. Since open cluster members share a common age, distance, and chemical composition, they provide an opportunity to study the magnetic activity of cool stars in a controlled astrophysical context. We used 120s cadence observations from the Transiting Exoplanet Survey Satellite (TESS) to study the flare activity of stars in three open clusters with different ages: the Pleiades (100 Myr), the Hyades (700 Myr) and Praesepe (700 Myr). We used the Ohio State Multi-Object Spectrograph (OSMOS) at MDM Observatory with the goal of identifying coronal mass ejections (CMEs) in the Pleiades and Praesepe. We investigated the flaring characteristics of the cluster members using the TESS light curves: we identified the flares, then divided the dataset into different categories based on the effective temperature and light curve amplitude. We calculated the flare energies and investigated the flare frequency distributions. We studied the dynamic spectra of the H$\alpha$ line and its environment to search for indication of CMEs. The power-law indices of the flare frequency distributions obtained in our analysis span the 1.8-2.8 range. We found the highest flare rates in the Pleiades for all investigated spectral types. Our results show that the flare rate of M dwarfs is similar in the Pleiades and the Hyades while for K-type stars the flare rate in the Pleiades is an order of magnitude higher. Our analysis reveals that the flare rate in M stars changes with their effective temperature: the rate is highest for T$_{eff}$ $\sim$3200-3300 K -coinciding with the transition between partially and fully convective stars - with smooth decrease in flare rate towards cooler and hotter M dwarfs. We used the MDM/OSMOS spectra to place an upper limit on the CME rate.

We characterize the oracle complexity of finding first-order stationary points in smooth nonconvex–strongly-concave (NC–SC) minimax optimization when each query provides the full Hessian in addition to the function value and gradient. For $\Phi(x)=\max_y f(x,y)$, assume that $f$ has an $L$-Lipschitz gradient, a $\rho$-Lipschitz Hessian, and is $\mu$-strongly concave in $y$. Let $\kappa=L/\mu$, let $\Delta$ denote the initial value gap, and define $r=\rho\kappa^{3/2}\varepsilon/L^2$. We establish matching deterministic upper bounds and randomized lower bounds, up to logarithmic factors and additive initialization costs. When the leading term dominates initialization, the resulting minimax complexity is \[ \widetilde{\Theta}\!\left( \frac{\Delta L}{\varepsilon^2}\Psi_\kappa(r) \right), \qquad \Psi_\kappa(r)= \begin{cases} r^{1/2}, & 0<r\le 1,\\ r^{2/7}, & 1<r<\kappa^{7/4},\\ \sqrt{\kappa}, & r\ge\kappa^{7/4}. \end{cases} \] Despite the stronger oracle, the optimal complexity exhibits a nontrivial dependence on accuracy, conditioning, and Hessian smoothness. In particular, these regimes exhibit accuracy dependencies $\varepsilon^{-3/2}$, $\varepsilon^{-12/7}$, and $\varepsilon^{-2}$, respectively. The upper bounds combine second-order regularity estimates for a saddle Moreau envelope with certified accelerated reduced-dual solves and amortized warm starts. The lower bounds combine an all-derivative lift with a serial composition of private-handle constructions, using hard instances chosen independently of the algorithm's realized random seed. The resulting characterization quantifies improvements over the classical first-order benchmark under gradient smoothness alone and identifies the regime in which that benchmark is recovered.

Digital Twin (DT) combined with reinforcement learning (RL) can support adaptive resource allocation and security-aware decision-making by comparing expected and observed network behavior. This paper presents a simulation-based DT reference and a belief-guided Q-learning (BGQL) for joint jammer identification and beam-power control in a site-specific 28-GHz network. For each action, the same channel simulator is evaluated under an attack-free and an attacked configuration. Receiver-level residuals are combined with spatial jamming footprints and accumulated to form a normalized suspicion vector. BGQL incorporates this vector into an aggregated state, a belief-concentration reward, and exploratory beam-selection rule. The BGQL scheme is compared with SARSA, Greedy, and Random under matched attacker sets. Across 30 paired Monte Carlo runs in four configurations, with the number of active jammers supplied to every method, BGQL achieves mean aggregate full-band link-rate scores of approximately 437.4–564.2~Mbit/s and rate-to-device-power scores of 60.37–76.79~Mbit/J. Its detection accuracy is 100% in one-jammer configurations and approximately 78%–81% in two-jammer configurations. BGQL requires approximately 80–130~s per run, compared with 5–14~s for SARSA, reflecting evaluation of 625 beam pairs during exploratory steps. These findings provide a matched-model simulation proof of concept for DT-referenced belief-guided learning for security-aware beam-power control in 6G networks.

Geospatial reasoning links VLMs to real-world action and decision making. Reliable reasoning requires accurate spatial information and effective spatial representations. However, current VLMs obtain this information mainly from language and vision. At larger geographic scales, limited visual observations make it difficult to establish accurate spatial references and recover precise spatial relations. This leads to a bottleneck for VLM spatial perception and reasoning. This paper proposes that geospatial vector geometry can become a native spatial modality within a VLM and introduces GeoVec-VLM. First, we develop a structured geometry representation that preserves the spatial structure and arrangement of vector objects, building an explicit spatial basis. Second, we introduce a geometry interaction strategy that brings this basis into multimodal computation, where it interacts with visual content and language references according to the queried spatial relations. Together, these designs allow perception and reasoning to operate on shared geometric references. Across five spatial reasoning tasks, GeoVec-VLM improves mean accuracy by about 11% relative to the strongest baseline, maintains its gains under geographic transfer, and shows greater geometric consistency. Our results show that geospatial vector geometry offers a promising internal spatial basis for VLM spatial reasoning. https://github.com/TXFR/GeoVector-VLM

The rapid growth of Artificial Intelligence (AI) data centers is introducing dynamic loads into power transmission systems as GPU clusters switch between computational phases with distinct power demands. These dynamics are naturally modeled by switched affine differential-algebraic equations (DAEs), where each mode induces a different equilibrium and consistency space. We study their stability using control and hybrid systems tools. Differential projectors derived from the quasi-Weierstrass form yield an equivalent hybrid representation, from which we characterize the $\omega$-limit set and establish Lyapunov conditions for practical stability with an explicit $\mathcal{KL}$ bound accounting for switching-induced resets. For stochastic inference workloads, we use Foster–Lyapunov techniques to establish probabilistic uniform global recurrence under mode-dependent dwell times and transition probabilities. The framework is validated on the IEEE 39-bus transmission network with co-located AI data centers using high-fidelity electromagnetic transient simulations of deterministic training and stochastic inference workloads.

Let $M$ be a connected Hamiltonian stationary Lagrangian surface of constant Gaussian curvature $K$ in a two-dimensional complex space form $\Mtilde^2(4\epsilon)$ of constant holomorphic sectional curvature $4\epsilon$, and let $H$ denote its mean curvature vector field. We prove that either $K=\epsilon$ or $K=0\ne\epsilon$ and $|H|$ is constant. In particular, if $|H|$ is non-constant, then $K=\epsilon$.

Controlling ferroelectric phase symmetry through strain engineering is crucial for tailoring polarization topology and functional properties in oxide-based devices. Here, we show that a thin conductive buffer layer can override substrate-induced strain in BaTiO$_3$ (BTO) films on MgO. Although the lattice parameter of MgO(001) would be expected to induce tensile misfit strain, in 500~nm BaTiO$_3$ films the thermal-expansion mismatch dominates, resulting in effective compressive stress upon cooling. Inserting a 50-nm La$_{0.67}$Sr$_{0.33}$MnO$_3$ (LSMO) buffer layer reverses the effective strain state from compressive to tensile. Using temperature-dependent polarized Raman spectroscopy, X-ray diffraction, and piezoresponse force microscopy, we reveal an unconventional phase sequence upon cooling: paraelectric $\rightarrow$ orthorhombic ($\textit{aa}$-phase, $\sim$407 K) $\rightarrow$ monoclinic ($\textit{r}$-phase, $\sim$300-345 K), characterized in-plane and tilted polarization components. The LSMO layer not only serves as a bottom electrode but also modifies the strain state, while interfacial charge redistribution induces a built-in electric field, evidenced by self-polarization and asymmetric PFM hysteresis. These findings highlight the critical role of conductive buffer layers in controlling ferroelectric symmetry and enabling oxide heterostructures with tailored polarization textures for low-power spintronics, tunable microwave devices, and neuromorphic computing.

We propose a subgradient-based block coordinate descent (BCD-SubG) framework for nonconvex optimization over products of probability simplices and a closed feasible set, motivated by semi-nonnegative independent component analysis (Semi-NNICA). Elementary column transformations are used to preserve simplex feasibility, while first-order information guides block and pair selection. We establish the global convergence of BCD-SubG using a constrained Lojasiewicz inequality; additional eventual-interiority conditions yield stationary limits and convergence rates. We then specialize BCD-SubG to the direct-fit and indirect-fit Semi-NNICA models and derive explicit updates that ensure global convergence without further assumptions. For both models, eventual interiority also yields stationary limits and convergence-rate estimates. Experiments on synthetic mixtures and simulated magnetic resonance spectroscopy data show generally lower recovery errors and shorter wall-clock times than the tested Semi-NNICA baselines. Joint diagonalization experiments further demonstrate lower final objective values.

In this short note, we prove that any closed interval in a well-ordered and discrete space is finite. The coincidence between finiteness and boundedness can then be established for transition systems where the state space is well-ordered and discrete. Finally, this result is also proven when the state space is a Cartesian product of $d$ discrete and well-ordered sets.

Relational learning typically predicts from a database state, but decision making asks a different question: how will that state change under an action? In operational systems, the answer depends on system-specific dynamics that may not be visible in the database itself. We view each such system as a relational "world" and ask whether a model can infer how it behaves from observed executions. We introduce TabWM (Tabular World Model) and WorldRel, a generator of executable relational worlds for pretraining. Given executions from an unseen world, TabWM uses them as context to predict the sparse structured edits caused by a new action without parameter updates. Across 512 held-out worlds, complete-edit F1 rises from 0.016 with no observed executions to 0.685 with 64, where a correct edit must match its operation, relational location, and value. Because these predictions are explicit relational edits, they can be applied recursively to imagine candidate futures and compare actions before they are taken. Broader search over these predicted futures improves the realized return of selected action sequences. Together, these results suggest that relational dynamics can be learned in context, broadening relational learning from modeling system state to modeling how that state changes under action.

Keypoint detection plays a central role in geometric vision pipelines. Existing detectors exhibit complementary strengths across different scene structures and keypoint budgets, and reliance on a single detector often results in suboptimal keypoint distributions. Motivated by this observation, we propose Mixture of Detectors (MoD) for dense matching pipelines, a unified framework for complementary keypoint detection through the adaptive composition of heterogeneous detectors. MoD first distills heterogeneous detectors into a unified model, allowing diverse detection maps to be predicted efficiently within a single forward pass. Detector selection is subsequently formulated as a patch-wise, budget-conditioned decision process, in which a lightweight router assigns the most suitable detector to each local region. To avoid heuristic supervision, the router is trained with task-driven rewards derived from downstream matching quality, jointly capturing both keypoint quantity and precision. Extensive experiments on MegaDepth, ScanNet, and HPatches demonstrate that MoD consistently outperforms strong baselines across a wide range of keypoint budgets, demonstrating its effectiveness in improving keypoint distribution and downstream geometric performance.

LLM-based information systems need safety guardrails. Most guardrails classify the prompt alone. If the prompt looks harmful, the system rejects it before any answer is generated. This is costly. Many rejected prompts would have received a safe response. Users lose help they should have received from the information system. This cost grows as conversational and generative search becomes common. Prompt-level labels treat harm as a property of the query. But harm depends on what the model actually writes. Existing input-output guards do look at responses. But they judge a finished response, so the decision comes after full generation. However, we observe that safety of model interaction with the input prompt can be inferred early with only partial output. So the system can start generating, watch the partial response, and stop only if it turns harmful. We test this idea in three steps. First, we build a dataset of 41,944 prompt-response pairs with seven open weights LLMs from three families: Llama, Gemma, and Qwen. Second, we show that prompt harmfulness and interaction safety differ. Prompt labels and response labels agree on only 50.46% of items (Cohen's $\kappa$ = 0.06). Of the prompts that make any model respond harmfully, only 3.5% do so for all seven LLMs. Third, we show that partial responses carry most of the signal. Fine-tuned classifiers predict response-level harm well (best AUPRC 0.885, F1 0.807). About one third of the response tokens recover almost full-response AUPRC.