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02.
arXiv (quant-ph) 2026-06-16

Encoding parameters by measurement: Forgetting can be better in quantum metrology

arXiv:2512.10541v2 Announce Type: replace Abstract: We introduce quantum parameter estimation with the encoding being via a quantum measurement. We quantify the precision for estimating parameters characterizing a general two-outcome qubit measurement, considering two cases: when the outcomes of the encoding measurement are recorded and when the same are ignored. We find that in a large variety of such estimation scenarios, forgetting the outcomes yields higher precision. We derive a necessary criterion under which remembering the measurement outcomes provides better precision in comparison to the outcome-forgotten strategy. Furthermore, we establish a necessary and sufficient criterion for the simultaneous estimation of multiple parameters encoded by an arbitrary quantum process, including those involving measurements, using qubit probes, and find when the quantum Cramér$-$Rao bound is valid and achievable. For simultaneous estimation of two parameters characterizing the measurement, we find that the achievable quantum Cramér$-$Rao bound can be a valid precision bound only when the measurement direction depends on the parameters of interest.

03.
arXiv (CS.CL) 2026-06-19

FineREX: Fine-Tuned NER-RE for Human Smuggling Knowledge Graphs

Court proceedings contain valuable evidence about human smuggling networks, but this information is often buried within unstructured, jargon-heavy legal documents. While large language models (LLMs) can support knowledge graph construction through automated information extraction, existing approaches rely on general-purpose models that are not tailored to the entity and relationship definitions required in this domain. We introduce FineREX, a streamlined knowledge graph construction pipeline built around a fine-tuned LLM for named entity recognition and relationship extraction (NER-RE). Using a manually annotated dataset of $512$ text chunks, FineREX achieves absolute improvements of 15.50% and 31.46% in entity and relationship F1-score, respectively, compared to a larger general-purpose baseline. These gains translate into higher-quality knowledge graphs, reducing legal noise by nearly half and lowering node duplication on long documents from 17.78% to 11.17%. By eliminating document rewriting and redundant extraction stages, FineREX also reduces end-to-end processing time by 50.0%. Our results demonstrate that domain-specific fine-tuning can substantially outperform larger general-purpose models while improving both the quality and efficiency of knowledge graph construction for illicit network analysis.

04.
medRxiv (Medicine) 2026-06-15

Multi-domain AD risk burden and plasma biomarkers in cognitively unimpaired adults

Introduction: Alzheimer's disease (AD) pathology accumulates decades before symptom onset, yet how the cumulative effect of genetic, familial, and modifiable lifestyle risk burden jointly affects plasma biomarker levels and trajectories in cognitively unimpaired older adults remains unknown. Methods: We analyzed data from 261 participants in the PREVENT-AD cohort. A composite risk score integrating APOE e4 status, polygenic score, family history, and modifiable/lifestyle risk was examined against six plasma biomarkers using linear regression and linear mixed-effects models. Results: APOE e4 was the strongest predictor of plasma biomarker levels. Higher composite risk burden was associated with elevated ptau181, ptau217, ptau217/Ab42, and GFAP levels, and lower Ab42/40 levels. A higher risk burden was predictive of accelerated ptau181 accumulation. Discussion: Cumulative AD risk burden is broadly associated with plasma biomarker levels and specifically predicts accelerated ptau181 accumulation in cognitively unimpaired older adults, supporting structured composite risk profiling as a framework for AD risk stratification.

05.
arXiv (CS.LG) 2026-06-11

Intermittent time series forecasting: local vs global models

arXiv:2601.14031v2 Announce Type: replace-cross Abstract: Forecasting intermittent time series, which contain zeros, is a crucial challenge in supply chains as inventory policies require probabilistic forecasts to establish safety levels. Intermittent time series are commonly forecast using local models, trained individually on each time series. In the last years global models, trained on a large collection of time series, have become popular for time series forecasting. Global models are often based on neural networks or gradient boosted trees. We carry out the first study comparing state-of-the-art probabilistic local and global models on intermittent time series. For global models we consider three different distribution heads suitable for intermittent time series: negative binomial, hurdle-shifted negative binomial and Tweedie. To the best of our knowledge, this is the first use of the latter two with neural networks. We perform experiments on five datasets comprising overall more than 40'000 real-world time series. Among global models, TiDE, a simple neural network architecture, achieves the best accuracy; it also consistently outperforms local models and has lower computational requirements. Large global models are instead much more computationally demanding and less accurate. Among the distribution heads, the Tweedie provides the best estimates of the highest quantiles.

06.
arXiv (CS.LG) 2026-06-12

Quantizing Time-Series Models As Dynamical Systems: Trajectory-Based Quantization Sensitivity Score

arXiv:2606.13300v1 Announce Type: new Abstract: We introduce the Trajectory-based Quantization Sensitivity Score (TQS), a metric that reframes post-training quantization (PTQ) through the lens of dynamical-systems stability. By modeling the network's rollout as a discrete-time dynamical system, TQS characterizes how quantization-induced errors propagate and amplify over the rollout horizon. Unlike conventional PTQ methods, where sensitivity analysis is often coupled to the quantization procedure, TQS enables a priori sensitivity estimation decoupled from quantizer selection and bit-width assignment. This separation allows for quantization budget planning even for black-box or compiled networks with fused operators. Building on this, we present TQS-PTQ, a flexible mixed-precision framework that requires no calibration data or costly second-order approximations. Our experiments show that a dynamical-systems perspective provides a robust, high-performing pathway for low-precision deployment in resource-constrained settings.

07.
Nature Medicine 2026-06-12

The Hong Kong Genome Project is a flagship initiative for precision medicine in Chinese populations

作者: 未知作者

The Hong Kong Genome Project established a genome sequencing database that provides improved diagnoses for patients and more efficient, population-tailored carrier status screening. Actionable pharmacogenomic variants were identified in almost all participants, informing drug prescriptions. This work establishes a genomic resource and a transferable model for equitable precision medicine in underrepresented populations worldwide.

08.
arXiv (quant-ph) 2026-06-19

Vine Codes: Low-Overhead Quantum LDPC Codes on a Planar Square Grid

arXiv:2606.20263v1 Announce Type: new Abstract: The surface code is a promising route towards large-scale quantum computing, requiring only nearest-neighbour gates amenable to superconducting hardware. However, surface codes incur large qubit overheads. Novel quantum low-density parity check (qLDPC) codes promise to reduce overheads but require long-range connections that are difficult to achieve on superconducting platforms. Here, we introduce "Vine Codes" - qLDPC codes that are implementable on a planar square grid through nearest-neighbour, two-qubit gates native to superconducting platforms (iSWAP and CZ). Our approach generalises "Directional Codes" recently introduced by Gehér et. al. (2025) which are constrained to a torus. In contrast, vine codes have open boundary conditions constructed with the aid of routing qubits. We perform extensive numeric searches and find promising candidate vine codes, e.g. [[121,4,6]], [[221,6,7]], and [[234,9,6]] codes. We verify the circuit distances and show that data and measure qubits required can be reduced by up to ~28% relative to the surface code at a circuit distance of 7. Even including routing qubits, vine codes require fewer total qubits than the surface code (e.g. ~18% reduction at circuit distance 10) and benefits are expected to increase at higher distances. We perform circuit-level noise simulations to demonstrate that under a realistic noise model and at a near-term noise rate of $10^{-3}$, vine codes can perform better than the surface code while using fewer qubits. We give an exhaustive list of all unique vine codes up to stabiliser-weight 9. We additionally introduce "Flip-Vine Codes" which possess single-qubit transversal Clifford gates useful for fault-tolerant logic and magic state cultivation. We furthermore construct examples of generalised open boundaries for vine codes that go beyond the familiar X/Z boundaries of the surface and tile codes.

09.
arXiv (CS.LG) 2026-06-19

Towards Graph-Based Deep Learning for Map Generalization: Insights from Building Footprints Simplification and Aggregation

arXiv:2606.19956v1 Announce Type: new Abstract: Map generalization remains one of the fundamental tasks in cartography, especially for the simplification and aggregation of complex building footprints. This study presents the first exploratory application of graph-based deep learning to both tasks, reformulating simplification as node movement prediction and aggregation as link prediction within a unified graph learning framework. We evaluate representative graph neural network architectures (GCN, GAT, and GraphSAGE) on multi-scale building datasets, showing that GraphSAGE demonstrates relative strengths in link prediction accuracy, while also revealing persistent challenges in precise node movement prediction. Beyond quantitative performance, the results highlight that aggregation poses greater complexity and challenges than simplification, underscoring the difficulty of capturing higher-level spatial relationships in map generalization with current deep learning approaches. Although limitations such as data imbalance and the need for post-processing remain, the study provides valuable insights and methodological directions for advancing automated map generalization with deep learning approaches.

10.
arXiv (CS.AI) 2026-06-19

CTS-MoE: Implicit Terrain Adaptation via Mixture-of-Experts for Perceptive Locomotion

arXiv:2606.19633v1 Announce Type: cross Abstract: Perceptive legged locomotion over discontinuous terrain (e.g., stairs, gaps, and obstacles) requires adaptive behavior, as a single conservative gait cannot produce the anticipatory maneuvers needed for abrupt topology changes. Cast as multi-task reinforcement learning, this problem introduces a tension between sharing and separation. Tasks use a common locomotion base but have conflicting rewards, so a policy must share behavior while avoiding value interference. Prior work addresses only one side, with monolithic policies sacrificing specialization and hierarchical sub-policies sacrificing generalization across transitions and unseen terrain. We propose CTS-MoE, which combines a dense mixture-of-experts actor with perception-based gating to compose shared behaviors and a multi-critic with task-specific value heads to prevent interference. The model is trained end-to-end in a single-stage concurrent teacher-student setup that handles partial observability and avoids sequential distillation, with task labels used only during training. At deployment, routing depends solely on perception, allowing terrain adaptation without a high-level selector or terrain classifier. Experiments on a Unitree Go1 in simulation and on hardware across seen and unseen terrains show task-aware specialization, with lower tracking error and higher success rates than monolithic baselines. Project Website: https://cts-moe.github.io/ .

11.
arXiv (CS.CV) 2026-06-16

Adaptive Inference-Time Scaling via Early-Step Latent Verification for Image Editing

Instruction-based image editing has made notable progress with recent advances in generative models. However, the quality of the edited result is still influenced by the randomly sampled initial noise, particularly in complex editing scenarios. An unsuitable initial noise may lead to unsatisfactory editing results. Recent inference-time scaling methods address this issue by sampling multiple initial noises and selecting better candidates. Nevertheless, most of them follow a decode-then-verify scheme which introduces an efficiency-accuracy trade-off. When decoding is performed after limited inference steps, the decoded images often remain too noisy for reliable assessment, whereas sufficiently denoised images require much higher computational cost. To address this issue, we propose VeriLatent, a plug-and-play adaptive inference-time scaling framework with early-step latent verification for image editing. Specifically, we propose a novel verifier that scores each initial noise through a latent-space editing activation map at an early stage. It identifies promising candidates by assessing whether they can induce an effective edit in the correct region. This enables efficient early pruning without decoding latents into images. Building on this, we further develop an adaptive search strategy for inference-time scaling. It allocates inference budgets according to editing difficulty, thereby reducing the number of function evaluations (NFE). Extensive experiments on multiple benchmarks and different base models demonstrate that VeriLatent consistently improves both editing performance and inference-time scaling efficiency.

12.
arXiv (CS.LG) 2026-06-19

Insulin4RL: Real-Time Insulin Management in the Intensive Care Unit for Offline Reinforcement Learning

arXiv:2606.19481v1 Announce Type: new Abstract: Offline reinforcement learning (ORL) offers the potential to improve the quality of clinical decision-making using historical electronic health record (EHR) data. Current training and evaluative practices in this field rely heavily on EHR datasets that have been temporally discretised into fixed, regular time intervals. Discretisation creates fictional representations of complex clinical scenarios and compromises the generalisability of retrospective model evaluations. In this paper, we introduce Insulin4RL, a healthcare ORL dataset featuring naturally irregular inputs and actions from real clinical trajectories. Derived from MIMIC-IV, Insulin4RL comprises over 375,000 labelled decisions across 12,209 patients requiring insulin infusion titration in the Intensive Care Unit. The dataset can thus be used for research into ORL model performance under realistic clinical sampling assumptions. We provide a description of the dataset's structure and characteristics, baseline performance metrics using model-free offline reinforcement learning, and a standardised evaluation protocol using fitted Q-evaluation. We conclude with suggested areas for future research that could be addressed using this resource.

13.
arXiv (CS.AI) 2026-06-15

Sorries Are Not the Hard Part: An Expert-Review Case Study of a Semi-Autonomous Formalization

arXiv:2606.13925v1 Announce Type: new Abstract: Large language models can often close proof gaps in interactive theorem provers, but a verified theorem is not the same thing as a reusable library contribution. We study this distinction through a detailed case study: a semi-autonomous formalization of Grothendieck's vanishing theorem. The initial version compiles with no sorries, but an expert review found serious problems in definitions, theorem generality, file organization, and the API. We then ran a review-driven refactor and compression process and obtained a second expert review. The before-and-after comparison shows a sharp split: agents adapted well to local, mechanically checkable feedback, but remained weak at choosing definitions and designing APIs. We argue that autoformalization should be evaluated not only by closed sorries, but by whether the resulting formalization survives expert review.

14.
arXiv (CS.CL) 2026-06-11

GraphInfer-Bench: Benchmarking LLM's Inference Capability on Graphs

Graph analysis underlies many applications whose answers cannot be looked up in a single record or retrieved along a path: laundering rings, drug repurposing, user preference, and scientific theme are all inferred from a node together with its neighbourhood. We introduce GraphInfer-Bench, a benchmark for whether LLMs can perform this graph inference: producing an open-ended answer that no single node supports and no path retrieves. Existing graph-QA protocols cannot test this capability: algorithm simulation, node classification, single-node description, KG-QA, and GraphRAG all admit answers retrievable from one node or along a path. GraphInfer-Bench defines five tasks along Description (what a region is) and Comparison (how regions differ), each constructed so the ground truth lives in no single node. The release contains 42,000 samples across six real-world graphs, produced automatically and screened by a four-layer quality-control protocol. We evaluate four method families against the same tasks: graph-token alignment models, zero-shot frontier closed-source LLMs, Graph2Text supervised fine-tuning, and plain GNNs as a structural reference. No method family closes the gap. Graph-token alignment partially handles description tasks (relational, theme) but collapses on comparison tasks. Frontier LLMs lead on outlier detection and community partition among LLM-based methods but lag on masked-node prediction. Graph2Text SFT is the strongest LLM-based method on the description side yet falls behind frontier LLMs on comparison. Across every task, plain GNNs match or beat the strongest LLM-based row, with the largest margin on community detection. GraphInfer-Bench surfaces graph inference as an open capability gap rather than a property of any one architecture.

15.
arXiv (CS.CV) 2026-06-12

From Seeing to Experiencing: Scaling Navigation Foundation Models with Reinforcement Learning

Navigation foundation models trained on massive web-scale data enable agents to generalize across diverse environments and embodiments. However, these models, which are trained solely on offline data, often lack the capacity to reason about the consequences of their actions or adapt through counterfactual understanding. They thus face significant limitations in real-world urban navigation, where interactive and safe behaviors, such as avoiding obstacles and moving pedestrians, are critical. To tackle these challenges, we introduce the Seeing-to-Experiencing (S2E) learning framework to scale the capability of navigation foundation models with reinforcement learning. S2E combines the strengths of pretraining on offline videos and post-training through reinforcement learning. It maintains the model's generalizability acquired from large-scale real-world videos while enhancing its interactivity through reinforcement learning in simulation environments. Specifically, we introduce two innovations: (1) an Anchor-Guided Distribution Matching strategy for offline pretraining, which stabilizes learning and models diverse motion patterns through anchor-based supervision; and (2) a Residual-Attention Module for reinforcement learning, which obtains reactive behaviors from simulation environments without erasing the model's pretrained knowledge. Moreover, we establish a comprehensive end-to-end evaluation benchmark, NavBench-GS, built on photorealistic 3D Gaussian Splatting reconstructions of real-world scenes that incorporate physical interactions. It can systematically assess the generalizability and safety of navigation foundation models.

16.
medRxiv (Medicine) 2026-06-17

Cross-Device Adaptation of Mirai for Mammography-Based Breast Cancer Risk Prediction

Fine-tuning can adapt pretrained medical imaging models to new clinical datasets, but device-specific domain shifts may limit generalizability. We evaluated Mirai, a mammography-based deep learning model for breast cancer risk prediction, in a large screening cohort containing Hologic and General Electric (GE) full-field digital mammography systems, including GE Premium View (GE PV) and Tissue Equalization (GE TE) post-processing software. Native Mirai showed lower performance on TE images than on Hologic or PV images. Fine-tuning on TE images improved TE performance, particularly for short-term risk prediction, but substantially reduced performance on Hologic images, consistent with catastrophic forgetting. To mitigate this effect, we developed a device-invariant model using interleaved multi-device sampling and conditional adversarial training. This approach largely restored Hologic performance while maintaining improved TE performance, providing better robustness across heterogeneous imaging platforms. Comparison of cumulative and annual risk AUCs over a five-year time horizon further showed that performance gains were driven mainly by short- and intermediate-term predictions. These findings highlight both the value and dangers of device-specific fine-tuning and support balanced domain-adaptation strategies for deploying mammography-based risk models across diverse clinical imaging environments.

17.
arXiv (CS.CV) 2026-06-17

WeaveLA: Event Driven Cross-Subtask Latent Memory Weaving for Repetitive Robot Manipulation

Vision-Language-Action (VLA) policies have achieved remarkable single-step manipulation, yet they remain brittle precisely where each stage depends on what was just completed. The core issue is structural: short-window VLAs lack an explicit channel for rouxting information across sub-task boundaries, and existing memory-augmented variants either write at every frame, retrieve from demonstration-time stages, or fire at sub-goal events without performing an explicit sub-task-to-sub-task hand-off into the action expert. We identify the sub-goal completion event as the natural temporal unit for cross-subtask memory hand-off, and present WeaveLA (Weave Latent memory for Vision-Language-Action policies), a cross-subtask memory interface that, on top of a frozen VLA backbone, compresses each completed segment into latent tokens via query-driven attention pooling and routes them directly into the action-generation path of the next sub-task. This event-triggered, action-side design preserves the base policy's short-window interface while adding a lightweight cross-subtask channel. Through stratified evaluation on RoboMME with a $\pi_{0.5}$ backbone, WeaveLA's gains land exactly where the channel is needed: on the hardest repetition slice (SwingXtimes, $N{=}3$), success rises from $0\%$ to $47.8\%$, while single-execution episodes remain unchanged. Per-episode paired analysis confirms the gains are confined to tasks whose causal structure requires cross-subtask information.

18.
arXiv (math.PR) 2026-06-16

Mean-field BSDEs with non-Lipschitz coefficients and double mean reflections

arXiv:2510.11228v2 Announce Type: replace Abstract: The present paper is devoted to the study of mean-field backward stochastic differential equations (MFBSDEs) with double mean reflections whose generators are not Lipschitz continuous. With the help of the Skorokhod problem and some a priori estimates for MFBSDEs, we establish the existence and uniqueness results for doubly mean reflected MFBSDEs.

19.
arXiv (CS.AI) 2026-06-16

Adaptive $k$NN graph model

arXiv:2601.16509v2 Announce Type: replace-cross Abstract: The $k$-nearest neighbors ($k$NN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size ($k$). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the inherent inference bottleneck of $k$NN, laying an adaptive structural foundation for graph-based nonparametric learning.

20.
arXiv (CS.LG) 2026-06-16

ROVE: Unlocking Human Interventions for Humanoid Manipulation via Reinforcement Learning

arXiv:2606.17011v1 Announce Type: cross Abstract: Human interventions provide crucial corrective signals for post-training Vision-Language-Action (VLA) models. However, enabling seamless humanoid interventions is a formidable systems challenge due to complex whole-body kinematics and dexterous-hand control. Consequently, the collected intervention trajectories are often suboptimal, and methods that rely on human interventions as expert supervision can absorb hesitant, inefficient, or even erroneous behaviors. To address both the system and algorithmic challenges, we propose ROVE, a reinforcement learning framework for humanoid VLA post-training with imperfect human interventions. First, ROVE introduces a human-in-the-loop pipeline capable of collecting deployment and intervention data for humanoid manipulation. Second, it utilizes Optimistic Value Estimation (OVE) to prioritize high-value behaviors from mixed-quality trajectories. To further robustify value estimation, we incorporate cross-embodiment human experience videos to provide rich supervision for long-tailed failure and recovery modes. The resulting critic yields informative advantage signals, steering the VLA actor to focus on high-value behaviors rather than indiscriminately imitating all actions. On challenging real-world contact-rich and fine-grained humanoid manipulation tasks, ROVE outperforms experience-learning baselines and consistently improves across multiple rollout-intervention iterations.

21.
arXiv (CS.LG) 2026-06-15

A Low-Rank Subspace Analysis of LLM Interventions

arXiv:2606.14388v1 Announce Type: new Abstract: Interventions designed to modify a particular behavior in LLMs, such as refusal or sycophancy, often produce unintended changes in other behaviors. This lack of targeted control makes it difficult to design and implement reliable safety controls. To understand these side-effects, we introduce a diagnostic framework for analyzing interacting behaviors in LLMs. We model behaviors as low-rank subspaces in activation space, and study how interventions influence across behaviors. Across multiple instruction-tuned models (7B-70B) and across refusal, jailbreak, and sycophancy settings, we find that different behaviors share internal representations, and intervening on one behavior alters others in asymmetric ways. Some behaviors act as upstream control points whose interventions propagate broadly across other behaviors, while others remain more isolated. We relate these effects to two geometric quantities: (i) the overlap between behavior subspaces, measured as the average squared cosine of principal angles, and (ii) the angle between each behavior subspace and the decision subspace (capturing the model's final decision e.g., refuse vs. comply). Empirically, intervention effects on other behaviors tend to be larger for behavior pairs with higher subspace overlap, and for source behaviors whose subspaces lie closer (smaller angle) to the decision subspace. These findings highlight a challenge for targeted behavior control: behaviors are difficult to modify independently, as interventions can propagate through shared representations and asymmetric interactions.

22.
arXiv (CS.CV) 2026-06-15

Fusion of Pervasive RF Data with Spatial Images via Vision Transformers for Enhanced Mapping in Smart Cities

In this paper, we present a deep learning-based approach that integrates the DINOv2 architecture to improve building mapping by combining (possibly erroneous) maps from open-source platforms with pervasive radio frequency (RF) data collected from multiple wireless user equipments and base stations. Unlike prior methods, our approach leverages a vision transformer-based architecture to jointly process both RF and map modalities within a unified framework, effectively capturing spatial dependencies and structural priors for enhanced mapping accuracy. For the evaluation purposes, we employ a synthetic dataset co-produced by Huawei. To address the challenges associated with real-world data imperfections, we introduce controlled noise to its RF data so as to simulate real-world conditions. Additionally, we develop and train a model that leverages only aggregated path loss information to tackle the mapping problem. We measure the results according to three performance metrics: the Jaccard index (intersection over union, IoU), the Hausdorff distance, and the Chamfer distance. Our design achieves a macro IoU of 65.3%, significantly surpassing (i) the erroneous maps baseline, which yields 40.1%, (ii) an RF-only method from the literature, which yields 37.3%, and (iii) a non-AI fusion baseline that we designed which yields 42.2%. The comparative evaluation highlights the limitations of relying solely on RF data or on spatial data, as well as the effectiveness that AI can have on fusing data towards enhancing smart city mapping accuracy. We further validate our method on real-world data from the Oslo region, complementing the synthetic evaluation with a real deployment setting, where our best fusion model reaches 64.9% macro IoU. We additionally outline a strategy for deploying the model over larger areas by tiling the region with overlapping windows.

23.
arXiv (CS.LG) 2026-06-19

Statistical Properties of Training & Generalization

arXiv:2606.20299v1 Announce Type: cross Abstract: Deep learning has managed to evade numerous intuitions from classical statistics to achieve unprecedented performance on a number of real-world tasks. In this article, we investigate the key features and surprises of deep learning from a physics-informed perspective, taking care to point out and justify where possible the many choices inherent in constructing a deep learning model. In particular, we review the phenomenon of neural scaling laws and discuss their interplay with the constraints and inductive biases which may be present when applying machine learning to problems in physics.

25.
arXiv (CS.LG) 2026-06-11

Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification

arXiv:2606.11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation. In this work, we construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates. Remarkably, the exterior calculus that imposes physical conservation structure also exposes topological structure that we use to build a Gaussian process (GP) representation of uncertainty in state-flux relationships, ultimately yielding a Dirichlet-to-Neumann map for quantities of interest with closed-form expressions for posterior uncertainty. We specifically propose structure-preserving $H(\mathrm{div})$–$L^2$ subspaces of conventional Raviart–Thomas and $dgP_0$ elements prescribed by a lightweight transformer. Reduced-order dynamics consistent with this subspace are learned by posing a conservation law in which a GP describes the fluxes between volumes. This work hinges on a novel interface between mixed FEM spaces and GP regression; when training is posed as the optimal recovery problem (ORP), the resulting GP regression can be written as an optimization problem with equality constraints that impose a conservation structure, amenable to a fast Schur-complement training strategy. The trained model can then be solved in real time with closed-form estimators for boundary fluxes driven by prescribed Dirichlet data. The paper includes RKHS posterior error bounds for linear functionals to support uncertainty quantification, as well as numerical experiments demonstrating the accuracy of the posterior distribution as a surrogate for error estimation.