Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits structured dependencies - particularly in applications like denoising score learning where multiple noisy observations derive from shared underlying signals. We present the first systematic study of KRR generalization for non-i.i.d. data with signal-noise causal structure, where observations represent different noisy views of common signals. By developing a novel blockwise decomposition method that enables precise concentration analysis for dependent data, we derive excess risk bounds for KRR that explicitly depend on: (1) the kernel spectrum, (2) causal structure parameters, and (3) sampling mechanisms (including relative sample sizes for signals and noises). We further apply our results to denoising score learning, establishing generalization guarantees and providing principled guidance for sampling noisy data points. This work advances KRR theory while providing practical tools for analyzing dependent data in modern machine learning applications.

Two-photon lithography (TPL) is a sophisticated additive manufacturing technology for creating three-dimensional (3D) micro- and nano-structures. Maintaining the health of TPL systems is critical for ensuring consistent fabrication quality. Current maintenance practices often rely on experience rather than informed monitoring of machine health, resulting in either untimely maintenance that causes machine downtime and poor-quality fabrication, or unnecessary maintenance that leads to inefficiencies and avoidable downtime. To address this gap, this paper presents three methods for accurate and timely monitoring of TPL machine health. Through integrating physics-informed data-driven predictive models for structure dimensions with statistical approaches, the proposed methods are able to handle increasingly complex scenarios featuring different levels of generalizability. A comprehensive experimental dataset that encompasses six process parameter combinations and six structure dimensions under two machine health conditions was collected to evaluate the effectiveness of the proposed approaches. Across all test scenarios, the approaches are shown to achieve high accuracies, demonstrating excellent effectiveness, robustness, and generalizability. These results represent a significant step toward condition-based maintenance for TPL systems.

The receiver operating characteristic (ROC) curve and its summary measure, the Area Under the Curve (AUC), are well-established tools for evaluating the efficacy of biomarkers in biomedical studies. Compared to the traditional ROC curve, the covariate-adjusted ROC curve allows for individual evaluation of the biomarker. However, the use of machine learning models has rarely been explored in this context, despite their potential to develop more powerful and sophisticated approaches for biomarker evaluation. The goal of this paper is to propose a framework for neural network-based covariate-adjusted ROC modeling that allows flexible and nonlinear evaluation of the effectiveness of a biomarker to discriminate between two reference populations. The finite-sample performance of our method is investigated through extensive simulation tests under varying dependency structures between biomarkers, covariates, and referenced populations. The methodology is further illustrated in a clinically case study that assesses daily physical activity - measured as total activity time (TAC), a proxy for daily step count-as a biomarker to predict mortality at three, five and eight years. Analyzes stratified by sex and adjusted for age and BMI reveal distinct covariate effects on mortality outcomes. These results underscore the importance of covariate-adjusted modeling in biomarker evaluation and highlight TAC's potential as a functional capacity biomarker based on specific individual characteristics.

Consider two sets of entities and their members' mutual affinity values, say drug-target affinities (DTA). Drugs and targets are said to interact in their effects on DTAs if drug's effect on it depends on the target. Presence of interaction implies that assigning a drug to a target and another drug to another target does not provide the same aggregate DTA as the reversed assignment would provide. Accordingly, correctly capturing interactions enables better decision-making, for example, in allocation of limited numbers of drug doses to their best matching targets. Learning to predict DTAs is popularly done from either solely from known DTAs or together with side information on the entities, such as chemical structures of drugs and targets. In this paper, we introduce interaction directions' prediction performance estimator we call interaction concordance index (IC-index), for both fixed predictors and machine learning algorithms aimed for inferring them. IC-index complements the popularly used DTA prediction performance estimators by evaluating the ratio of correctly predicted directions of interaction effects in data. First, we show the invariance of IC-index on predictors unable to capture interactions. Secondly, we show that learning algorithm's permutation equivariance regarding drug and target identities implies its inability to capture interactions when either drug, target or both are unseen during training. In practical applications, this equivariance is remedied via incorporation of appropriate side information on drugs and targets. We make a comprehensive empirical evaluation over several biomedical interaction data sets with various state-of-the-art machine learning algorithms. The experiments demonstrate how different types of affinity strength prediction methods perform in terms of IC-index complementing existing prediction performance estimators.

Background: Cribriform morphology in prostate cancer is a histological feature that indicates poor prognosis and contraindicates active surveillance. However, it remains underreported and subject to significant interobserver variability amongst pathologists. We aimed to develop and validate an AI-based system to improve cribriform pattern detection. Methods: We created a deep learning model using an EfficientNetV2-S encoder with multiple instance learning for end-to-end whole-slide classification. The model was trained on 640 digitised prostate core needle biopsies from 430 patients, collected across three cohorts. It was validated internally (261 slides from 171 patients) and externally (266 slides, 104 patients from three independent cohorts). Internal validation cohorts included laboratories or scanners from the development set, while external cohorts used completely independent instruments and laboratories. Annotations were provided by three expert uropathologists with known high concordance. Additionally, we conducted an inter-rater analysis and compared the model's performance against nine expert uropathologists on 88 slides from the internal validation cohort. Results: The model showed strong internal validation performance (AUC: 0.97, 95% CI: 0.95-0.99; Cohen's kappa: 0.81, 95% CI: 0.72-0.89) and robust external validation (AUC: 0.90, 95% CI: 0.86-0.93; Cohen's kappa: 0.55, 95% CI: 0.45-0.64). In our inter-rater analysis, the model achieved the highest average agreement (Cohen's kappa: 0.66, 95% CI: 0.57-0.74), outperforming all nine pathologists whose Cohen's kappas ranged from 0.35 to 0.62. Conclusion: Our AI model demonstrates pathologist-level performance for cribriform morphology detection in prostate cancer. This approach could enhance diagnostic reliability, standardise reporting, and improve treatment decisions for prostate cancer patients.

Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging recent techniques to incorporate structural priors derived from optimization dynamics. Central to our approach is modeling the trajectory induced by gradient descent as a trajectory inference problem. We unify several trajectory inference techniques towards matching a gradient flow, providing a theoretical framework for treating optimization paths as inductive bias. We further explore architectural and algorithmic choices, including reward fine-tuning by adjoint matching, the use of autoencoders for latent weight representation, conditioning on task-specific context data, and adopting informative source distributions such as Kaiming uniform. Experiments demonstrate that our method matches or surpasses baselines in generating in-distribution weights, improves initialization for downstream training, and supports fine-tuning to enhance performance. Finally, we illustrate a practical application in safety-critical systems: detecting harmful covariate shifts, where our method outperforms the closest comparable baseline.

Defective surgical instruments pose serious risks to sterility, mechanical integrity, and patient safety, increasing the likelihood of surgical complications. However, quality control in surgical instrument manufacturing often relies on manual inspection, which is prone to human error and inconsistency. This study introduces SurgScan, an AI-powered defect detection framework for surgical instruments. Using YOLOv8, SurgScan classifies defects in real-time, ensuring high accuracy and industrial scalability. The model is trained on a high-resolution dataset of 102,876 images, covering 11 instrument types and five major defect categories. Extensive evaluation against state-of-the-art CNN architectures confirms that SurgScan achieves the highest accuracy (99.3%) with real-time inference speeds of 4.2-5.8 ms per image, making it suitable for industrial deployment. Statistical analysis demonstrates that contrast-enhanced preprocessing significantly improves defect detection, addressing key limitations in visual inspection. SurgScan provides a scalable, cost-effective AI solution for automated quality control, reducing reliance on manual inspection while ensuring compliance with ISO 13485 and FDA standards, paving the way for enhanced defect detection in medical manufacturing.

Causal discovery algorithms often perform poorly with limited samples. While integrating expert knowledge (including from LLMs) as constraints promises to improve performance, guarantees for existing methods require perfect predictions or uncertainty estimates, making them unreliable for practical use. We propose the Guess2Graph (G2G) framework, which uses expert guesses to guide the sequence of statistical tests rather than replacing them. This maintains statistical consistency while enabling performance improvements. We develop two instantiations of G2G: PC-Guess, which augments the PC algorithm, and gPC-Guess, a learning-augmented variant designed to better leverage high-quality expert input. Theoretically, both preserve correctness regardless of expert error, with gPC-Guess provably outperforming its non-augmented counterpart in finite samples when experts are "better than random."

Motherboard defect detection is critical for ensuring reliability in high-volume electronics manufacturing. While prior research in PCB inspection has largely targeted bare-board or trace-level defects, assembly-level inspection of full motherboards inspection remains underexplored. In this work, we present BoardVision, a reproducible framework for detecting assembly-level defects such as missing screws, loose fan wiring, and surface scratches. We benchmark two representative detectors - YOLOv7 and Faster R-CNN, under controlled conditions on the MiracleFactory motherboard dataset, providing the first systematic comparison in this domain. To mitigate the limitations of single models, where YOLO excels in precision but underperforms in recall and Faster R-CNN shows the reverse, we propose a lightweight ensemble, Confidence-Temporal Voting (CTV Voter), that balances precision and recall through interpretable rules. We further evaluate robustness under realistic perturbations including sharpness, brightness, and orientation changes, highlighting stability challenges often overlooked in motherboard defect detection. Finally, we release a deployable GUI-driven inspection tool that bridges research evaluation with operator usability. Together, these contributions demonstrate how computer vision techniques can transition from benchmark results to practical quality assurance for assembly-level motherboard manufacturing.

Mammography, the current standard for breast cancer screening, has reduced sensitivity in women with dense breast tissue, contributing to missed or delayed diagnoses. Thermalytix, an AI-based thermal imaging modality, captures functional vascular and metabolic cues that may complement mammographic structural data. This study investigates whether a breast density-informed multi-modal AI framework can improve cancer detection by dynamically selecting the appropriate imaging modality based on breast tissue composition. A total of 324 women underwent both mammography and thermal imaging. Mammography images were analyzed using a multi-view deep learning model, while Thermalytix assessed thermal images through vascular and thermal radiomics. The proposed framework utilized Mammography AI for fatty breasts and Thermalytix AI for dense breasts, optimizing predictions based on tissue type. This multi-modal AI framework achieved a sensitivity of 94.55% (95% CI: 88.54-100) and specificity of 79.93% (95% CI: 75.14-84.71), outperforming standalone mammography AI (sensitivity 81.82%, specificity 86.25%) and Thermalytix AI (sensitivity 92.73%, specificity 75.46%). Importantly, the sensitivity of Mammography dropped significantly in dense breasts (67.86%) versus fatty breasts (96.30%), whereas Thermalytix AI maintained high and consistent sensitivity in both (92.59% and 92.86%, respectively). This demonstrates that a density-informed multi-modal AI framework can overcome key limitations of unimodal screening and deliver high performance across diverse breast compositions. The proposed framework is interpretable, low-cost, and easily deployable, offering a practical path to improving breast cancer screening outcomes in both high-resource and resource-limited settings.