Papers

We propose a nonparametric approach that fuses deterministic initial forecasts and a partial realization into a probabilistic forecast using the framework of functional curve completion. Our motivation is to construct intra-day forecasts for renewable energy generation, which is a key operational task in modern power grids. The aim is to combine the day-ahead (DA) forecast and the morning realized generation profile to create trajectories for the rest of the day, quantifying operational uncertainty. Starting with a large database of complete forecast-actual pairs across many assets, we adopt a functional point of view and construct a weighted neighborhood based on similarity metrics for the observed partial curve, the DA forecast, the day, and the geographical location. The selected complete nearest-neighbor curves provide a full predictive distribution, including functional focal envelopes and predictive bands based on functional depth. The hyperparameters governing neighborhood size, distances, and fusion rates are tuned across forecast update times and directly target probabilistic calibration in terms of the predictive probability integral transform. Three case studies using synthetic wind and solar assets, as well as real-life regional wind generation, showcase that our algorithm is able to achieve excellent calibration.

Secure multi-party computation (MPC) lets parties evaluate a function over private inputs without revealing them. In garbled-circuit (GC) protocols, prior optimization has largely treated the number of non-linear gates, especially AND gates, as a proxy for cryptographic cost, and has focused on minimizing multiplicative complexity. We identify an orthogonal source of savings: a gate need not be garbled when one party knows or can locally compute its inputs; that party can evaluate it outside the secure protocol, even when the gate is non-linear. We introduce ownership-aware optimization for GC-based MPC, which minimizes non-linear gates requiring joint evaluation rather than total non-linear gates. We formalize this objective in a cost model and implement a compiler-integrated, gate-level framework that restructures Boolean circuits to increase party-local computation while preserving secure-computation semantics. The method is automated and general-purpose, and composes with existing multiplicative-complexity optimization. Experiments show that it reduces jointly evaluated computation and improves end-to-end GC performance on circuits with party-local structure, revealing protocol-cost savings missed by conventional GC cost models.

In Nonlinear Model Predictive Control (NMPC), the control law is implicitly determined by the solution of an Optimal Control Problem (OCP). Consequently, OCP design is often tailored to specific platforms and tasks, demanding extensive expert knowledge and tuning effort. To address this, we propose a unified NMPC framework that directly plans and controls the robot joints subject to task-space motion and force requirements and is capable of seamlessly generalizing across multiple robotic platforms and diverse tasks. Furthermore, optimization-based methods often treat interactions as rigid contacts, making the torque solution sensitive to the modeling errors of the robot dynamics and the environment. We study the intrinsic task-space impedance of our proposed controller, its partial contraction for differential stability and differential passivity under unmodeled interactions. As a result, our framework enables closing the force-feedback loop in the high-level planning layer to achieve precise motion-force tracking performance, addressing the long-standing challenge of force-feedback NMPC. Finally, we validate our framework on physical hardware, demonstrating hybrid motion-force control on a redundant manipulator and compliant locomotion on a quadruped, while preserving core NMPC advantages such as hard constraint satisfaction, optimal redundancy exploitation, and real-time planning under unforeseen interactions.

Misperceptions can run in two directions. Individuals can either believe false information or reject true information, with experimental work finding that debunking efforts are effective at correcting both forms of misperception. Yet despite the efficacy of true corrections, current debunking systems focus almost entirely on the correction of falsehoods, with professional fact-checkers publishing few true verdicts and crowdsourced systems like X's Community Notes program unable, by rule, to display notes verifying true claims. As a result, we do not have a clear understanding of the extent to which overall misperceptions are driven by doubting true information. To answer this question we first draw on a novel dataset of 47,899 queries to X's AI assistant which track users asking for verification on post content. Surprisingly, among questioned posts that received a true or false verdict, Grok judged nearly identical shares as either accurate or inaccurate. Of the questioned posts, more than 83% were not flagged by Community Notes and only 3.3% carried a displayed note. Among questioned posts judged accurate by Grok, nearly 90% received no note at all while fewer than 2% displayed a note flagging them as misleading. This discrepancy does not seem to have stemmed from a lack of effort, with contributors writing 2,981 notes verifying questioned posts despite there being no way for Community Notes to display them publicly. Alongside further exploration of these findings we discuss both the system- and code-level changes that would be required to effectively address this asymmetric correction paradigm.

Automating aerial wildlife surveys requires reliable animal detection, consistent delineation of observation strips, and correction for repeated coverage between successive images. We present a unified three-branch deep learning framework that integrates these tasks through WildSeg, WildMatch and WildDet. WildSeg combines rod segmentation with geometric refinement to delineate counting strips from aircraft-mounted markers. WildMatch uses teacher-student distillation to learn dense image correspondences and identify overlapping survey areas without relying on geolocation metadata. WildDet combines dual-scale detection with feature fusion, density supervision and empty-image gating to support animal detection and counting. We evaluated the framework using oblique aerial imagery of four antelope species from the Great Nile Migration Landscape in South Sudan. WildSeg achieved reliable rod extraction, while WildMatch approached teacher-level accuracy with a substantially lighter and faster model. Both modules maintained high accuracy on resized images, improving processing efficiency. WildDet improved detection performance across all four species and reduced detection-based count MAE, RMSE and mean bias by 21.0%, 4.6% and 27.8%, respectively, relative to YOLO11. By connecting spatial survey constraints with animal detection, the framework provides a practical and computationally efficient approach to processing large aerial image collections for wildlife monitoring and population surveys.

Virtual cell models should capture phenotypes induced by specific perturbations. However, image-based models are typically trained and evaluated to match real-image distributions, which alone does not explicitly prioritize perturbation-specific biological responses. Recent approaches add biological signals through reinforcement-learning post-training or inference-time steering, raising a central question: where should biological response information enter the generative pipeline? We introduce PerturbBridge, a stochastic data-to-data bridge model that directly supervises perturbation-specific phenotypes in predicted perturbed images during training. PerturbBridge jointly optimizes bridge regression and differentiable biological response losses, with biological gradients passing through a frozen image encoder. We further introduce perturbation-response evaluations based on downstream classification and retrieval. Across three microscopy benchmarks for perturbation profiling and subcellular imaging, PerturbBridge surpasses CellFlux in biological fidelity, image quality, and sampling efficiency. On BBBC021, mechanism-of-action classification improves by 5.66 and 7.5 percentage points with morphological and learned visual features, respectively. On JUMP and AllenCell, retrieval Hit@10 and Hit@1 improve by 1.77 and 7.15 percentage points, respectively. On BBBC021 and JUMP, PerturbBridge achieves lower FID with 80% fewer model evaluations than CellFlux. Overall, these results show that directly supervising perturbation responses during training improves phenotypic fidelity while enabling efficient cellular image generation. Code is available at https://github.com/yyc1215lll-creator/PerturbBridge.

Real-world tables are often heterogeneous, combining numerical features with free-form string columns. Table foundation models (TFMs) excel on numerical tables but require strings to be encoded numerically, while large language models (LLMs) hold semantic knowledge but are not designed for tabular predictions. Most existing bridges use LLMs as plug-in encoders for cell strings, yet how to extract representations effectively for tabular learning remains underexplored. We show that the interface between LLMs and tables matter as much as the LLM itself. Applied cell-wise, larger LLMs do not give better features. With our interface, the same LLMs improve steadily with size. TILE (Table-Interfaced LLM Embeddings) combines four ingredients: row serialization to provide cross-column context, intermediate-layer extraction to avoid layers specialized for next-token prediction, columnar pooling to remove mean pooling's length bias, and by-pass features to route numbers and categories past the LLM. Paired with TFMs, TILE sets a new state of the art for tables with strings. Across 100 datasets, it beats the strongest baseline on 89% of splits, with gains across 7 LLMs and 10 tabular learners, and ranks first on the 108-dataset STRABLE benchmark.

Anomalous diffusion in heterogeneous media is ubiquitous across physical and biological systems, where spatially varying microstructures give rise to distinct transport regimes. Variable-order nonlocal operators provide a natural modeling framework for describing heterogeneity and transitions between diffusion regimes. However, the position-dependent long-range interactions inherent in these operators impose prohibitive memory costs and make numerical methods developed for constant-order operators computationally impractical. Consequently, accurate and computationally efficient numerical methods for variable-order nonlocal operators remain scarce. In this paper, we propose accurate finite difference discretizations for the variable-order fractional Laplacian $(-\Delta)^{\alpha(\mathbf{x})/2}$ and develop a fast Fourier transform (FFT)-accelerated scheme for their efficient implementation. The computational and memory costs are $O\!\big(MN\log(2N)\big)$ and $O(MN)$, respectively, where $N$ is the total number of spatial points and $M \ll N$. The method is also naturally parallelizable. We establish its consistency and accuracy through a rigorous error analysis that quantifies the local interplay between solution regularity and the spatially varying order $\alpha(\mathbf{x})$. To the best of our knowledge, this is the first work to quantify how these two factors jointly determine convergence rates, with numerical experiments demonstrating this dependence. Extensive numerical experiments confirm the accuracy and efficiency of the proposed method. Applications to anomalous diffusion in composite materials further demonstrate its ability to capture the effects of material heterogeneity.

We propose a mitigation to reward hacking in reinforcement learning. Our setup involves a misspecified reward function that gives rise to unintended behavior, and a monitor used to detect unintended behavior. As with frontier AI systems, the monitor makes systematic errors. Consequently, using the monitor for data filtering or to apply a reward penalty fails to prevent the model from learning unintended behavior ("reward hacking"). To address this problem, we introduce GRAFT: Gradient Routing Adapter Fine Tuning. Rather than penalizing or filtering flagged samples during training, GRAFT constrains gradient updates on those samples to a sacrificial set of new parameters. This has two benefits: First, because the monitor is not part of the reward function, the model does not learn to hide misbehavior. Second, ablating the sacrificial parameters reduces or entirely stops the unintended behavior while maintaining improved performance on target tasks. We demonstrate these benefits in RL environments where reward penalties cause models to learn to reward hack in undetected ways, training models ranging from 135M to 8B parameters. Additionally, we show a similar effect at a larger scale by distilling frontier LLM trajectories containing reward hacking into Qwen3-32B, without teaching that model to reward hack. Overall, our work suggests GRAFT may be a promising approach for leveraging imperfect monitors during post-training in settings where true performance is difficult to evaluate.

We study in-context binary classification in a simple attention model trained to minimise a logistic loss. Each prompt has a latent logistic teacher, and the learner must infer its direction from Bernoulli-labeled context examples. We derive an asymptotic prediction for the test logit in a high-dimensional regime with context length proportional to token dimension, and total training prompts proportional to dimension squared. Our formula cleanly separates calibration, test-time context noise, and non-isotropic parameter-estimation noise as interpretable effects on in-context performance. Our analysis also identifies the ridgeless separability regime and addresses the effects of context length, pretraining-set size, regularisation, and sampling temperature on in-context classification performance. The theory's predictions closely agree with finite-dimensional simulations and fully trained linear-attention models, while experiments with standard softmax attention show qualitatively related behaviour beyond the regime assumed by our analysis.

Clinical decisions depend on anticipating how a patient's condition will evolve as treatment is adjusted and new evidence becomes available. Existing medical world models capture patient-state evolution, but often define the evolving state around a particular modality or task, limiting reuse as inputs or prediction targets change. These models also retain history through observation sequences or recurrent or latent summaries rather than exposing preceding patient states and clinical actions as an ordered transition context. This distinction matters because similar current measurements may follow different recent changes, treatment exposures, and observed responses. To tackle these limitations, we propose PatientWM, a clinical world-model framework built around a unified patient state and sequential latent history. Availability-aware encoders integrate observations available at each decision time into the patient state, while typed decoders produce task-specific clinical readouts without defining the state around any single target. PatientWM further conditions each next-state prediction on the current state and supplied action together with a bounded, ordered history of preceding latent patient states and clinical actions, preserving recent treatment and response context. Experiments across MIMIC-III, MIMIC-IV, and three external clinical datasets show superior performance in clinical prediction, multi-step forecasting, and action-planning evaluation. Transfer experiments further demonstrate the generalizability of PatientWM's patient state. Together, these results establish its ability to forecast clinical evolution and support planning.

Scaling fault-tolerant quantum computing (FTQC) requires orchestrating millions of operations continuously across a tightly coupled classical-quantum control stack. A critical challenge in this orchestration is determining the optimal hardware-software boundary, i.e., the Quantum Instruction Set Architecture (QISA). We focus on cryogenic, fixed-connectivity qubit platforms, such as superconducting and topological Majorana qubits. For these, existing QISA choices either operate at too low a level, violating cryogenic thermal budgets at scale, or at too high a level, imposing unrealizable complexity on the control engine. To reason about these tradeoffs, we introduce the ARIES instruction set hierarchy, which categorizes QISAs into distinct abstraction levels. To systematically evaluate these levels, we develop an end-to-end evaluation toolflow featuring a cycle-accurate classical driver and hardware engine simulator. Using eight quantum applications across superconducting and topological qubit platforms, we measure instruction bandwidth, transceiver power dissipation, and measurement processing overheads. We demonstrate that while physical-level abstractions exceed the thermal limits of dilution refrigerators by orders of magnitude, canonical-level abstractions significantly underestimate hardware routing congestion and execution runtimes. Our Level 4 QISA (local logical operations) offers an optimal architectural balance. As quantum hardware platforms scale toward FTQC in the coming years, our findings provide concrete architectural guidance for the design of their classical control stacks and instruction interfaces.

Vision-based document retrieval has improved rapidly, but current evaluation settings still emphasize short documents and single relevant pages. This leaves an important gap between leaderboard performance and realistic long-document retrieval, where the evidence needed to answer a query may span multiple pages or even multiple documents. We present VL-DocIR, a page-level benchmark for evidence-complete visual long-document retrieval. VL-DocIR is built from 29,641 HTML-born documents rendered into 388,548 page images from Wikipedia, arXiv, PubMed, and SEC proxy statements. It contains 271,760 queries across 23 domains and six evidence structures, covering single-page, within-document multi-page, and cross-document evidence configurations. Evidence annotations are grounded to rendered pages and HTML element identifiers, and queries are filtered with a cleaning pipeline targeting clarity, correctness, closedness, and the absence of explicit layout references. We evaluate leading single-vector and multi-vector visual retrievers together with diagnostic retrieval settings such as document-context scoring, query splitting, reranking, and round-robin ensembles. The strongest evaluated configuration reaches 69.3 nDCGAll@10 and 80.6 RecallAll@10 under structure-balanced Macro evaluation, but source- and evidence-structure breakdowns show that cross-document retrieval remains substantially harder than single-page retrieval, and that document-context scoring is especially helpful for within-document multi-page queries. VL-DocIR exposes these failure modes and provides a more demanding target for visual long-document retrieval. The new dataset and code will be made publicly available at https://yufanchen96.github.io/VL-DocIR.

Let $q$ be a prime power. An $(r, i)$-regular fat $\mathbb F_q$-linear set has exactly $r$ points of weight $i\ge2$, called fat points. All of its remaining points have weight one, and at least one such point occurs. We solve two open problems posed by three of the authors of this paper. First, we derive divisibility constraints on the point weights using the scalar stabilizer of the defining subspace. Consequently, a regular fat linear set of rank $2i$ in $\operatorname {PG}(1,q^n)$ has at most two or exactly $q + 1$ fat points. In the latter case, the fat points form an $\mathbb F_q$-subline. Second, we construct higher-dimensional regular fat linear sets whose fat points do not form an $\mathbb F_q$-subgeometry. In particular, for every $k\geq 3$ we obtain examples of rank $2k$ whose fat locus consists of an $\mathbb F_q$-subgeometry $\operatorname {PG}(k-2,q)$ in $\operatorname {PG}(k-1,q^4)$ together with one external point. This construction is then generalized further. Finally, we apply our projective-line results to $q$-matroid representability and present an infinite family of non-representable rank-two $q$-matroids arising from partial spreads.

Shapley-based measures are widely used for measuring variable importance in statistics and machine learning. However, these measures have a serious issue–a nonactive variable can get a positive importance measure when it is correlated with an active variable. Herin et al. recently proposed a measure called proportional marginal effects (PME) that mitigates this spurious effect. However, PME is developed for deterministic models and has high computational cost. In this article, we propose a new measure called proportional inclusive marginal effects (PRIME) that overcomes these two limitations of PME. The key idea in PRIME is to use a novel model-free variable selection technique to identify the active variables and include only them in the computation of the importance measure. Analysis of test functions and real datasets show that PRIME can accurately and reliably quantify variable importance from noisy input-output data.

Large audio-language models (LALMs) have become highly capable on a wide range of tasks spanning speech, music, and environmental sound. However, many modern LALMs resample input audio to 16 kHz mono, making all frequencies above 8 kHz unobservable. We present SpectralBridge, a lightweight extension that gives such a model access to the 8-16 kHz band by joining low- and upper-band representations with time-aligned paired cross-frequency attention. Applied to Audio Flamingo Next, the method trains only a small adapter and rank-8 LoRA modules, while leaving the original audio encoder, audio projector, and base language model frozen. SpectralBridge improves both zero-shot transfer and downstream fine-tuning: it raises zero-shot balanced accuracy on the ESC-50 audio classification dataset from 75.5 to 90.5, and when fine-tuned on Insect-10, a 10-way insect species task we construct from InsectSet459 recordings, under the same budget as a LoRA fine-tuned baseline, it reaches 55.4 balanced accuracy against the baseline's 26.2. On a benchmark where the answer depends only on the 8-16 kHz band, it gains 30 mAP over the frozen model. Erasing the upper-band stream from the trained model removes these gains, showing that they come from the high-frequency signal itself rather than from extra tokens or the adapted prompt format.

Recent multimodal deep search agents have advanced tool use and visual content retrieval, yet they still struggle to convert intermediate visual evidence into actionable guidance for subsequent search, limiting their effectiveness in long-horizon settings. To address this gap, we present Neos, a multimodal deep search framework that learns both how to acquire evidence and how to use it to guide subsequent decisions. To make this coupling learnable, Neos constructs training tasks with intermediate visual dependencies while filtering out textual shortcuts, and introduces a lightweight, trainable Multimodal Evidence Interface (MEI) that transforms retrieved content into goal-conditioned observations. At its core, an agent-environment co-evolution procedure treats MEI as a co-adaptive component of this loop. Specifically, reference-guided credit assignment uses verified successful trajectories to localize critical policy errors while preserving credit for useful decisions in failed searches, whereas rollout feedback selects informative local evidence-processing interactions for MEI supervised fine-tuning (SFT). By alternating policy reinforcement learning (RL) with MEI SFT, Neos allows the policy's evolving evidence requests to shape MEI training and the adapted MEI to reshape subsequent observations, closing the loop between evidence acquisition and evidence-conditioned action. Across ten benchmarks, Neos-9B and Neos-35B demonstrate leading performance among specialized multimodal deep-search agents.

Audio description (AD) aims to enhance the accessibility of visual media for blind and low-vision (BLV) persons. However, in higher education, where slide-based lectures are a default mode of teaching, lecture AD remains largely underexplored. The main reason is that existing production guidelines, evaluation metrics, and benchmark datasets are oriented toward entertainment content and do not transfer to lectures, where ADs must complement the lecturer's speech, resolve deictic references, and fit within narrow pauses. In this work, we propose AD4Edu, consisting of an AD benchmark, AD4Edu-Bench, and a rule-diagnosable evaluation metric, AD4Edu-Eval, for generating and evaluating ADs in higher education. Specifically, we consolidated established accessibility guidance, including WCAG 2.2, the DCMP Description Key, and NCAM's STEM description practices. We further collected silver reference ADs, judge-ordered preference pairs, and pairwise preferences from four BLV raters, and post-trained models with direct preference optimization (DPO) for detailed analysis. Our findings indicate that while the metric reliably detects violations of the standard, ADs that comply with it do not necessarily fulfill the subjective preferences of BLV persons, most notably on description length, underscoring the necessity of active participation of BLV persons in co-designing inclusive AI solutions.

While language models provide powerful mechanisms for evaluating textual predictability, it remains unclear whether the relative extents of LM surprisal remain stable across models. This study presents empirical evidence of the invariance of ranking based on cross-entropy related measures (e.g. mean, variance of each data-point), across four distinct small scale transformer-based models, for a given dataset of text sources. We consider two stylistic environments: a corpus of contemporary poetry and a corpus of academic research papers. We demonstrate that mean and variance of cross-entropy maintain robust cross-model rank correlation ($\rho > 0.90$) across both regimes. To test whether this agreement merely reflects generic differences in textual complexity, we compare it against six parameter-free compression baselines. The extent of agreement among language models is found to be substantially higher than that among model-baselines, for most of the measures. Geometric analysis of the structurally constrained academic regime reveals that higher-order moments are sensitive to specific models, although strong agreement persists. The findings suggest that relative extents of textual unpredictability may be independent of the language model they are computed against.

Tool-using LLM agents are increasingly used to automate workflows governed by procedural manuals, such as company rules for booking travel or procuring hardware. These manuals are written in natural language for humans and describe general requirements over such complex workflows. Ensuring compliance of LLM agents with these manuals is difficult, and state-of-the-art techniques use either LLM judges or manually written rules to forbid problematic tool-calls locally at runtime. This is insufficient because (i) only blocking tool calls keeps the agent clueless about how to make correct progress towards fulfilling its task, and (ii) can lead to overly conservative behavior of the agent, as tool calls might only be problematic in certain contexts. To overcome these challenges, we introduce MENTOR, which (i) additionally provides guidance for the agent to make procedural-compliant progress on the task, and (ii) ensures that this compliance is context-aware. We achieve these goals by building a novel history-dependent runtime shield that is obtained from the procedural manual via a multi-step autoformalization pipeline. At its core, MENTOR utilizes a game-based technique to ensure robustness against runtime uncertainty without over-resticting agents' behavior. This yields a formally assisted framework for procedural shielding of LLM agents that improves compliance well beyond existing methods. In particular, MENTOR lifts the compliance of shielded light-weight open-source LLMs above that of non-shielded proprietary models. Since a shield is synthesized once per manual and then serves every task, a MENTOR-shielded agent becomes a viable choice for repeatedly executed workflows, potentially reducing deployment costs when the offline construction cost is amortized over repeated tasks.

In many practical applications of Bayesian inference, it is difficult or undesirable to compute the gradient of the negative log-posterior, motivating the study of derivative-free samplers, also called zeroth-order samplers. The aim of this paper is to generalize and rigorously analyze a multiscale derivative-free sampler recently proposed in the literature by Pavliotis, Stuart and Vaes (2022). In the discrete-time setting, the multiscale sampler we study bears a strong resemblance to other recently proposed methods, such as the so-called zeroth-order perturbed stochastic gradient descent algorithm (Jin et al., 2018) and the zeroth-order Langevin Monte Carlo algorithm by Roy et al. (2022). We present error estimates with respect to all the parameters of the problem, both in the continuous-time and discrete-time settings. The error estimates are in three different metrics: strong convergence, convergence of ergodic averages, and uniform-in-time weak convergence.

Effective vocal coaching connects performance issues with corrective advice, but recordings paired with expert diagnoses and advice are scarce. Online singing communities provide a potential source of supervision, but observations and advice are scattered across unstructured comments. We introduce PitchIn, audio-language models for natural-language vocal coaching, and the PeerCoach Dataset: 14,445 instruction examples covering Focused QA, Overall Feedback, and Recognition QA. We compare target combinations on Qwen2.5-Omni and train PitchIn on Focused QA and Overall Feedback using Qwen2.5-Omni and MOSS-Music. On VocalCoachBench, the proportion of requested diagnosis-correction pairs matching an expert issue with valid advice rises from 21.3% to 61.0% for Qwen2.5-Omni and from 31.4% to 51.2% for MOSS-Music. Direct training on source comments yields only 19.8% for Qwen2.5-Omni. For Qwen, Focused QA alone reaches 65.6%, but adding Overall Feedback improves alignment with expert reviews and human preference. Both models improve expert-review alignment over pretrained baselines and are significantly preferred for usefulness (92.0% and 67.3%, respectively). Demo examples are available at https://hayeonbang.github.io/PitchIn.

Artificial intelligence faces two growing challenges: computational bottlenecks and energy inefficiency inherent to the von Neumann architecture. Neuromorphic computing offers a promising alternative, yet its immature ecosystem still relies on conventional systems for data supply, requiring efficient conversion between tensor and spike dataflow. We observe a clear mismatch, where data conversion is slow while downstream computation is fast. As data size grows quadratically with large language models, this mismatch becomes a major bottleneck. In this work, we examine the data-conversion components that appear on the critical path of training and inference in neuromorphic LLMs. The work presents FlashT2S (Flash Tensor-to-Spike): GPU-Accelerated Tensor-to-Spike Conversion Operators, which applies architecture-aware and data-centric optimizations to reduce conversion latency. Experimental results show that FlashT2S delivers an average speedup of 850.78x over the native operators across individual operators and 802.83x in realistic workloads. Additionally, compared with GPU kernels automatically generated by torch.compile, our kernels achieve 5-11x speedups. Notably, it achieves near-optimal absolute performance: large-scale conversions are reduced to tens of microseconds (10-99 us), while small-scale conversions reach single-digit microsecond levels (less than 10 us). Furthermore, its standardized output enables seamless integration across heterogeneous backends, including diverse neuromorphic hardware.

We present and analyze a spatially and temporally adaptive high-order method for the one-dimensional Richards equation describing vertical water transport in unsaturated soil, with an emphasis on resolving sharp wetting fronts while satisfying a fully discrete water mass balance. The spatial discretization uses an arbitrary-order local discontinuous Galerkin spectral-element formulation with collocated Legendre-Gauss-Lobatto quadrature, and the time integration is based on a high-order Rosenbrock-Wanner method. We focus primarily on the mixed formulation of the Richards equation, which advances water content as the conserved variable while evaluating the nonlinear diffusion operator in terms of pressure head; the resulting fully discrete scheme satisfies the water mass balance in exact arithmetic, independent of spatial resolution and time step size, including under spatial and temporal adaptivity. In contrast, the pressure-head formulation advances pressure head through a nonlinear capacity function and satisfies the corresponding conservation identity only at the semi-discrete level. Numerical experiments examine convergence through spatial and temporal refinement studies, with mass conservation assessed under spatial and temporal adaptivity using the solver flux output method (SFOM). The SFOM results confirm machine-precision mass conservation for the mixed formulation, whereas the pressure-head formulation exhibits mass balance errors above roundoff. Moreover, in the temporal refinement studies, the mixed formulation yields more accurate solutions than the pressure-head formulation for a prescribed time step size. The combination of high-order accuracy, spatial and temporal adaptivity, and fully discrete mass conservation makes the proposed mixed-form discontinuous spectral-element method a promising approach for simulating unsaturated flow in next-generation land models.

A two-dimensional electron gas in a uniform neutralizing background forms a triangular Wigner crystal at low density. In a strongly mass-asymmetric electron-hole bilayer, localized heavy holes instead provide a nonuniform positive background that supports an electron crystal at densities two orders of magnitude higher than for a homogeneous electron gas in the same material. Here we show that correlated mobile electrons can overturn the preference for triangular order, stabilizing a honeycomb electron-hole crystal. Using the powerful real-space neural-network variational Monte Carlo in the Born-Oppenheimer limit with fixed holes, we find that increasing the density drives a transition from a triangular electron-hole crystal to a honeycomb crystal, which eventually melts into itinerant electrons coexisting with the honeycomb or the triangular hole lattice at fixed interlayer separation. Relative to triangular order, honeycomb order emerges when gains in electronic kinetic energy and electron-hole attraction outweigh its higher intralayer Coulomb repulsion, a threshold never reached in the rigid point-dipole model. Moreover, the honeycomb hole lattice supports paramagnetic, antiferromagnetic, and stripe-ordered spin states. Complex polarization indicates a metal-insulator transition, while the states on the honeycomb hole lattice are consistent with a stripe-ordered Dirac semimetal and paramagnetic or antiferromagnetic Mott insulators via mapping to the half-filled Hubbard model. We further propose a BLG/hBN/WS$_2$-WSe$_2$ heterostructure as a platform for the predicted honeycomb crystal, at an experimentally feasible density $n\sim10^{11}~\text{cm}^{-2}$.

Neural operator splitting composes a library of neural operators, one per physical mechanism, into zero-shot simulators of new equations. Existing approaches, however, require these mechanisms and their labels to be specified in advance. We ask whether a pretrained library can instead be adapted and grown from unlabeled trajectories in which multiple mechanisms act simultaneously. We introduce SPLICE, a framework that discovers operators without mechanism labels on mixture data. The contributions of the candidate operators to each trajectory are inferred by solving a convex optimization problem. A calibrated test then assigns each discovered operator the mechanism it implements. Failure cases are also detectable, when the library lacks the required physics or when mechanisms are insufficiently separable. Across one and two dimensional systems, the discovered operators recover mechanisms from unlabeled mixtures and compose into zero-shot simulators of unseen equations; a frozen library can also grow an operator for physics absent from pretraining, without labels and without forgetting. On Navier-Stokes, the discovered operators compose about as accurately as their supervised counterparts.

Detecting credit card fraud is notoriously difficult because fraudulent charges make up less than 0.2% of total transactions. Quantum Machine Learning (QML), particularly Quantum Kernel Support Vector Machines (QSVM), promises richer feature representations by embedding classical data into high-dimensional Hilbert spaces. However, whether this theoretical advantage holds up when managing real-world financial data bottlenecks remains unclear. We designed a controlled benchmark comparing three quantum encodings, Angle, ZZFeatureMap, and IQP against classical models while keeping sample sizes, feature counts, and scaling strictly matched. To handle class skew without corrupting quantum state overlaps, we embedded synthetic minority oversampling (SMOTE) directly into the quantum Gram matrix workflow, raising PR-AUC scores by roughly +0.04 across feature maps. When trained on the full European credit card dataset with 30 features, classical baselines reached a top PR-AUC of 0.983. However, restricting classical models to match QSVM hardware constraints (500 samples, 4 PCA features) dropped their PR-AUC to 0.750. This puts our best quantum result 0.730 PR-AUC using IQP encoding on 150 samples into realistic context. Testing on physical quantum hardware reduced performance further to 0.62 due to CNOT gate errors and thermal noise. Overall, our findings pinpoint two main operational bottlenecks for near-term quantum kernels: the scaling of Gram matrix evaluation and heavy information loss from squeezing features onto small qubit registers.

We study the boundary corrector $\theta_\epsilon$ in the two-scale expansion for periodic elliptic problems with Dirichlet conditions. By results of Gérard-Varet–Masmoudi and Prange, on smooth uniformly convex domains $\theta_\epsilon$ converges to the solution $\theta^*$ of a homogenized problem with boundary data given by the boundary layer tail $d(n)$, which is determined by a half-space problem for each normal $n$. In the lifted form of Gérard-Varet and Masmoudi, $d(n)$ is given explicitly by the cell correctors and the Dirichlet-to-Neumann operator $N_n$ of this half-space problem. Our main result is that $N_n$ satisfies a nonlinear equation on the period cell alone, so that $d(n)$ and the boundary density that represents it can be computed on the cell. This equation is a Riccati equation in which the derivative in depth is replaced by a commutator with the derivative along $n$. This cell problem can therefore be solved by a Riccati doubling algorithm, and we can compute $d(n)$ at irrational normals without rational approximation. Dropping the commutator term in the cell equation gives an operator square root approximation for $N_n$ that captures the leading term of $d(n)$ for small contrast, for the truncated problem. Finally, we approximate $\theta_\epsilon$ at finite $\epsilon$ by the sum of two solutions of constant coefficient problems, one with oscillatory boundary data and the other $\theta^*$, and test it on the disk.

This paper investigates a shift-sum decoding algorithm that employs dual codewords. Existing dual codeword shift-sum decoding schemes mainly rely on minimum-weight dual codewords. However, the number of such codewords is often limited, which restricts the amount of reliability information available to the decoder. To address this issue, we extend the component counting mechanism from minimum-weight dual codewords to dual codewords whose Hamming weights lie within a prescribed upper bound. We further introduce a normalized component counting rule to suppress the overcounting bias caused by the much larger populations of higher-weight classes. Based on this framework, we develop a hard-decision iterative error reduction decoder and a soft information-aided iterative error reduction decoder. Numerical results show that the proposed method consistently outperforms existing minimum-weight shift-sum baselines especially for short codes where additional dual codeword information is particularly valuable.

Recovering piecewise-smooth functions with jump discontinuities from noisy, indirect, and incomplete data is a central task in computational inverse problems. Bayesian neural networks (BNNs) with heavy-tailed weight priors have emerged as effective edge-preserving priors for such problems. However, posterior inference for these models remains computationally challenging, and existing approaches settle for point estimates obtained by directly optimizing heavy-tailed log-densities. We propose GSBL-BNNs, which model the neural network parameters hierarchically using sparsity-promoting priors from generalized sparse Bayesian learning (GSBL). The hierarchical formulation recovers several popular marginal priors, including Laplace and Student's $t$ (including Cauchy). A key modeling ingredient, novel among edge-preserving BNNs and native to the hierarchical formulation, couples each neuron's bias to its weights through a shared hyperparameter, so that the induced jump discontinuities are free to occur anywhere in the domain while the conditionally Gaussian structure underlying efficient inference is preserved. Furthermore, we develop a block-coordinate descent (BCD) algorithm for maximum a posteriori (MAP) estimation. This BCD approach alternates between standard network training with iteratively reweighted $\ell^2$-regularization and exact, closed-form hyperparameter updates for gamma and inverse gamma hyperpriors. Building on the BCD algorithm, we perform approximate Bayesian inference and uncertainty quantification (UQ) using deep ensembles. Computational experiments—including signal denoising, deblurring, and inverting a two-dimensional hyperbolic conservation law— show that GSBL-BNNs deliver accurate, edge-preserving reconstructions with built-in UQ. Compared with Gaussian- and Cauchy-BNNs, they yield more accurate predictive means and avoid overconfident uncertainty estimates.