Papers

A method for solving the two-center Dirac equation using a Gaussian-product basis set tailored to the axial symmetry of diatomic systems is presented. For the ground state of H$_2^+$ at an internuclear distance $R=2.0~a_0$, we obtain a relativistic energy with relative precision at the $10^{-18}$ level. The properties of the basis set allow for an analytic Fourier transform of the wave function. As a first application we evaluate, for the first time, the zero-potential contribution to the one-loop self-energy for H$_2^+$ in Feynman and Coulomb gauges. Although this contribution is not separately gauge invariant, its calculation provides a proof of principle for the use of the present framework in prospective QED calculations.

Kernel Singular Value Decomposition (KSVD) learns a pair of singular vectors w.r.t. an asymmetric kernel matrix, which can be induced by two data sources, e.g., the queries and keys in self-attention or the rows and columns of a given matrix. In this work, we extend KSVD to multiple data sources, namely eKSVD, which conducts joint nonlinear feature learning upon asymmetric kernels. In the primal formulation, the projections associated with each data source are jointly learned to capture maximal information, while incorporating pair-wise couplings. With the Lagrangian and its Karush-Kuhn-Tucker (KKT) conditions, the optimization in the dual leads to a generalization of the shifted eigenvalue problem in Lanczos decomposition theorem of KSVD. Further, a covariance-based framework is derived together with using neural networks (NNs) for explicit feature mappings, complementary to the kernel-based interpretation and optimization. Numerical experiments verify the effectiveness of our eKSVD compared to methods based on Mercer kernels for tackling multiple data sources, and our innovation of deploying NNs demonstrates great flexibility for kernel methods.

StanceEval 2026 is the second edition of the StanceEval shared task series on stance detection in Arabic social media text. Stance detection aims to identify a writer's stance toward a given topic. Given a tweet and a target, participating systems must determine whether the writer's stance is Favor, Against, or None. This edition focuses on cross-target generalization across two distinct evaluation tracks: Track 1 evaluates thematically related cross-target transfer (testing on Women Driving, related to Women Empowerment from training data), while Track 2 evaluates cross-domain transfer to completely unseen targets (E-Cars and Trimester System). The shared task attracted 80 registered teams from 12 countries. During the evaluation phase, 30 unique teams submitted entries, with 21 teams officially ranked in Track 1 and 13 in Track 2 following validation filtering, and 20 teams submitting system-description papers. Participating teams employed diverse methodologies, including fine-tuned pretrained language models, prompt-based and retrieval-augmented large language models (LLMs), fine-tuned LLMs, and hybrid cascades. Top systems achieved impressive $F_{avg2}$ scores of 0.8994 on Track 1 and 0.9400 on Track 2, substantially outperforming the strongest baselines (0.7366 and 0.7475, respectively), where $F_{avg2}$ denotes the macro-averaged F1 score over the Favor and Against classes. Counterintuitively, performance on the unseen targets was higher than on the related target, a disparity could be driven by extreme target polarization, class imbalance, and dialectal or sarcastic nuance across topics.

Quantum error correction protects quantum information by encoding it in a code described by three numbers: how many physical qubits it uses, how many logical qubits it protects, and the smallest error it cannot detect. The last is an optimum over exponentially many candidates, so it is read off a solver rather than checked. Here we show that code parameters can be certified by a short certificate, a list or a pairing or a symbolic instance, whose correctness the kernel of a proof assistant decides by computation, and whose size is itself a theorem rather than an estimate. Two published code families have distances settled here: the bivariate bicycle code's $[[144,12,12]]$, certified, and the affine-permutation codes printed at $[[1152,580,\le 12]]$ and $[[2304,1156,\le 14]]$, settled at twelve and fourteen. Eleven code families and thirty-nine parameter sets follow, with nothing beyond three standard axioms trusted and the pipeline's specification step preset to twenty columns.

Tool-equipped AI agents use tool calls to access data and act on external systems. Horizontal growth of agentic systems increases the number of these interactions, and further motivates the need for automated, per-call oversight that can operate at low latency and/or on-prem. Conventional authorization schemes can determine whether an agent is allowed to invoke a tool, but cannot assess the agent's underlying cognition, specifically, whether the tool selection represents a logical, relevant step toward satisfying the intent of the task or not. Consequently, an allowed call may still deviate from the task's intent: a rogue agent might deviate the calls or nudge other agents to make a combination of calls that would not align with the intent of the task. Therefore, every call needs to be verified. In this study we investigate the applicability of Small Language Models (SLMs) to this purpose: an SLM functions as a task-tool relevance classifier that evaluates every selected tool independently against the assigned task and returns a relevance signal for downstream enforcement. Equipped with a novel dataset with multi-tool tasks whose required tools span distinct Model Context Protocol (MCP) servers, we used prompt-optimization, supervised fine-tuning, and reinforcement learning through GRPO to optimize and specialize SLMs.

To a coprime triple $a+b=c$ we attach two coordinates, the quality $X$ and the logarithmic mass $Y$, whose ratio $\lambda$ measures the balance of the triple and lies asymptotically between $2$ and $3$. In these coordinates the $abc$ conjecture and Szpiro's conjecture for Frey curves become asymptotic bounds with thresholds $X=1$ and $Y=3$, and the direct implications between them follow from the range of $\lambda$. We then place the approximation and power gains of Müller, Taktikos and de Weger in the same plane. Relative to a chosen presentation of the triple, one exponent factor $f$ relates the gains to the coordinates, and Szpiro's conjecture for this family is equivalent to the asymptotic bound $f\le 3$ uniformly over all presentations. Under the two separate asymptotic gain bounds for a fixed choice of presentations, we obtain $\limsup X\le 9/2$ and $\limsup Y\le 27/2$ as the radical tends to infinity. Stronger conclusions depend on the presentation or on a joint bound for the gains. We close with numerical data and two research objectives.

Self-supervised hypergraph representation learning can produce informative node embeddings, but existing methods often require deep encoders trained for hundreds of epochs, making embedding generation costly even for hypergraphs with a few thousand nodes. This limits applications requiring embeddings for many or evolving hypergraphs. We present HyperFuse, a label-free pipeline for fast hypergraph representation learning. HyperFuse (i) computes structural node coordinates by maximizing a spectral relaxation of hypergraph modularity using Banerjee's hypergraph adjacency and a matrix-free operator with cost linear in node-hyperedge incidences; (ii) constructs multi-scale feature summaries and assigns bounded utility weights to hyperedges based on member stability under feature and membership masking; and (iii) trains a lightweight utility-weighted hypergraph encoder for 100 epochs using an invariance-decorrelation objective. We compare HyperFuse with TriCL, SE-HSSL, VilLain, and HypeBoy on nine public hypergraphs using six downstream classifiers and k-means clustering. On the eight datasets where all methods completed, HyperFuse required 8.7 s per dataset on average, achieving 13-179x geometric-mean speed-ups over the baselines. It achieved the highest average accuracy with five of six classifiers, while classification and clustering performance was not significantly different from TriCL and SE-HSSL. Compared with HypeBoy, HyperFuse was 13x faster and 2.1-4.1 percentage points more accurate across all classifiers. HyperFuse provides a practical approach for fast, repeated hypergraph embedding generation.

Air-conditioning and road-traffic noise are common in classrooms, and their effects are often judged by cognitive performance. However, a sound that leaves performance unchanged may still be perceived differently or alter brain activity. In a within-participant design, this study tested whether perceived, cognitive, and EEG responses are consistent, and whether perceived and EEG responses distinguish conditions that performance does not. Sixteen students completed cognitive tasks in a university classroom under air-conditioning and road-traffic noise, each played back at 55, 60, and 65 dBA. Participants rated acoustic appraisal and perceived workload after each condition, and EEG was recorded during the tasks. The results show that cognitive performance did not differ significantly between conditions in any task. By contrast, noise was rated louder, less pleasant, and more arousing than a no-noise control, and all three ratings varied with sound level; perceived workload was also higher under noise. Task-period EEG power also showed significant differences between sources or levels in specific tasks and scalp regions. Within participants, relative EEG band power covaried mainly with loudness and pleasantness; louder and less pleasant ratings coincided with higher relative theta and lower relative gamma power. Associations with arousal and performance were rare, and none were found for workload. The three response types were thus only partly consistent, and perceived responses and EEG distinguished conditions that performance did not. Non-significant performance differences do not mean the conditions were equivalent for students. Assessments of air-conditioning and road-traffic noise in classrooms should therefore consider perceived responses alongside cognitive performance, with EEG providing complementary information on neural activity during tasks.

In Fifth-Generation (5G) wireless networks, Quality of Service (QoS) flow management supports diverse applications with heterogeneous QoS requirements, including latency-sensitive and high-throughput services. 5G architectures adopt a flow based QoS framework, where QoS flows are mapped to Data Radio Bearers (DRBs) to achieve the desired radio resource allocation. Existing mapping strategies typically rely on static one-to-one QoS-to-DRB mappings per PDU session, leading to inefficient spectrum utilization or inadequate support for delay sensitive traffic. This work presents a hybrid QoS-aware DRB mapping mechanism based on standardized 5G QoS Identifier (5QI) characteristics. The proposed framework incorporates multiple QoS flows within a single PDU session, supporting both many-to-one and one-to-one mapping strategies. The hybrid framework improves radio resource utilization and reduced bearer overhead by enabling flexible DRB utilization, where compatible non critical flows share DRBs while delay-critical flows are assigned dedicated DRBs to ensure strict QoS guarantees. The proposed hybrid QoS-aware DRB mapping is implemented using the open-source OpenAirInterface (OAI) mobile stack platform to demonstrate the integration of the proposed features within the existing 5G framework.

Building on work of Turner, we propose a proof in characteristic two of Quillen's conjecture on finiteness properties of the cotangent complex for homomorphisms between noetherian rings of possibly infinite flat dimension.

We give an exact counterexample to the eight-point angular-energy conjecture stated by Mouchet in 2005 and published in 2006. The conjecture specifies both a radical value for the global maximum and a square antiprism with unit-side horizontal squares separated by $h_0=\sqrt{1+2\sqrt{2}}/2$. We prove that the same family at the rational separation $489/500$ has a strictly larger angular sum. The proof reduces the sum of all $168$ angle cosines to a one-variable formula, factors its derivative, and certifies its sign using rational inequalities. We also characterize the unique maximizing separation within this family. All comparisons needed for the counterexample are exact. The result disproves the exact stated conjecture.

We consider a continuous-time particle system with exclusion interaction on the integer lattice. Each particle is assigned intrinsic left and right jump rates by an independent draw from a common random environment. We identify the decomposition of the system into maximal stable subsystems, which we call clouds. We show different qualitative behaviour for the cloud decomposition corresponding to different regimes for the random environment law that parallel the classical Sinai and Kesten–Kozlov–Spitzer regimes from one-dimensional random walk in random environment. Our main result in the Sinai regime is that the system is decomposed into an infinite number of finite clouds which all go to minus infinity with rapidly decreasing speed magnitudes, and we obtain explicit associated distributional limits. We analyse the model through the potential function associated with the random environment. In the Sinai regime, deep potential wells trap particles, producing stable clouds whose speeds are exponentially small in the well depth. Since successive wells are deeper, the resulting clouds are successively slower. Thus the localization mechanism of Sinai's random walk manifests itself here as a jamming phenomenon, in which a potential well traps not one walker but an entire block of mutually excluding particles.

We establish lower bounds for Hamiltonian property testing with access to the time-evolution operator but not its inverse. Each experiment may query the time-evolution operator multiple times, and distances between Hamiltonians are measured in the normalized Frobenius norm. In this model, we show that testing whether a Hamiltonian is $k$-local or $\varepsilon$-far from every $k$-local Hamiltonian requires $\Omega(1/\varepsilon^2)$ total evolution time, matching the upper bound of Kallaugher and Liang (TQC'25). We also prove that testing whether an unknown Hamiltonian equals a target Hamiltonian or is $\varepsilon$-far from it requires $\Omega(1/\varepsilon^2)$ total evolution time, matching the upper bound of Sinha and Tong (2025). These are the first lower bounds for natural problems in Hamiltonian learning and testing that rule out Heisenberg-limited scaling of $1/\varepsilon$. As a third result, we show that amplitude estimation to precision $\varepsilon$ requires $\Omega(1/\varepsilon^2)$ total time evolution, recovering the result of Tang and Wright (QIP'26) in the continuous-time query model. All three results follow from the hardness of distinguishing the zero Hamiltonian from a suitably chosen ensemble of random Hamiltonians. We establish this hardness by adapting the continuous-time adversary method to forward Hamiltonian evolution.

We present a simple proof of the $\varepsilon$-Dvoretzky conjecture, which asserts that the dependence on the approximation parameter $\varepsilon$ in Dvoretzky's theorem is polynomial in $1/\varepsilon$. In particular, if $n \geq (C/\varepsilon)^{\ell/2+1}$, then any $n$-dimensional convex body has, through any given interior point, an $\ell$-dimensional section that is $\varepsilon$-close to a Euclidean ball. Here, $C > 0$ is a universal constant. We in fact obtain a sharper dependence on $\varepsilon$. The proof is probabilistic, but uses a different probabilistic model from those employed previously. We also prove a simultaneous version of our theorem for a finite family of convex bodies with the origin in their interior, yielding a common linear subspace on which all of the bodies have nearly-Euclidean sections. Finally, we compare the radius of the approximating Euclidean ball with familiar geometric parameters, such as the mean widths of the body and its dual.

Efficient serving of Mixture-of-Experts (MoE) models is challenging due to large expert parameters, input-dependent expert activation, and dynamic workloads. Expert parallelism distributes expert computation across GPUs, while attention-FFN disaggregation (AFD) separates attention and feed-forward computation into independent worker pools. However, we observe that a naive AFD implementation could make expert load imbalance more harmful: once FFN computation becomes an independent pipeline stage, overloaded experts directly slow the FFN stage and degrade end-to-end serving performance. To solve this problem, we present AFORE, a timely expert reconfiguration system for AFD-based MoE serving. AFORE exploits two architectural properties of AFD. First, AFD exposes the expert-token distribution of upcoming microbatches before they reach FFN execution, enabling placement decisions based on near-future demand instead of stale historical profiles. Second, AFD creates a pipeline window in which expert migration for a target microbatch can be overlapped with the computation of preceding in-flight microbatches. AFORE formulates expert reconfiguration as a microbatch-aware scheduling problem and uses a migration-aware scheduler to decide when and which experts to migrate. AFORE further implements lightweight demand prefetching and NVLink-based GPU-GPU expert migration to reduce reconfiguration overhead. Evaluation on a 110B-parameter MoE model across four dynamic workloads shows that AFORE improves output throughput by 10.1-17.6% and reduces P95 inter-token latency by 7.1-9.5% compared with the strongest competing baseline. Compared with static placement, AFORE improves throughput by 29.8% on average and reduces P95 inter-token latency by 18.2% on average. Migration profiling further shows that AFD pipeline overlap can fully hide expert-migration latency.

Flow Matching enables high-quality visual generation via continuous-time dynamics, but inference remains costly due to multiple sequential function evaluations. Existing acceleration methods reduce the number of function evaluations but often introduce additional training overhead, degrade quality, or fail to account for input-dependent variability. We propose COFLOW, an inference-time method that adaptively selects the step counts each generation based on the prompt features. Our context-aware COFLOW is trained online with an unsupervised reward that balances inference efficiency and generation fidelity. Our method is plug-and-play, requiring no retraining of the underlying generative model. It generalizes to image and video generation, achieving over 2.5x speedup while preserving perceptual and semantic quality. We further provide a theoretical analysis establishing an O(1/K) forward-Euler discretization error bound under standard regularity conditions.

Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitioners to make a number of design decisions, such as the choice of the kernel and the observation model. Suboptimal choices can produce misspecified models that do not capture the underlying data generating process. We introduce Predictively Oriented Gaussian Processes (PrO-GPs), which treat predictive uncertainty as the primary inferential target and provide a robust alternative to standard GPs. Although direct computation of a PrO posterior for nonparametric models is intractable, we derive a reduced formulation and practical sampling scheme for efficient computation. Through synthetic and real data experiments, we show that PrO-GPs produce better calibrated predictive distributions under model misspecification compared to standard GP approaches.

We prove strict necessary density conditions for smooth coherent frames and Riesz sequences in the orbit of a connected, simply connected, nilpotent Lie group. This extends previous results for homogeneous groups to general nilpotent Lie groups. The main novelty in our approach is that we prove a stability result for coherent frames and Riesz sequences based on deforming their representation rather than their index set.

Large language models fine-tuned from a shared base can be merged by averaging their task vectors, but some merges collapse far below the base model, and common merge operators give no warning before evaluation. We show that one statistic of the specialists' task vectors both predicts this collapse and calibrates its repair. The power that averaging removes equals the variance of the task vectors across specialists, our measure of interference. Under a working noise model, the disturbance that a merge injects grows with the merge coefficient and with interference, yielding a pre-merge score. In our experiments on twenty-two merge configurations from four model families, only destructive merges exceed a threshold on this score. We find that statistics of sign conflict between specialists, a common target of existing merge operators, are anti-predictive. We then predicted the outcomes of fourteen merges before evaluating them, and twelve predictions were correct, including the destructive outcome of a specialist pair pushed past the threshold by continued pretraining. To address this collapse, we introduce PRISM, an operator that averages the task vectors first and then soft-thresholds each layer at a level set by the layer's interference. Without data or tuning, PRISM keeps all five destructive merges above the threshold within evaluation noise of the base model, where plain averaging falls at least 14.4 points below it or collapses entirely. We apply PRISM only above the threshold and keep the plain average for merges below it, which include all fifteen harmless ones. Code is available at https://github.com/js-lee-AI/PRISM.

The memory footprint of the key-value (KV) cache constrains the practical use of long-context models, and it dominates cost when one prefilled context must later serve many different queries. In this reusable setting, query-agnostic compression trades cost against quality: lightweight estimators are cheap but less accurate, whereas full-context reconstruction scoring is more accurate yet reprocesses the entire prompt. We introduce KV$^2$, a query-agnostic KV-cache compression method based on selective reconstruction. KV$^2$ first uses a lightweight proxy scorer to identify informative in-context tokens, then reprocesses only this subset to compute final eviction scores. On RULER, Needle-in-a-Haystack, and LongBench, KV$^2$'s margin over baselines widens as the budget tightens: on RULER 16K at a 2% KV-cache budget it improves the average score over the next-best baseline by more than 40 percentage points, and on LongBench it attains the highest average across 2%-10% budgets at lower compression-stage runtime and peak memory than full-context reconstruction. Reusable KV-cache compression thus does not require reprocessing the full context. Our code is available at https://anonymous.4open.science/r/KVsquared-0B97.

A companion paper derives a weighted, communication free partition for heterogeneous, multi institution device ensembles from each device measured shape, rho_machine(d), validated on real hardware. Its experiments show rho_machine is incomplete: fp32 to fp16 speedup and power shifts are not fully indexed, and memory capacity predictions rely on an assumed, not measured, reservation overhead. This paper closes that gap, indexing five unmeasured fields in the psi selection vocabulary: memory capacity $M_i^{cap}$, power draw $P_i$, execution unit capability $X_d$, compiler directive configuration $C_d$, and memory reservation overhead $R_d$. We introduce reached(d), a Boolean for whether compiled code dispatches to specialized hardware, explaining the NVIDIA fp16 power shift that hardware availability alone cannot predict. MoA fixes a computation independently of its target, so compiler directives get a two part admissibility criterion: select a real hardware quantity without discretionary reordering, and be deterministic, not compiler overridable. Across Intel, AMD, NVIDIA, OpenMP, OpenACC, and Open MPI, this admits only cache placement controls, deterministic vector or tile widths, and occupancy caps; heuristics like autotuning are excluded and absorbed into a residual epsilon$(k)_d$. We validate on five devices: A100, H100, V100, MI100, and Max 1550, measuring or establishing all five fields on each. Reachability proves real but partial, occupancy limits are device specific, and reservation overhead ranges about 0.004 to 0.030. A residual of negative 9.8 percent for the excluded Triton autotuner shows an unvalidated heuristic can act opposite a presumed penalty. These results close all five fields for every device in the companion ensemble, converting assumed behavior into measured, target specific quantities.

A reinforcement-learning (RL) pipeline for a legged robot is assembled from proxies. A reward stands in for intended behaviour, a curriculum gate stands in for competence, an evaluation statistic stands in for robustness, and a reference motion stands in for an achievable skill. The traditional view treats only the first of these as optimised against, and so locates specification failure (reward hacking) in the reward alone. I argue that all four are proxies in the same formal sense, that each has a characteristic divergence mechanism, and that each admits a reformulation that closes it. For every layer I state the traditional formulation, derive the condition under which it diverges from its target, and give the alternative: first-order (L1) costs where quadratic kernels are flat, peak and outcome statistics where curriculum gates average, gate reachability and information checks, deterministic and phase-desynchronised evaluation, curriculum state treated as part of the model, feasibility-first reference design with residual feed-forward, and function-preserving input widening that lets one policy grow instead of being retrained. The arguments are illustrated by measurements from one continuous lineage of a PPO policy for a simulated 1.91 m humanoid, grown over four stages and 13,500 iterations on a single laptop GPU. Among them, a curriculum gate built on averaged error advanced at its rate limit on every check while the skill it gated was absent, and a batched push test whose synchronised resets aliased the gait phase ranked a 0.5 m/s push as more dangerous than a 2.0 m/s one.

As LLM agents decide on users' behalf which product to buy, which hotel to book, or which paper to cite, a preference for items from certain sources (the sites or services they come from) shapes what users receive and which sources are selected. We study source preference in end-to-end search with 12 agent models across three domains. Comparing items from different sources that satisfy the same requirements at the same position, we find that each model prefers some sources and avoids others in every domain, largely agreeing on which. This preference can outweigh how well items satisfy the request: an item satisfying one requirement fewer is selected about two-thirds of the time when it comes from a preferred source and the better one from a dispreferred source, but almost never in the reverse case. The information identifying an item's source affects selection by itself: hiding it weakens the preference, and relabeling an item with a preferred source raises its selection rate. We test two routes to this preference: training that rewards better items can make a source a shortcut for requirement satisfaction, and missing information can trigger preconceptions about the source. Supplying missing information or a prompt countering these preconceptions reduces source preference.

We investigate how dissipation can emerge in a quantum network from temporal fluctuations of the interaction topology. For a network whose graph is redrawn at short time intervals, the averaged dynamics yields a Markovian master equation: the mean network fixes the coherent part and the covariance fixes the dissipative structure. The covariance eigenvalues set the noise strengths, while its eigenvectors determine the collective operators on which those strengths act. Two ensembles with identical mean adjacency and covariance spectra but different eigenvectors produce distinct dynamics despite identical purity. A physically realizable model yields an analytically predicted dissipative gap, giving quasi-protected dynamics. These results establish fluctuating connectivity as a resource for engineering quantum dissipation and protection.

The application of machine learning to dermatology has grown substantially in recent years, moving beyond proof-of-concept studies toward potential applications. However, clinical dermatology remains a challenging and still open problem. Diagnostic assessment is often ambiguous, and skin lesions exhibit high variability, compounded by differences in acquisition modality, device quality, and patient demographics. These factors hinder the development of robust models suitable for safe and equitable clinical use. To support translation into practice, it is essential to systematically evaluate how contemporary models generalize across heterogeneous data sources. In this work, we benchmark a diverse set of architectures on recent dermatology datasets, spanning dermoscopic images and smartphone-based clinical photographs. We assess the robustness of recent general-purpose and medical vision-language models, as well as foundation models, and compare them against task-specific dermatology classifiers, including embedding-based approaches and convolutional neural networks. Our study provides an evaluation of model performance under distribution shifts, modality changes, and demographic variability. By quantifying the gap between current state-of-the-art models and the requirements of clinical deployment, we aim to contribute to the development of reliable, accessible, and clinically applicable AI systems for dermatology.

Mobile Gaussian reconstruction must satisfy two requirements: the reconstruction model must execute within a device resource envelope, and the resulting Gaussian asset must expose a representation size suited to downstream mobile use. Existing feed-forward Gaussian reconstructors commonly decode dense, image-aligned candidates whose final cardinality is implicitly determined by the input resolution and number of views. We present PocketSplat, a feed-forward framework for budgeted mobile Gaussian asset construction. Given a prescribed output budget, PocketSplat organizes dense geometry-aware latent candidates in predicted world space, allocates exact integer capacity across local latent cells, and decodes complete Gaussian attributes only for retained candidates. Cell-conditioned latent fusion aggregates repeated multi-view evidence before decoding, while spatial responsibility decoding adapts Gaussian support after local sparsification. Experiments on DL3DV and out-of-distribution benchmarks establish a strong quality–budget trade-off against feed-forward Gaussian reconstruction baselines. On Mip-NeRF 360, PocketSplat executes directly on a target iPhone and constructs compact, higher-quality Gaussian assets substantially faster than a deployable streamed MVSplat variant; native MVSplat and DepthSplat exceed the device memory budget.

In this paper, we study the problem of sampling from a probability distribution using Langevin-type dynamics. We consider overdamped Langevin dynamics perturbed by adding a Stratonovich perturbation that preserves reversibility. We prove an optimal scaling for the Stratonovich perturbation applied to Gaussian target distributions and derive an algorithm to construct such perturbation. Our theoretical results are supplemented by numerical experiments in which we compare our proposed method with nonreversible samplers and overdamped Langevin dynamics. Our numerical experiments demonstrate the efficiency of the approach beyond the quadratic case.

Accident, defect and outage investigations end with a decision that ordinary question answering never faces: whether the evidence gathered so far is enough to close the case. We study this decision for LLM investigators, which request evidence from a case file, revise their hypotheses, and either close the case with a conclusion grounded in what they read or leave it open and name what is missing. This judgment does not come with capability: an untrained 9B model overstates its evidence in 97% of its answers, and a frontier model that identifies the right cause in 84% of cases still overstates in 91% and closes 17 of the 41 cases whose official finding is "cause undetermined". Measuring it is also non-trivial: the source of a case largely predicts its label, and a rule that reads only the source reaches 83.0 balanced accuracy on our test cases. We therefore evaluate closure with three tests: closure accuracy, reported against this rule and within each source; evidence dependence, which removes the grounds of a conclusion and checks whether the model stops closing; and conclusion and gap quality, a judged checklist of what the model asserts and what it says is missing. We build Nautil, 731 audited cases from aviation, rail, maritime, chemical-safety and vehicle-defect reports and production server incidents, with teacher trajectories, an out-of-distribution test set and counterfactual evidence versions. Fine-tuning a 9B model on these trajectories makes its closures follow the evidence: removing the grounds lowers its closure rate by 26 points relative to a matched control, overstatement falls from 97% to 35%, and correct, non-overstated conclusions rise from 3% to 43%. Reinforcement learning that rewards only the closure decision then raises balanced accuracy from 69.2 to 83.3, on par with the teacher, and within-source accuracy from 60.4 to 74.1, at some cost in evidence dependence.

Hawkes processes are widely used to model temporal point patterns exhibiting self-exciting behavior. In this work, we consider a Hawkes model with a baseline intensity depending on a set of dynamic covariates and an exponential triggering function. A Bayesian approach is applied to variable selection in this context. Spike-and-slab priors are proposed to enable a parsimonious choice of relevant variables. We also provide practical simulation procedures for the fitted covariate-driven Hawkes model, which support posterior predictive checks and probabilistic forecasting. This approach is illustrated by the example of spore release of Venturia inaequalis, the fungus responsible for apple scab disease. We study the dependence of primary spore releases on environmental covariates and highlight the self-exciting behavior of subsequent releases. The Bayesian framework also provides a natural basis to forecast future spore releases. By delivering interpretable posterior inclusion probabilities alongside uncertainty-aware predictive risk bands, this new methodology provides a rigorous foundation for managing temporal event risks driven by both external environmental forcing and internal contagion.

We investigate collective charge excitations in three-dimensional semimetals with dipole-like Berry-curvature (BC) profiles, focusing on vortex nodal-ring semimetals (VNRs) and Hopf semimetals (HSMs). The VNR hosts a continuous ring of dipole-like BC sources generated by its winding pseudospin texture, whereas the HSM hosts an ideal BC dipole. This allows us to examine how distinct realisations of dipole-like BC structure affect collective charge dynamics. While plasmon modes in $\mathcal{PT}$-symmetric nodal-ring semimetals (PTNRs) and their gapped cousins were studied in a companion work, arXiv:2609.35373, here we analyse the density response, Drude weights, dielectric function, and plasmon modes of VNRs and HSMs at low doping within the random-phase approximation. For VNRs, we consider untilted, in-plane tilted, and axially tilted systems. Although VNR and PTNR have identical energy dispersions, their distinct eigenstates introduce a toroidal-angle dependence in the band-overlap factor, yielding additional interband contributions for in-plane wavevectors and weak corrections to the screened plasmon frequencies. The toroidal Fermi surface also produces intrinsically anisotropic bare plasmons. In contrast, HSMs have isotropic bare plasmons, with anisotropy arising only through their interband response. Our results show that collective charge dynamics can distinguish different realisations of dipole-like BC structure and reveal pseudospin information beyond the single-particle dispersion.