To present Mercer large-scale kernel machines from a ridge function perspective, we recall the results by Lin and Pinkus from {\it Fundamentality of ridge functions}. We consider the main result of the recent paper by Rachimi and Recht, 2008, {\it Random features for large-scale kernel machines} from the Approximation Theory point of view. We study which kernels could be approximated by a sum of products of cosine functions with arguments depending on $x$ and $y$ and present the obstacles of such an approach. The results of this article are applied to Image Processing by procedure "one-vs-rest".

Implicit generative modeling (IGM) aims to produce samples of synthetic data matching the characteristics of a target data distribution. Recent work (e.g. score-matching networks, diffusion models) has approached the IGM problem from the perspective of pushing synthetic source data toward the target distribution via dynamical perturbations or flows in the ambient space. In this direction, we present the score difference (SD) between arbitrary target and source distributions as a flow that optimally reduces the Kullback-Leibler divergence between them. We apply the SD flow to convenient proxy distributions, which are aligned if and only if the original distributions are aligned. We demonstrate the formal equivalence of this formulation to denoising diffusion models under certain conditions. We also show that the training of generative adversarial networks includes a hidden data-optimization sub-problem, which induces the SD flow under certain choices of loss function when the discriminator is optimal. As a result, the SD flow provides a theoretical link between model classes that individually address the three challenges of the "generative modeling trilemma" -- high sample quality, mode coverage, and fast sampling -- thereby setting the stage for a unified approach.

Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional integration methods. Here, methods (1) and (2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3) relying on convolutional neural networks. Pure ML methods to solve (nonlinear) PDEs are represented by Physics-Informed Neural network (PINN) methods, which could be combined with attention mechanism to address discontinuous solutions. Both LSTM and attention architectures, together with modern and generalized classic optimizers to include stochasticity for DL networks, are extensively reviewed. Kernel machines, including Gaussian processes, are provided to sufficient depth for more advanced works such as shallow networks with infinite width. Not only addressing experts, readers are assumed familiar with computational mechanics, but not with DL, whose concepts and applications are built up from the basics, aiming at bringing first-time learners quickly to the forefront of research. History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics, even in well-known references. Positioning and pointing control of a large-deformable beam is given as an example.

We present an efficient frequency-based neural representation termed PREF: a shallow MLP augmented with a phasor volume that covers significant border spectra than previous Fourier feature mapping or Positional Encoding. At the core is our compact 3D phasor volume where frequencies distribute uniformly along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored and efficient Fourier transform that combines both Fast Fourier transform and local interpolation to accelerate naïve Fourier mapping. We also introduce a Parsvel regularizer that stables frequency-based learning. In these ways, Our PREF reduces the costly MLP in the frequency-based representation, thereby significantly closing the efficiency gap between it and other hybrid representations, and improving its interpretability. Comprehensive experiments demonstrate that our PREF is able to capture high-frequency details while remaining compact and robust, including 2D image generalization, 3D signed distance function regression and 5D neural radiance field reconstruction.

With the periodic rise and fall of COVID-19 and countries being inflicted by its waves, an efficient, economic, and effortless diagnosis procedure for the virus has been the utmost need of the hour. COVID-19 positive individuals may even be asymptomatic making the diagnosis difficult, but amongst the infected subjects, the asymptomatic ones need not be entirely free of symptoms caused by the virus. They might not show any observable symptoms like the symptomatic subjects, but they may differ from uninfected ones in the way they cough. These differences in the coughing sounds are minute and indiscernible to the human ear, however, these can be captured using machine learning-based statistical models. In this paper, we present a deep learning approach to analyze the acoustic dataset provided in Track 1 of the DiCOVA 2021 Challenge containing cough sound recordings belonging to both COVID-19 positive and negative examples. To perform the classification on the sound recordings as belonging to a COVID-19 positive or negative examples, we propose a ConvNet model. Our model achieved an AUC score percentage of 72.23 on the blind test set provided by the same for an unbiased evaluation of the models. The ConvNet model incorporated with Data Augmentation further increased the AUC-ROC percentage from 72.23 to 87.07. It also outperformed the DiCOVA 2021 Challenge's baseline model by 23% thus, claiming the top position on the DiCOVA 2021 Challenge leaderboard. This paper proposes the use of Mel frequency cepstral coefficients as the feature input for the proposed model.

This paper significantly improves on, and finishes to validate, an approach proposed in previous research in which safety outcomes were predicted from attributes with machine learning. Like in the original study, we use Natural Language Processing (NLP) to extract fundamental attributes from raw incident reports and machine learning models are trained to predict safety outcomes. The outcomes predicted here are injury severity, injury type, body part impacted, and incident type. However, unlike in the original study, safety outcomes were not extracted via NLP but were provided by independent human annotations, eliminating any potential source of artificial correlation between predictors and predictands. Results show that attributes are still highly predictive, confirming the validity of the original approach. Other improvements brought by the current study include the use of (1) a much larger dataset featuring more than 90,000 reports, (2) two new models, XGBoost and linear SVM (Support Vector Machines), (3) model stacking, (4) a more straightforward experimental setup with more appropriate performance metrics, and (5) an analysis of per-category attribute importance scores. Finally, the injury severity outcome is well predicted, which was not the case in the original study. This is a significant advancement.

In light of the increasing availability of digitally recorded safety reports in the construction industry, it is important to develop methods to exploit these data to improve our understanding of safety incidents and ability to learn from them. In this study, we compare several approaches to automatically learn injury precursors from raw construction accident reports. More precisely, we experiment with two state-of-the-art deep learning architectures for Natural Language Processing (NLP), Convolutional Neural Networks (CNN) and Hierarchical Attention Networks (HAN), and with the established Term Frequency - Inverse Document Frequency representation (TF-IDF) + Support Vector Machine (SVM) approach. For each model, we provide a method to identify (after training) the textual patterns that are, on average, the most predictive of each safety outcome. We show that among those pieces of text, valid injury precursors can be found. The proposed methods can also be used by the user to visualize and understand the models' predictions.

The advent of machine learning (ML) and computer vision has significantly accelerated seismic inversion workflows by reducing the computational cost of traditionally expensive iterative methods. However, the development and evaluation of ML methods remain limited by the scarcity of realistic velocity models, as most high-quality data are privately owned by oil and gas companies. To address this gap, we present OpenSeisML, a collection of real seismic datasets designed to support generative AI (Gen-AI) workflows for seismic inversion. The datasets are curated from publicly available surveys in the UK National Data Repository (NDR). When seismic volumes are in the time domain and wells are in depth, a time-to-depth conversion is required. We use checkshot data to establish the time-depth relationship and construct a velocity model through interpolation for accurate conversion of post-stack seismic data. Here, we present an automated data curation pipeline that enables seismic data preparation while ensuring reproducibility. The objective is to train a generative model that captures the statistical distribution of subsurface properties, enabling the synthesis of multiple statistically consistent realizations for uncertainty quantification which can act as a prior for seismic inversion.

Evolving data streams induce joint nonstationarity in continual semantic segmentation, where semantic classes, input distributions, and supervision availability change simultaneously over time. This setting reflects practical structured prediction systems, yet remains largely unexplored in prior continual learning work, which typically studies these factors in isolation. We formalize continual segmentation under coupled class, domain, and label shifts and investigate learning in heterogeneous dense prediction environments with limited annotations and abundant unlabeled data. To address instability and overfitting arising from few-shot supervision under distribution drift, we introduce gradient-adaptive stabilization, a parameter-wise regularization mechanism implemented via gradient-scaled stochastic perturbations that promotes a principled stability-plasticity tradeoff. We further leverage unlabeled data through semi-supervised learning and introduce prototype anchored supervision that validates pseudo-labels via joint confidence and prototype consistency. Together, these mechanisms enable learning under joint nonstationarity in continual segmentation. Extensive empirical evaluation across class-incremental, domain-incremental, and few-shot regimes demonstrates consistent improvements over prior methods in heterogeneous structured prediction settings. Our results expose fundamental failure modes of existing continual segmentation approaches and provide insight into learning robust dense predictors in dynamically evolving environments.

Biomedical named entity recognition (NER) and entity linking (EL) strongly depend on annotated corpora, but the utility of these resources for benchmarking is often assumed rather than characterized. We present a corpus-centric framework for diagnosing benchmark-relevant properties directly from corpus annotations, concept links, train-test splits, document metadata, and terminology mappings. The framework organizes standardized statistics into five families: (1) scale, density and label distribution, (2) lexical and conceptual structure, (3) train-test overlap, (4) metadata composition, and (5) terminology coverage where applicable. Applying the framework to nine corpora spanning diseases, chemicals, and cell types, we find that corpus properties can differ substantially, even when they address the same apparent task. We find differences in the evaluation signal they provide, the generalization demands they impose, the degree of train-test reuse they permit, and the regions of biomedical literature and concept space they represent. These differences suggest that commonly reported corpus statistics can be insufficient to characterize what biomedical NER and EL benchmarks evaluate. We argue that corpus-centric diagnostics provide a practical framework for analyzing corpora beyond surface descriptors such as corpus size and entity type, for identifying potential transfer risks, and for interpreting the scope of benchmarking conclusions. We release the framework as open-source code with an interactive dashboard to support reproducing our analyses and characterizing additional corpora.

Accurate classification of breast ultrasound images into benign, malignant, and normal categories is a critical clinical task complicated by speckle noise, acoustic shadowing, and inter-class visual ambiguity. Existing deep learning methods rely on single-stream architectures with generic augmentation that ignores ultrasound acquisition physics, and no prior method dedicates a stream to the lesion boundary features identified as the most diagnostically significant visual cue. We propose HADS-Net, a Hybrid Attention-Augmented Dual-Stream Network exploiting global texture and local boundary cues through two parallel pathways. Stream 1 applies physics-informed augmentation simulating speckle noise, acoustic shadowing, and gain variation before extracting features via pretrained EfficientNet-B3 projected to 512 dimensions. Stream 2 extracts Sobel edge maps processed by a lightweight CNN projected to the same 512-dimensional space. A cross-attention fusion module allows the texture stream to selectively query boundary features, producing a jointly optimised representation classified by an MLP trained with adaptive class-weighted focal loss. Five-fold stratified cross-validation with cosine annealing over 50 epochs is used, with the globally best checkpoint selected by lowest validation loss evaluated on a held-out test set. On the BUSI dataset, HADS-Net achieves 96.58% accuracy, macro ROC-AUC of 0.9978, macro F1 of 0.9654, and per-class F1-scores of 0.970, 0.951, and 0.976 for benign, malignant, and normal. No malignant lesion is misclassified as normal. These results confirm that modality-specific augmentation with cross-modal attention fusion is an effective strategy for ultrasound-based breast cancer diagnosis.

While deep neural networks have achieved remarkable success across a wide range of domains, their underlying mechanisms remain poorly understood, and they are often regarded as black boxes. This gap between empirical performance and theoretical understanding poses a challenge analogous to the pre-axiomatic stage of classical geometry. In this work, we introduce the Pursuit of Subspaces (PoS) hypothesis, an axiomatic framework that formulates neural network behavior through a set of geometric postulates. These axioms, together with their derived consequences, provide a unified perspective on representation, computation, and generalization in both shallow and deep architectures. We show that this framework yields geometric explanations for fundamental questions in deep learning, including representation structure, architectural mechanisms, and generalization behavior, offering a principled step toward a coherent theoretical foundation.

Optimization algorithms are core methods by which machine learning models iteratively minimize loss functions, update parameters, learn from data, and improve performance. Momentum SGD and AdamW represent two important optimization paradigms. AdamW produces stable updates and usually has strong robustness across training scenarios, but its generalization performance is sometimes weaker than that of momentum methods. Momentum SGD can often obtain better generalization after careful tuning, but it is more sensitive to gradient-scale variation and hyperparameter settings. To balance the strengths and weaknesses of the two paradigms, this paper proposes Ada2MS, an optimization algorithm that achieves a smooth transition between AdamW-like behavior and momentum-SGD-like behavior through continuous exponential interpolation between elementwise second-moment estimates and global second-moment estimates. On the visual tasks evaluated in this study, Ada2MS obtains competitive results under a unified optimizer-comparison protocol. The code will be released at https://github.com/mengzhu0308/Ada2MS

In what ways might statistical signals in linguistic input assist with the acquisition of syntax? Here we hypothesize a mechanism called collocational bootstrapping, in which regularities in word co-occurrence patterns can provide cues to syntactic dependencies. We investigate whether this mechanism can support the acquisition of English subject-verb agreement. First, we simulate language acquisition by training neural networks on synthetic datasets that vary in how predictable their subject-verb pairings are. We find that there is a range of variability levels at which these statistical learners robustly learn subject-verb agreement. We then analyze the variability of subject-verb pairings in child-directed language, and we find that the variability in such data falls within the range that supported robust generalization in our computational simulations. Taken together, these results suggest that collocational bootstrapping is a viable learning strategy for the type of input that children receive.

We present NeuroQA, a large-scale benchmark for visual question answering in 3D brain magnetic resonance imaging (MRI), with 56,953 QA pairs from 12,977 subjects across 12 datasets. It spans ages 5-104 and five clinical domains: Alzheimer's, Parkinson's, tumors, white matter disease, and neurodevelopment. Unlike prior medical Visual Question Answering (VQA) efforts that operate on 2D slices or rely on narrow diagnostic labels, NeuroQA pairs every item with a full 3D volume. It evaluates 11 clinically grounded reasoning skills across Yes/No, multiple-choice, and open-ended formats. Of the 203 templates, 131 are image-grounded (answerable from a 3-plane viewer) and 72 are image-informed (ground truth from quantitative volumetry or clinical instruments). To remove text-only shortcuts, we apply answer-distribution refinement, reducing closed-format text-only accuracy from $>$80% to 44.6%; image necessity is assessed separately through an image-grounding protocol released with the benchmark. A 38-rule deterministic pipeline and two rounds of expert review verify every QA pair against FreeSurfer measurements, metadata, or radiology report fields, with zero same-subject contradictions across templates. We conduct a clinician evaluation in which two clinicians independently assess 100 frozen test items on a three-plane viewer. On closed-format (Yes/No + multiple-choice) test-public items, the best zero-shot vision-language model and a supervised 3D CNN baseline reach 47.5% and 43.7% accuracy respectively, both below the 49.4% text-only majority-template floor. NeuroQA adopts a two-tier release with public QA pairs for open-access datasets and reproducible generation scripts for datasets restricted by data use agreements (DUAs), plus subject-level splits, a held-out private test set, and an online leaderboard.

Advanced fibrosis is a major determinant of liver-related morbidity in metabolic dysfunction-associated steatotic liver disease (MASLD). FIB-4 is widely used as a first-line non-invasive test, but its fixed formula may underuse diagnostic information contained in age, aspartate aminotransferase, alanine aminotransferase, and platelet count. We evaluated whether machine-learning-enhanced non-invasive testing (MLE-NIT) can improve advanced fibrosis detection while preserving this FIB-4 variable space. We used three biopsy-confirmed MASLD cohorts from China, Malaysia, and India (n=784). The Chinese cohort was split into 486 training and 54 internal validation/tuning patients; final performance was reported only on the Malaysian and Indian external cohorts. Models used five variables: age, FIB-4, aspartate aminotransferase, platelet count, and alanine aminotransferase. We compared FIB-4 with a shallow-deep neural network (s-DNN), TabPFN, and gpt-4o-2024-08-06. FIB-4 achieved external ROC-AUCs of 0.75 and 0.60 in Malaysia and India, respectively. TabPFN achieved 0.69 and 0.66, fine-tuned GPT-4o achieved 0.75 and 0.63, and the s-DNN achieved 0.77 and 0.67, respectively. The s-DNN contained only 354 trainable parameters, compared with 7,244,554 for TabPFN, yet provided a more balanced external operating profile. Calibration showed s-DNN Brier scores of 0.18 and 0.22, and permutation importance identified AST and FIB-4 as dominant variables. Compact non-linear MLE-NITs may enhance FIB-4-based fibrosis assessment without increasing clinical data requirements.

Fine-tuning adapts a pretrained machine learning model to a small, sensitive dataset, but this process risks memorizing individual new data points, making the model vulnerable to adversaries who seek to extract sensitive information. In this work, we develop a randomized algorithm based on the exponential mechanism for fine-tuning while ensuring differential privacy. Our key idea is to construct a simple utility function that combines a local quadratic approximation of the pretrained model with information from the new dataset. The resulting exponential mechanism admits exact sampling from a multivariate normal distribution in closed form. We establish theoretical privacy guarantees, sensitivity bounds, and accuracy estimations for our method. We further introduce a random-projection strategy that makes the approach scalable to high-dimensional models. Numerical experiments on the MNIST benchmark and the MIMIC clinical dataset demonstrate competitive performance against existing differentially private fine-tuning techniques.

Benchmark-based evaluation remains important for tracking frontier AI progress. But it can both overstate and understate deployed capability because it privileges tasks that can be precisely specified, automatically graded, easy to optimize for, and run with low budgets and short time horizons. We advocate for a complementary class of evaluations, which we term open-world evaluations: long-horizon, messy, real-world tasks assessed through small-sample qualitative analysis rather than benchmark-scale automation. In this paper we survey recent open-world evaluations, identify their strengths and limitations, and introduce CRUX (Collaborative Research for Updating AI eXpectations), a project for conducting such evaluations regularly. As a first instance, we task an AI agent with developing and publishing a simple iOS application to the Apple App Store. The agent completed the task with only a single avoidable manual intervention, suggesting that open-world evaluations can provide early warning of capabilities that may soon become widespread. We conclude with recommendations for designing and reporting open-world evals.

Modern artificial intelligence systems require calibrated uncertainty estimates that remain reliable in sequential and non-stationary environments. Online conformal prediction (OCP) addresses this challenge through adaptively updated prediction sets that provide deterministic long-run miscoverage guarantees. These guarantees, however, hinge on the assumption of perfect feedback about the coverage of past prediction sets. In practice, the observed miscoverage indicator may be corrupted by noise, communication failures, or adversarial manipulation, which can severely degrade OCP's calibration guarantees. In this paper, we study OCP under corrupted feedback. We first model feedback corruption as an arbitrary binary flip sequence, and analyze how feedback corruption affects and degrades the miscoverage performance of standard OCP. We then propose two robust schemes: robust OCP via filtering, which leverages the structural properties of the predicted threshold to filter corrupted feedback, and robust OCP via active compensation, which incorporates an active compensation mechanism to mitigate the effect of corrupted feedback. For both methods, we establish explicit miscoverage guarantees, which are further specialized for an independent stochastic flip model and for an arbitrary error model with memory bounds. Experiments on real-world datasets validate the proposed approach, showing markedly improved calibration and significantly smaller prediction sets compared with baseline OCP methods under corrupted feedback.

Urban heat exposure is becoming an increasingly critical challenge due to the intensifying urban heat island effect. Fine-grained shade patterns, especially those induced by urban buildings, strongly influence pedestrians' thermal exposure and outdoor activity planning. However, accurately modeling and analyzing urban shade at scale remains difficult because of the lack of large-scale datasets and systematic evaluation frameworks. To address this challenge, we present ShadeBench, a comprehensive dataset and benchmark for urban shade understanding. ShadeBench contains geographically diverse urban scenes with temporally varying simulated shade maps and textual descriptions, together with aligned satellite imagery, building skeleton representations, and 3D building meshes. Built upon this multimodal dataset, ShadeBench supports a range of downstream tasks, including shade generation, shade segmentation, and 3D building reconstruction. We further establish standardized evaluation protocols and baseline methods for these tasks. By enabling scalable and fine-grained shade analysis, ShadeBench provides a foundation for data-driven urban climate research and supports future studies in heat-resilient urban planning and decision-making. The code and dataset are publicly available at https://darl-genai.github.io/shadebench/.

Humans learn social norms and behaviors from verbal feedback (e.g., a parent saying "that was rude" or a friend explaining "here's why that hurt"). Yet, learning from feedback for LLMs has largely focused on domains like code and math, where RL rewards are directly verifiable and condensed into scalar values. As LLMs are increasingly used to simulate human behavior, e.g., standing in for users, patients, students, and other personas, there is a pressing need to make them more human-like, which requires embracing a fundamentally different kind of signal: feedback that is verbal, subjective, and multi-faceted. We present DITTO, a model trained by treating verbal feedback as a first-class signal in reinforcement learning. After each rollout, DITTO receives verbal feedback and generates a feedback-conditioned improved rollout; both outputs are jointly optimized with GRPO, distilling verbal guidance into the base policy without requiring feedback at test time. We also introduce SOUL (Simulation gym Of hUman-Like behavior), a unified benchmark and training data suite spanning 10 tasks across six categories: Theory of Mind, character role play, social skill, learner simulation, user simulation, and persona simulation. DITTO achieves an average 36% improvement over the base model and exceeds GPT-5.4 on 6 of 10 SOUL benchmarks, demonstrating that RL with verbal feedback is a promising direction for training LLMs to simulate human behavior.

We address out-of-distribution (OOD) detection across the full spectrum of distribution shifts -- global domain changes, semantic divergence, texture differences, and covariate corruptions -- through a multi-encoder fusion of per-encoder representation-space diffusion models (RDMs). We statistically identify each encoder's sensitivity to specific shift types from ID data alone and introduce EncMin2L -- an encoder-agnostic two-level $\min(\cdot)$-gate that combines and calibrates per-encoder diffusion-based likelihood detectors without OOD labels, outperforming monolithic multi-encoder baselines at $2.3\times$ lower parameter cost. Two ID-data diagnostics: $η^2$ (class-conditional F-test) and $Δμ$ (log-likelihood shift under synthetic corruptions) -- quantify encoder specialization, while a Tippett minimum $p$-value combination aggregates per-encoder scores into a single, calibration-stable OOD signal. EncMin2L achieves $\geq 0.94$ AUROC across all four shift types simultaneously, outperforming the state-of-the-art representation-space diffusion OOD detectors across overlapping benchmarks.

Deep-learning pipelines for microscopy image classification often require expensive, labor- and time-intensive expert annotation to produce high-quality ground truth for training. Recent work has shown that prompt tuning of vision-language models (VLMs) can reduce manual annotation by constructing a small prompt set of expert-verified image-caption exemplars that is reused as few-shot context to classify all remaining images at inference time. To further reduce effort, the VLM can draft captions for candidate exemplars, which experts then verify and lightly edit instead of writing text de novo. However, two practical questions remain unaddressed: (1) which unlabeled images should be prioritized for verification, and (2) how many verified exemplars are needed to reach a performance target. In this work, we address these questions by formulating prompt-set construction as a target-driven active learning problem that prioritizes which images to annotate. We study three complementary selection criteria under strict low-resource constraints with small unlabeled pools. Experiments show that our methods reach the target performance with substantially fewer expert-verified images than random selection, achieving 100% test accuracy with as few as 20 annotated images on average. More broadly, our human-in-the-loop framework demonstrates a human-centered use of generative AI in biomedical image analysis, where experts remain actively involved in verifying and refining model output while significantly reducing annotation cost. Code and data will be publicly available.

Reliable assessment of tropical cyclone (TC) risk is limited by the brevity and spatial sparsity of the historical record, particularly for the rare, high-intensity landfalls that dominate insured loss. We present WHITS (Wind-focused Hurricane Interactive Track Simulator), a non-parametric semi-Markov track generator that extends the HITS framework of Nakamura et al. (2015) in three ways: transitions between historical track segments are conditioned on local wind speed in addition to position, age, and forward vector; the kernel selection on the comparative-vector term is sharpened to suppress dynamically inconsistent jumps; and a short smoothing window is applied across each transition to remove the position and wind discontinuities reported by downstream surge users. WHITS is fit to the full available best-track record in each of six basins in IBTrACS, extending in the North Atlantic to 1851 and in other basins to the earliest year of reliable best-track data. The resulting 10,000-yr global synthetic catalog reproduces observed track density and the annual hurricane/typhoon-force wind-hit probability across all basins. The catalog is intended for catastrophe-risk applications where a large, low-bias sample of physically plausible tracks is more useful than a small, statistically corrected one.

As autonomous agents increasingly execute end-to-end tasks under fixed monetary budgets, the pressing open question shifts from whether the budget is respected, to how to spend it effectively. Existing budget-aware methods typically control reasoning step-by-step within a single agent, or learn resource allocation policies via RL. None address how to split a budget across the composing phases of a multi-agent pipeline at inference time. We propose ZEBRA, a zero-shot framework that reduces multi-phase budget allocation to a continuous nonlinear knapsack problem: an LLM controller estimates per-phase utility curves, and a water-filling search on the Lagrange multiplier returns the per-phase split. Additive and multiplicative aggregations are unified under the same solver. On a $150$-task APPS coding benchmark, both ZEBRA variants outperform LLM-direct (budget allocation directly by an LLM) on every aggregate metric. At a budget of $α= 0.5$ of the unconstrained spend, ZEBRA recovers $94.4\%$ of unconstrained quality, versus $88.1\%$ for LLM-direct. The advantage is statistically significant and transfers beyond coding: on a $3$-phase HotpotQA pipeline, ZEBRA beats LLM-direct by $14.3$pp, with allocations empirically robust to curve-estimation noise. On HotpotQA, ZEBRA arrives at a different budget split (near-balanced) compared to the APPS one (skewed towards a refinement phase), showing adaptation to the pipeline structure. More broadly, we show that lightweight algorithmic guidance at inference time can improve the economic behavior of autonomous multi-agent systems.

Autonomous navigation in GNSS-denied environments remains a core challenge for legged robots, where exteroceptive sensors such as LiDAR are prone to elevation drift in geometrically sparse or repetitive scenes. We present a factor graph architecture that augments the LIO-SAM framework with a parallel kinematic lane driven by proprioceptive leg odometry, coupled to the main LiDAR-inertial lane via an identity relative pose constraint with a selective noise model. Applied to a Linxai D50 quadruped platform across two outdoor loops totaling over one kilometer, our approach reduces elevation drift from over 30m to under 30cm and enables convergence in a scene where the baseline pipeline fails entirely. These results suggest that proprioceptive data, already computed onboard for gait control, constitutes a lightweight and effective vertical anchor for SLAM in GNSS-denied settings.

Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified quadratic characterizations of scalar relations in the two-dimensional real plane. Candidate quadratic inequalities are locally generated by solving convex quadratic programs using samples from the relation and exterior sample points. They are then verified globally using sum-of-squares certificates over an exact semialgebraic description or, in the case of nonpolynomial relations, over relaxed polynomial descriptions. The resulting verified constraints define a sound overapproximation of the scalar relations over the considered domains. These constraints are directly compatible with existing analysis frameworks based on QCs and pointwise integral quadratic constraints (IQCs) for static nonlinearities and uncertainties, and they can also be embedded in QC-based semidefinite programs for reachability and safety analysis of feedforward neural networks. For smooth activations such as $\tanh$, the method yields domain-dependent quadratic characterizations that constitute an alternative to generic sector- or slope-based descriptions. For ReLU networks, we give methods to reduce conservatism in QC-based reachability analysis of feedforward networks by exploiting dependencies between neurons and tighter local bounds. Numerical examples demonstrate improved reachability results for smooth activations, reduced conservatism for ReLU networks, and applicability beyond neural networks through an example involving saturation.

Hyperparameter prediction is a critical practical bottleneck for model-based image denoisers, ranging from classical TV/TGV variational solvers to modern diffusion-based models such as DiffPIR. While existing learned predictors can achieve near-oracle performance, this approach scales poorly: each new configuration conventionally requires its own oracle-labeled training set, and each label requires a hierarchical grid search evaluated against clean ground truth. We therefore ask whether oracle supervision collected on source configurations can transfer to target configurations with few or no target oracle labels. We propose HyperDn, a single configuration-conditioned predictor that pools oracle supervision across source configurations and predicts heterogeneous hyperparameters for new denoiser--noise configurations. In a cross-paradigm experiment, HyperDn transfers from relatively cheap TV/TGV variational sources to more expensive diffusion-based DiffPIR. With only $2$ target oracle labels, it reaches $30.23$\,dB, within $0.90$\,dB of the oracle, and outperforms the $64$-label per-configuration predictor trained from scratch, using $1/32$ as many target labels as that baseline point. Without any target oracle labels, HyperDn also reaches near-oracle PSNR on two unseen mixtures of seen noise types and on transfer from relatively cheap $96\times 96$ source images to $512\times 768$ targets. Together, these results show that expensive oracle supervision for hyperparameter prediction can be transferred from source to new target configurations, reducing the need to rebuild oracle labels for each new denoising configuration.

LLM-curated tables can appear source-grounded while containing unsupported rows: the curator may recall entries from parametric memory and retroactively attach page-level citations that are not the actual source. We study this hazard in Seed2Frontier discovery: the task of finding complement Wikipedia pages from a seed page to assemble a structured table. Stage-Audit addresses it with disjoint curator-auditor write rights, a row-level source-citation gate, and a 12-check audit taxonomy over keys, schema, source roles, cardinality, and scope. On a curated 51-instance Seed2Frontier evaluation set spanning 15 top-level domains, Stage-Audit improves source-frontier precision over a vanilla LLM curator from 0.356 to 0.505 (+42% relative) and F1 from 0.334 to 0.451 (+35%), while maintaining explicit per-row source traceability. The vanilla-LLM-vs-Stage-Audit comparison isolates the policy contribution rather than LLM-based discovery in general.

Language agents can adapt from experience in interactive environments, but current reflection-based methods can only self-correct within a single task instance. Whether such experience can be distilled into reusable lessons that improve performance on future unseen tasks remains unclear. We address this problem by introducing the In-context Training (ICT) task, a framework for evaluating cross-task self-improvement in language agents. In ICT, a reflector model observes trajectories collected by an actor model and generates system prompts intended to improve the actor's performance on future unseen tasks. We then propose an RL-based training pipeline for learning such reflections directly from experience, without human-provided examples. Across ALFWorld and MiniHack, our trained reflectors outperform an untrained baseline on most held-out task families, showing that the ability to learn from experience can itself be learned. In some cases, we observe generalisation beyond the benchmark on which the reflector was trained, to substantially different environments. Finally, we introduce MetaGym, a generic Python library for constructing meta-environments, enabling future research on self-improving language agents.