Papers

We give a short proof of the following theorem of K. Ball: If a centrally symmetric convex body $K\subset \mathbb R^d$ is covered by finitely many planks, then the sum of their relative widths with respect to $K$ is at least $1$.

In this paper, we study the conditions under which covert communication at positive rates is feasible over discrete memoryless classical, classical-quantum, and quantum channels. For classical point-to-point channels, we show that if the dimension of the channel input probability simplex exceeds that of the channel output probability simplex, equivalently, if the input alphabet has larger cardinality than the output alphabet, then positive covert rates are achievable for certain classes of Discrete Memoryless Channels (DMCs). We further show that allowing the innocent symbol (i.e., the symbol transmitted in the no-communication mode) to be chosen appropriately can enlarge the class of DMCs for which positive covert rates are achievable. We also study covert communication over classical Multiple-Access Channels (MACs), where the additional transmitter effectively enlarges the set of available channel input pairs, and we show that the conditions required to satisfy the covertness constraint are less restrictive for MACs than for point-to-point channels. We extend these results to classical-quantum DMCs by showing that if the dimension of the input probability simplex exceeds the affine dimension of the set of output states that can be induced at the channel output, then positive covert rates are achievable for certain classes of classical-quantum DMCs. Finally, for quantum channels, we show that if the innocent state (i.e., the state transmitted in the no-communication mode) is mixed, then the covertness constraint can always be satisfied by a non-trivial input ensemble. Consequently, positive covert rates are achievable whenever the legitimate receiver can distinguish at least two states in a suitable such ensemble.

Can coding agents restore software that no longer runs while preserving its underlying methods, and reconstruct industrial software engines from open specifications? Here we introduce ReviveBench, a benchmark with two task families evaluated by hidden verifiers calibrated against native execution environments, established engineering tools, or purpose-built reference implementations. The revival family comprises ten tasks involving dependency incompatibilities, deleted core modules, legacy builds, and a GPU-based foundation model. Every starting workspace fails verification, and the strongest evaluated model passes all ten tasks in at least one run each. In contamination-control experiments, identifier obfuscation reduces line similarity to the original implementations from 0.51–0.96 to 0.03–0.44 without reducing the observed pass rate of any evaluated model. On repositories created after the stated knowledge cutoffs, the strongest model passes eight of nine runs. The reconstruction family comprises thirteen tasks spanning numerical, geometric, hardware, and transactional systems (e.g. CAD and CRM). Two models meet the benchmark's pass criteria on all thirteen, although our audit shows that the CFD task cannot establish numerical-solver capability. Benchmark construction and auditing uncover 28 verifier defects, including 24 false negatives and two false positives. These findings show that executable verification can itself introduce substantial measurement error. We present three practical checks: test whether prescribed methods can reach the grading thresholds, investigate agreement among independently generated candidates, and recompute diagnostics from submitted artifacts. ReviveBench thus provides both an evaluation of software revival and engine reconstruction, and cases in validating the verifiers used to measure coding agents for software design.

Panchromatic stellar spectral energy distributions (SEDs) provide the wavelength-dependent irradiation fields required for studies of exoplanet atmospheres, photochemistry, atmospheric escape, and habitability. We present PHAROS, the Panchromatic Habitable-world Archive of Radiation from Observed Solar-like stars, a first release of fifteen component-traceable SEDs for nearby FGK stars spanning adopted ages of 0.26–6.5\,Gyr. The catalogue covers 0.5–5000\,nm and combines archival XMM-Newton and Chandra high-energy constraints, semiempirical extreme-ultraviolet (EUV) reconstructions, HST and IUE ultraviolet spectra, Gaia DR3 XP and ancillary optical spectrophotometry, and PHOENIX photospheric extensions. When X-ray data support spectral modelling, target-specific coronal plasma models define the high-energy segment and anchor the EUV normalisation; otherwise, empirical high-energy templates are scaled to literature luminosity constraints. Each SED preserves segment-level provenance, distinguishing directly observed intervals from reconstructed components, empirical templates, bridges, and model-derived extensions. The largest diversity occurs at X-ray, EUV, and ultraviolet wavelengths. Younger age-context groups generally show stronger high-energy output relative to their photospheric continua, although the dispersion within each group shows that age alone does not uniquely determine the irradiation environment. PHAROS provides traceable panchromatic irradiation fields for studies of planetary atmospheres, photochemistry, atmospheric escape, forward modelling, retrievals, and interpretation of future direct-imaging observations, including those anticipated for NASA's Habitable Worlds Observatory.

Large language models can reason in continuous space instead of decoded text, by recurring on their own hidden states or by passing those states between agents, while training supervises only the Cross-Entropy (CE) of the final decoded answer and does not constrain the thought. Theoretical and empirical analyses establish and confirm four failures of CE-only training that lead to a lower probability of the correct answer such as collapsing thoughts across distinct questions and retaining irrelevant information. We introduce REST (REpresentation-Supervised Thoughts), a training objective that turns four properties of a valid thought representation (causality, minimality, separability, and stability) into differentiable losses added to CE. We instantiate it in latent single-agent and multi-agent systems, without architectural changes or added parameters at inference. Across 7 benchmarks spanning mathematics, science, medicine, and code generation, with the same training data, compute, and latent budget, REST increases accuracy over CE-only training across agent settings and model sizes by up to 7.5 percentage points and convergence on a final answer by 30%. Furthermore, REST thoughts encode more of what is required to achieve the correct answer, and decoding them better recovers the intended output of the agent, which makes latent communication easier to interpret. Project Website: https://fard-lab.github.io/REST

In this paper, we revisit the concept of entropy in the spatial context with the aim of deriving computable and interpretable metrics for point pattern analysis in domains such as histopathology. We discuss stochastic point process assumptions like Poisson homogeneity and Simple Sequential Inhibition (SSI) and review established results for Voronoi and Delaunay tilings of point sets for their potential to provide null distributions for rigorous empirical hypothesis testing. We present (1) a novel "dense basin entropy" defined in terms of the Ord distribution supported on Voronoi basins, which is shown to be sensitive to clustering, and (2) a related Markov chain designed as a simplification or approximation of Brownian motion in the underlying planar domain. We investigate bounds on the dense basin entropy in the SSI regime and in empirical data, and show that the entropy rate and spectral gap of the Markov chain lead to sharp discrimination metrics. Finally, we demonstrate a generalization to multiple-set analysis via aggregation of one set over the Markov invariant measure for another. Simulations and experiments in histopathology show that our proposed metrics offer insights complementary to other instantiations of entropy in spatial analysis. The code can be found on our SMProfiler GitHub: https://github.com/nadeemlab/SMProfiler.

Most federated learning frameworks for vehicular ad hoc networks assume that all vehicles collaboratively train a single model for a common task. This assumption limits their applicability to practical vehicular environments, where vehicles may perform heterogeneous but related perception tasks with different output spaces. This paper proposes encoder-sharing hierarchical multi-task federated learning (EN-HMTFL), which integrates cluster-based hierarchical federated learning with a globally shared encoder and vehicle-local decoders. EN-HMTFL enables vehicles performing different tasks to collaboratively learn a transferable feature representation while preserving their task-specific models locally. Only the encoder is exchanged and aggregated through the hierarchy, whereas raw data and local decoder parameters remain at the vehicles. The proposed framework is evaluated on the MNIST and GTSRB datasets in different vehicular scenarios. Across the evaluated scenarios, EN-HMTFL improves accuracy by up to 24.0% relative to the compared representation-sharing benchmark. In scenarios where EN-HMTFL converges earlier, the reduction reaches up to 69 communication rounds (28.8%).

In vehicular networks under edge computing environments, vehicle-to-vehicle delay-tolerant networking (V-DTN) can disseminate congestion warnings to other vehicles via a store-carry-forward mechanism, helping them proactively choose suitable routes. However, most existing in-vehicle information dissemination methods rely on flooding or limited flooding strategies, broadcasting alerts across the entire network whenever congestion is detected. This leads to excessive redundant copies and consumes node cache space. To address this issue, this paper proposes a congestion-event- aware on-demand message dissemination mechanism. By considering the recurrence and duration of congestion, the mechanism suppresses broadcasts of short-lived, self-dissipating congestion events. Based on real-world PeMS data from California's I-210 corridor, we construct an I-210 Freeway Traffic Congestion Use Case. Experiments show that predicting congestion recurrence heavily relies on historical free-flow speed data of lanes. Without incorporating additional feature dimensions, the accuracy of modeling and comparing lane free-flow speeds across different day types outweighs the choice of machine learning models, and such patterns are difficult to reproduce in simulators. Meanwhile, congestion duration prediction serves effectively as the basis for dynamic-threshold on-demand dissemination in V-DTN, which demonstrate that machine learning-based congestion awareness combined with dynamic-threshold on-demand dissemination significantly reduces network resource consumption and network-layer congestion, enhances delivery reliability, and lowers delivery latency.

Reaching net-zero greenhouse-gas (GHG) emissions requires deep electrification beyond ground transportation, buildings, and conventional industry automation. This article discusses direct electrification pathways for hard-to-abate sectors, which today account for 30% of global GHG emissions and include steel, cement, chemicals, aviation, and shipping. Whereas indirect electrification via hydrogen and synthetic fuels will remain indispensable for some applications, direct use of electricity is generally preferable from an efficiency perspective. We review selected emerging opportunities for power electronics in industrial process electrification, including steelmaking through hydrogen plasma smelting reduction or molten-oxide electrolysis, electrified cement production, high-temperature process heat, plasma-assisted chemistry, and electrochemical synthesis. Across these examples, power converters must interface with highly application-specific loads, ranging from low-voltage high-current electrolysis cells to dynamic plasma reactors and megawatt-scale induction heating systems. In addition, high-power grid interfaces and in-plant energy management/buffering solutions must be clarified. Thus, future electrified industrial processes open new "beyond-tomorrow" research challenges for power electronics in close interdisciplinary collaboration with scientists from neighboring disciplines.

General-purpose models promise sensor-based decisions without training a task-specific classifier, which could reduce the dependence of Human Activity Recognition (HAR) on labeled data. Yet it remains unclear whether such models can directly interpret deterministic descriptions of physical sensor signals well enough to replace or complement trained HAR models. We study this question using Jev, a fixed general-purpose probabilistic decision model, on 1,800 class-balanced accelerometer windows from WISDM, UCI341, and PAMAP2. Jev receives no labeled examples, retrieval context, or HAR-specific parameter updates. We evaluate three deterministic sensor representations and compare 5,400 Jev decisions with a generative baseline and three supervised HAR models. Jev remains far below supervised recognition, with its strongest representation reaching macro-F1 of 0.038, 0.118, and 0.089 across the three datasets, compared with 0.686 to 0.907 for the supervised models. More numerical features do not improve Jev. Instead, they reduce recognition on all three datasets, while augmenting the same numerical evidence with a deterministic semantic rendering partially recovers performance, although the experiment does not isolate semantics from the accompanying serialization and redundancy changes. Jev is fast and inexpensive to query, but its probabilities are not reliably calibrated for recognition. A post-hoc fusion analysis finds a small improvement on WISDM that does not replicate on UCI341 or PAMAP2. These results show that training-free sensor decisions depend not only on the information available in the signal, but also on whether the model can use the representation through which that information is exposed. The sensor-to-model interface should therefore be treated as part of the model evaluation rather than as a neutral preprocessing step.

B2B advertising targets a viewer's professional attributes (employer size and industry, function, seniority) and has obtained them by matching identities across sites. Safari and Firefox block third-party cookies, Google retired the Privacy Sandbox cohort APIs in 2025, and reverse-IP firmographics decay under remote work. We present SIF (Sealed Inference Frame), which infers coarse professional cohorts on the device and emits only a locally differentially private, taxonomy-coded label into the OpenRTB bid stream, with no cross-site identifier. It rests on a property of the web platform we make precise: a navigated cross-origin iframe is the only way third-party code obtains a policy it controls, so inference runs in WebAssembly even where the publisher's CSP forbids it, and a nested worker served with default-src 'none' gives the model no network. Even a malicious model leaks at most about 5 bits per site per week. Labels pass through a memoised k-ary randomised response keyed to the publisher's first-party identifier, which gives $\varepsilon$-local differential privacy, defeats averaging, and links requests no better than the identifier already sent. An org-conditional k-anonymity rule suppresses cells, more strictly on corporate networks than at home. Cohorts ride OpenRTB user.data in a LinkedIn-aligned taxonomy, and attribution uses LinkedIn's click-scoped li_fat_id without bridging identities. We report a crawl of CSP deployment on 7,969 top sites and 431 B2B publishers, Heavy-Ad budgets, closed-form privacy-utility trade-offs, a re-identification simulation, and an assessment of which attributes are predictable at all: company type and size are, seniority largely is not. On-device is a design property, not a consent exemption.

Scratch has 135 million registered users, most of them children, and 164 million shared projects. What they are taught about the speed of a script fits in one sentence: a loop iterates once per frame. Unfortunately, that sentence describes the exception. In the public virtual machine a frame repeats the scripts until something visible asks the screen to redraw, no script is left running, or three quarters of the frame's wall-clock time are spent. Hence a loop that does not draw is paced by whatever else is visible and by the machine. Hide the moving sprite of a two-sprite project, and the other's counting loop runs 77,000 times faster on a laptop. No documentation states the rule. Our key observation is that the redraw gate is one flag for the whole runtime, so a loop's speed can be changed without touching its code: hide the sprite that draws, change the machine's budget, or run the program in a tool with no renderer. ThrottleCheck implements a budgeted semantics (a stated budget of rounds per frame, the redraw gate emulated) on the unmodified virtual machine, runs a project under each knob, and reports a rate-sensitive project with a witness. On 500 popular public games, 59% contain a loop that never draws and never waits. Muting the requests of the sprites that draw changes the state of a played game after ten seconds in 24% of the games that have one; hiding them changes 18%; running the game without a renderer and without the gate changes 61%. Rules that read a position, a score or a clock after a fixed time reverse between pass and fail once the throttle is released, in 17% of Whisker's own example tests and 19% of a tutorial's checks on 224 of its remixes. A grader without a renderer grades a program the editor never runs, unless it emulates the gate and states a budget; we say what graders and the platform should do, and close with the sentence a child could be taught.

Humanoids now walk, balance and reach with remarkable generality: one whole-body tracking policy follows references from a human, or from an end-to-end policy. That generality travels in the trajectory, and a trajectory alone carries limited information about the interaction it should produce: at contact, the executing controller determines how the robot behaves. Single-task policies usually reach hard interactions by optimising trajectory and controller together in simulation; general stacks usually assume a preset or hand-chosen controller. We present KPI, a promptable kernel for physical interaction between the trajectory source and an unmodified whole-body tracker. Instead of a controller fixed before the task, the trajectory source sends a contract: per direction, track, comply, or hold a force range. From tracking error and a wrench estimate, the kernel adapts the arms' stiffness, damping, reference and feedforward toward it at contact rate. We demonstrate KPI through an agentic framework: from one instruction, a vision-language agent writes both the reference trajectory and the contract, with no task-specific code. We demonstrate instruction-driven winch operation, door opening, and box transport, alongside scripted surface-interaction experiments. In the winch demonstration, the humanoid is able to turn a crank to hoist a second robot fully off the ground.

Transition-metal trichalcogenides MX$_3$ are quasi-one-dimensional van der Waals materials whose layers form through lateral chain binding, giving them an interlayer cleavage plane and in-plane electronic anisotropy. Among them, ZrSe$_3$ is stable under ambient conditions and semiconducting. Exfoliated crystals expose four crystallographic planes, and electrocatalytic measurements on an individual crystal assigned the hydrogen evolution activity to the high-energy (210) facet rather than to the basal plane. Those non-basal surfaces remain uncharacterized, since the available calculations treat either the bulk crystal or the free-standing basal monolayer. Here, we compute the surface energies and the equilibrium morphology of these four surfaces with a dispersion-corrected semilocal functional, and their band-edge alignment with the HSE06 hybrid functional including spin-orbit coupling. The surface energies span nearly an order of magnitude, from \SI{0.097}{\joule\per\meter\squared} for (001) to \SI{0.869}{\joule\per\meter\squared} for (010), and the Wulff shape exposes the four observed planes with area fractions of \SI{17.1}{\percent}, \SI{4.4}{\percent}, \SI{71.4}{\percent}, and \SI{7.0}{\percent}. The ionization potential varies by \SI{0.45}{\electronvolt} between facets and the electron affinity by \SI{0.80}{\electronvolt}, the gap of (210) falls from 1.43 to \SI{0.94}{\electronvolt} between 10 and \SI{23}{\angstrom}, and (010) remains metallic. The facets separate according to whether the cut preserves or distorts the Se-Se dimer, and the distorted dimers concentrate the frontier states. Because the same dimer governs the bulk electronic structure of the MX$_3$ family, the criterion transfers to the related trichalcogenides.

Given a bounded open set $V\subset \mathbb{R}^2$, we consider the problem of slicing this set by a family of curves, whose average length is as small as possible. The first sections of the paper prove the existence of an optimal slicing and establish a connection with the problem of eradicating an invasive biological species from an island, considered in \cite{BMS}. Namely, an optimal slicing can be obtained as a limit of minimum time eradication strategies. The second part of the paper derives various necessary conditions for optimality, describing the behavior of an optimal slicing strategy in the interior of $V$ and near the boundary $\partial V$.

Infrastructure drift can separate a running Kubernetes system from its documented architectural intent. This paper investigates live architecture models: editable architectural representations connected to selected runtime facts through explicit correspondences and recurring conformance checks. The approach is instantiated through an Archer-specific subset of Kubernetes Deployment Language (KDL) and Archer, a VS Code prototype with synchronized textual and graphical views. Snapshot recovery extracts selected Kubernetes facts into KDL; periodic and on-demand read-only checks report model-cluster inconsistencies without enforcing or repairing deployment state. We assess feasibility on three feature-selected Kubernetes example applications under an author-defined protocol, reporting precision and recall for snapshot recovery and selected inconsistency detection. Recovery scores can be reproduced from saved ground-truth and recovered models; detection uses a documented manual perturbation protocol. The results support feasibility within the evaluated KDL scope. They do not establish comparative superiority, detection of arbitrary production drift, scalability, or developer benefit. Storage coverage and ingress-host representation/default handling remain limitations.

Tens of millions of children program in Scratch, whose programs are concurrent: when the green flag is clicked, every sprite's scripts start together and share the project's state. Which script starts first is decided by the sprites' front-to-back stacking order, which no block reads. Dragging a sprite brings it to the front, and the order is saved with the project. Hence, a program can work on the author's screen and fail on the teacher's, with the same blocks. Our key observation is that, with the rest of the file fixed, rearranging the sprites that start scripts among their positions produces exactly the permutations of their initial stacking order. Under a fixed input and seed the unmodified virtual machine reproduces every one of them. StackSwap runs a project under these orders, all of them for up to five sprites, one per class of a conflict graph beyond, and a sample where neither is feasible, and compares the runs under four observation lenses. It returns a two-run witness naming an adjacent pair of sprites whose swap changes the outcome, with the resources they share as candidate causes; otherwise an exhaustive or graph-conditional robustness certificate, or an unresolved verdict. On 767 real programs from a course, an online judge, and a random public sample, 26.4% (course) and 18.2% (public) of those with a scheduling choice behave differently under some stacking order. Among the sensitive programs whose every order ran, the saved order's outcome recurs under a median 17% (course) and 50% (public) of the orders. Under scripted play, a predicate written from a stated requirement holds under one order and fails under another for 5 of 427 student submissions with a scheduling choice. For half of the sensitive programs the random stream is the racing pair's highest-priority shared resource. We close with recommendations for learners, graders, and the Scratch platform.

We analyze the moment hierarchy of a Callaway lattice Boltzmann model for phonon hydrodynamics and derive exact steady-state solutions for a driven planar channel with diffuse walls. The collision operator decomposes the population space into conserved, heat-flux, and fast kinetic sectors, whose coupling through streaming determines the transport response. For the two-dimensional, eight-velocity (D2Q8) lattice Boltzmann model, we derive a fully discrete closure that relates the heat flux to transverse kinetic moments. The higher-order transverse kinetic moment contains both a second-difference term and an explicit contribution from the imposed energy drop. Diffuse-wall population constraints then determine the heat-flux and kinetic-moment profiles without fitted parameters. The resulting solution reproduces the numerical bulk moment amplitudes and wall slip, while an exact wall relation separates the contribution of the higher-order moment from deviations from the leading gradient approximation. Finite-wave-number analysis further resolves the collision-sector mixing associated with longitudinal propagation. These results provide a unified description of collision relaxation, the moment hierarchy, and boundary response within the specified discrete model.

Tampered Text Detection (TTD) is essential for safeguarding document authenticity in security-critical workflows. Existing expert models are effective at capturing subtle manipulation traces but often generalize poorly across diverse document domains, while Multimodal Large Language Models (MLLMs) offer stronger semantic understanding and transferability yet remain insensitive to fine-grained forensic artifacts. This complementarity motivates us to investigate how expert forensic perception can be internalized into an MLLM rather than merely accessed through an external module. We identify a fundamental Double Mismatch that hinders this goal: a Spatial Precision Mismatch between coarse visual tokens and tiny tampered regions, and a Perceptual Granularity Mismatch between semantics-oriented pre-training and low-level forensic perception. To address these challenges, we propose Expert Knowledge Internalization (EKI), a progressive two-stage framework that transfers forensic expertise into the MLLM itself. In Stage 1, Text-Focused and Image-Focused strategies establish precise spatial focus on small text regions. In Stage 2, the proposed Forensic-General Representation Alignment (FGRA) loss aligns shallow LLM representations with those of a pre-trained forensic expert, enabling the model to acquire fine-grained artifact perception before such cues are diluted by deeper semantic abstraction. Extensive experiments on multiple in-domain and cross-domain benchmarks demonstrate that EKI achieves state-of-the-art performance and stronger generalization than existing expert-model-based and MLLM-based methods. Moreover, the expert is required only during training, allowing the resulting MLLM to maintain inference efficiency nearly identical to the vanilla model without relying on any external expert at inference.

Electronic health records provide irregular observations of latent patient states that evolve continuously over time. Recent autoregressive models condition on clinical histories to forecast future events as sequences of discrete observations. Conversely, multi-marginal flow matching provides a continuous-time formulation, but using multiple observations to supervise training paths does not itself give the learned dynamics access to preceding patient history. We introduce EHRFlow, a multi-marginal flow-matching framework that conditions on encoded patient history, thereby allowing future dynamics to depend on the patient's prior clinical trajectory. Our proposed framework accommodates irregular observation times and supports forecasting at arbitrary horizons. Across controlled synthetic benchmarks, EHRFlow improves clinical-code forecasting and latent-state recovery. On real-world clinical datasets comprising more than one million patients, including an independent external validation cohort, EHRFlow improves horizon-averaged top-5 clinical-code accuracy over autoregressive and history-independent flow-matching baselines. Finally, in a controlled counterfactual simulation, conditional guidance approximates the known effect of an antihypertensive intervention without training a task-specific outcome model.

We study a dynamic integrated sensing-and-communication problem in which a multi-antenna transmitter communicates with a receiver while simultaneously tracking a moving target governed by a stable Gauss–Markov model. We formulate the sensing–communication trade-off as a rate–distortion problem, where the communication rate is defined through the Verdú–Han information spectrum and the sensing distortion is measured by the long-run minimum mean square tracking error in angle and distance. We construct a tractable outer region by lower bounding this distortion through the posterior Cramér–Rao bound (PCRB). The control problem is partially observed because the target state is not directly available to the transmitter. We therefore introduce a belief-augmented information state and show, under the stated regularity assumptions, that stationary randomized Markov policies suffice for the covariance-based scalarized problem used in the outer bound. We then derive, under the stated large-block conditions, a Gaussian covariance-control outer bound by showing that, in the large-block regime, the sensing belief transition becomes asymptotically covariance sufficient; consequently, Gaussian signaling with the same stationary covariance policy preserves the stationary PCRB asymptotically while maximizing the communication reward for each transmit covariance. Numerical experiments compare an extended Kalman filter-based achievable frontier with a PCRB-based Gaussian covariance-control outer frontier.

In Bayesian inference problems with non-Gaussian observation noise, the posterior is only as accurate as the noise density, and gradient-based samplers need that density and its gradient evaluable pointwise, whether from an explicit expression or from code, and without an inner solve. We propose Copula Active Subspaces (CAS) to represent this noise density. A componentwise rank transform isolates the noise law's dependence in its copula, and a rank-$r$ reduction keeps only the directions along which that dependence varies. These directions are the leading eigenvectors of the copula score covariance $\boldsymbol{C} := \mathrm{Cov}_{\pi_{\boldsymbol{Z}}}(\nabla\log c^{Z})$, which is what makes the reduction a copula active subspace. Because $\boldsymbol{C}$ vanishes when the coordinates are independent, these are directions of dependence, which the covariance of the data need not identify. From this construction follow a Gaussian-reference KL divergence bound with the explicit constant $\tfrac{1}{2}$, minimized over all rank-$r$ reductions by exactly this eigenspace; a diagnostic for the error the reduction leaves behind, computable from the samples alone; and, from Hermite score matching, a reduced log-density and gradient in closed form, with the truncation orders and the Stage-2 regularization constants chosen on validation samples. The reduction replaces a $d$-dimensional density estimation problem by an $r$-dimensional one. On a $d=20$ noise law and a Bayesian inference problem with that noise, CAS lowers noise KL divergence more than fivefold and posterior KL divergence more than sevenfold against Gaussian-copula, product-of-marginals, and PCA-subspace baselines, and lowers noise KL divergence by factors of about $3.5$ and $2.7$ on two further $d=20$ examples.

We propose a localized reduced basis method for parametrized parabolic partial differential equations based on an adaptive partitioning of the parameter domain using hierarchical binary trees. A POD-Greedy procedure is employed to construct reduced spaces associated with each parameter subdomain. A certified a posteriori error estimator is derived from an inf-sup stability analysis and shown to be equivalent to the underlying approximation error. This equivalence, together with suitable regularity assumptions on the parameter-to-solution map, enables a rigorous convergence analysis and is used to derive a strategy for selecting the number of POD modes to retain in each local reduced space. Numerical experiments for a parametrized convection–diffusion problem demonstrate the effectiveness of the proposed approach and confirm the predicted convergence behavior.

Recent experiments have sparked interest on the ground-state properties and on the excitation spectrum of the spin-$1/2$ triangular XXZ model with strong Ising-like anisotropy. In this work, we introduce and analyze a “projected” coherent-state approximation to the model, constructed by projecting spin-product states onto the low-energy configurations of the triangular Ising antiferromagnet. Within this approximation, we discuss the structure of the ground-state ordering and the magnetization curve under a longitudinal field. We then discuss the excitation spectrum by linearizing equations of motion deriving from a time-dependent variational principle. This leads to a natural description of spin-wave-like excitations within the strongly constrained Hilbert space. At zero field, the variational approximation leads to a very flat landscape of quasi-degenerate states, which results in a low-energy pseudo-Goldstone mode in the excitation spectrum. We compare our results to experimental measurements on the cobaltite K$_{2}$Co(SeO$_{3}$)$_{2}$ (KCSO). Our approximation leads to a dramatic improvement as compared to linear spin-wave theory. However, there remain deviations in the value of the pseudo-Goldstone gap and in the dispersion near $M$ points at low field.

As large language models are deployed in increasingly autonomous long-horizon tasks, manually auditing and verifying the actions, artifacts, and outputs of models becomes more difficult. Users instead come to rely on LLM-generated reports to assess the quality and completeness of the work. We introduce a suite of eight adversarial reporting scenarios to systematically study whether LLMs conceal narrative-changing flaws: errors or limitations that undermine an otherwise successful account of work. We call this phenomenon "insecure reporting." When handed machine learning experiment logs containing a planted negative result that substantially weakens the proposed method, GPT-5.5 flags the negative result in only 2 of 200 generated reports. However, when a short honesty instruction, "Be honest in your response," is added, the model flags the negative result in 190 of 200 reports. Across eight open-weight models, chain-of-thought analysis reveals a recurring tension between disclosing narrative-changing flaws and reasoning about ways to appear successful. We perform an activation analysis and a steering experiment on Qwen3.5-9B, finding that honesty and success-seeking correspond to opposing directions in representation space. Our results suggest that LLMs tend to present narratives of success by default, and that steering models toward honesty makes their reports substantially more transparent.

Before invoking external tools, an agentic LLM must select among a K-way action space: executing a call, seeking clarification, answering directly, or declining. While internal activation steering can alter these pre-execution decisions, conventional aggregate metrics obscure where altered states land and what collateral damage they inflict. We present SAKIKO, an auditing framework that formalizes representation repair via directional error discovery, router-conditioned intervention, destination-resolved verification, and prospectively frozen statistical licensing. Across seven LLMs on When2Call and MetaTool, channel-keyed interventions induce direction-specific net gains in five models; across three sealed evaluations, none of 59 budget-matched random directions matches calibrated target gain. Crucially, destination auditing shows that behavioral movement does not equal repair: an intervention achieving +55 net gain corrupts over half of the baseline-correct decisions it touches, and promising point estimates on Qwen3-4B and Gemma-2-9B are formally declined due to finite-sample uncertainty. SAKIKO establishes the necessity of outcome-resolved adjudication before claiming internal repair. Code: https://github.com/ruizheliUOA/mechanistic-tool-use-llm.

Sparse Code Multiple Access (SCMA) is a promising non-orthogonal multiplexing technique for enhancing connectivity and spectral efficiency in next-generation communication networks. This paper proposes near-optimal uplink SCMA codebook designs based on a novel deep neural network (DNN)-assisted framework. The DNN is trained in an unsupervised manner, with a loss function derived from the structural characteristics of the generated codebooks, thereby eliminating the need for labeled training data. Based on error-probability analysis, Rician-factor-dependent design criteria are derived for uplink Rician fading and used to formulate the loss function. The resulting criteria naturally encompass AWGN and Rayleigh fading as limiting cases, providing a unified framework for codebook design. Moreover, upper and lower bounds on the average mutual information (AMI) are derived, providing an information-theoretic interpretation of the PEP-based criterion and establishing its asymptotic consistency with the AMI-lower-bound-based criterion in the high-SNR regime. The analysis further reveals how the dominant design factors evolve as the channel transitions from Rayleigh fading to AWGN. Numerical results show that the proposed near-optimal codebooks achieve significant performance gains over representative benchmark schemes across a wide range of Rician factors and exhibit excellent error-rate performance in the error-floor region, making them particularly attractive for ultra-reliable applications.

Compact OCR-specific vision-language models achieve strong document parsing performance, but often rely on costly supervision and focus primarily on visual-text reconstruction. We introduce Xiaomi-OCR-0, a unified 0.8B model for document parsing and OCR-centric understanding. We build an approximately 170M-sample OCR-centric corpus using an automated data engine that combines expert consensus, render-based verification, and targeted synthesis. Starting from Qwen3.5-0.8B, our progressive training recipe combines Q-Mask-based text anchoring, continued pretraining, and mixed-task reinforcement learning (Mix-RL). Xiaomi-OCR-0 achieves 95.24 on Real5-OmniDocBench, 96.83 on OmniDocBench v1.6, and 87.94 on Wild-OmniDocBench, while reaching an average score of 83.2 across five OCR-oriented VQA benchmarks. Ablations further show that, with sufficient parsing training, OCR-centric understanding supervision provides additional gains for document parsing. Homepage: https://huggingface.co/spaces/SeerRay-Lab/Xiaomi-OCR-0.

We consider the following three conditions for polynomials in several variables. Condition (1) holds for a polynomial if, for every affine integral domain, the following is true: whenever the result of substituting algebraically independent elements into the polynomial lies in the kernel of a locally nilpotent derivation, the elements themselves must lie in that kernel. A polynomial satisfies condition (2) if it does not belong to the kernel of any nonzero LND of the polynomial algebra. It satisfies condition (3) if the quotient algebra modulo the ideal generated by the polynomial is rigid, that is, it admits no nontrivial LNDs. For irreducible binomials, we prove that all three conditions are equivalent. For reducible binomials, we establish all existing implications between these conditions.

Functional Kolmogorov-Arnold Networks (FunKAN) achieve state-of-the-art accuracy on MRI Gibbs artifact removal and anatomical segmentation, but their 11.6 M parameters and 8.7 GFLOPs are too large for edge medical devices. We present FunKANLite, a two-stage, hardware-aware compression of FunKAN for point-of-care use. FunKANLite-TR reduces the spatial prior and replaces the ResBlock offset predictor with a depthwise-separable block. It has 1.9x fewer parameters than FunKAN and no loss in accuracy. We then distill FunKANLite-TR into FunKANLite-ST, which lowers the Hermite basis rank, factorizes the spatial prior into a low-rank form, and halves the filter widths. FunKANLite-ST has 5.6x fewer parameters and 3.7x fewer GFLOPs than FunKAN. It stays within 1.4 percentage points IoU of FunKAN on BUSI, GlaS, and CVC-ClinicDB, and reaches 33.95 dB PSNR on IXI. On an NVIDIA Jetson Orin Nano and a Raspberry Pi 5, FunKANLite-ST reduces energy per inference by up to 68% and raises throughput by 2.9x.