Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.

Diffusion models have demonstrated competitive performance in missing data imputation (MDI) task. However, directly applying diffusion models to MDI produces suboptimal performance due to two primary defects. First, the sample diversity promoted by diffusion models hinders the accurate inference of missing values. Second, data masking reduces observable indices for model training, obstructing imputation performance.

The efficacy of Artificial Intelligence (AI) in micro/nano manufacturing is fundamentally constrained by the scarcity of high-quality and physically grounded training data for defect inspection. Lithography defect data from semiconductor industry are rarely accessible for research use, resulting in a shortage of publicly available datasets. To address this bottleneck in lithography, this study proposes a novel methodology for generating large-scale, physically valid defect datasets with pixel-level annotations. The framework begins with the ab initio synthesis of defect layouts using controllable, physics-constrained mathematical morphology operations (erosion and dilation) applied to the original design-level layout. These synthesized layouts, together with their defect-free counterparts, are fabricated into physical samples via high-fidelity digital micromirror device (DMD)-based lithography. Optical micrographs of the synthesized defect samples and their defect-free references are then compared to create consistent defect delineation annotations. Using this methodology, we constructed a comprehensive dataset of 3,530 Optical micrographs containing 13,365 annotated defect instances including four classes: bridge, burr, pinch, and contamination. Each defect instance is annotated with a pixel-accurate segmentation mask, preserving full contour and geometry. The segmentation-based Mask R-CNN achieves AP@0.5 of 0.980, 0.965, and 0.971, compared with 0.740, 0.719, and 0.717 for Faster R-CNN on bridge, burr, and pinch classes, representing a mean AP@0.5 improvement of approximately 34%. For the contamination class, Mask R-CNN achieves an AP@0.5 roughly 42% higher than Faster R-CNN. These consistent gains demonstrate that our proposed methodology to generate defect datasets with pixel-level annotations is feasible for robust AI-based Measurement/Inspection (MI) in semiconductor fabrication.

Abstract-- This paper presents a cutting-edge robotic inspection solution (Figure 1) designed to automate quality control in automotive manufacturing. The system integrates a pair of collaborative robots, each equipped with a high-resolution camera-based vision system to accurately detect and localize surface and thread defects in aluminum high-pressure die casting (HPDC) automotive components. In addition, specialized lenses and optimized lighting configurations are employed to ensure consistent and high-quality image acquisition. The YOLO11n deep learning model is utilized, incorporating additional enhancements such as image slicing, ensemble learning, and bounding-box merging to significantly improve performance and minimize false detections. Furthermore, image processing techniques are applied to estimate the extent of the detected defects. Experimental results demonstrate real-time performance with high accuracy across a wide variety of defects, while minimizing false detections. The proposed solution is promising and highly scalable, providing the flexibility to adapt to various production environments and meet the evolving demands of the automotive industry. Quality control plays a crucial role in automotive manufacturing. Even minor defects introduced during production can result in significant performance issues and safety risks, emphasizing the importance of stringent quality inspections [1]. Traditionally, quality control processes in automotive production have been heavily dependent on skilled human operators to inspect components visually. This approach is not only costly and time-intensive but also susceptible to inconsistencies arising from operator fatigue and subjective decision-making [2].

Anomaly detection in multivariate time series is crucial to ensure the quality of data coming from a physics experiment. Accurately identifying the moments when unexpected errors or defects occur is essential, yet challenging due to scarce labels, unknown anomaly types, and complex correlations across dimensions. To address the scarcity and unreliability of labelled data, we use the Lorenzetti Simulator to generate synthetic events with injected calorimeter anomalies. We then assess the sensitivity of several time series anomaly detection methods, including transformer-based and other deep learning models. The approach employed here is generic and applicable to different detector designs and defects.

Large language models have made significant progress in mathematical reasoning, which serves as an important testbed for AI and could impact scientific research if further advanced. By scaling reasoning with reinforcement learning that rewards correct final answers, LLMs have improved from poor performance to saturating quantitative reasoning competitions like AIME and HMMT in one year. However, this approach faces fundamental limitations. Pursuing higher final answer accuracy doesn't address a key issue: correct answers don't guarantee correct reasoning. Moreover, many mathematical tasks like theorem proving require rigorous step-by-step derivation rather than numerical answers, making final answer rewards inapplicable. To push the limits of deep reasoning, we believe it is necessary to verify the comprehensiveness and rigor of mathematical reasoning. Self-verification is particularly important for scaling test-time compute, especially for open problems without known solutions. Towards self-verifiable mathematical reasoning, we investigate how to train an accurate and faithful LLM-based verifier for theorem proving. We then train a proof generator using the verifier as the reward model, and incentivize the generator to identify and resolve as many issues as possible in their own proofs before finalizing them. To maintain the generation-verification gap as the generator becomes stronger, we propose to scale verification compute to automatically label new hard-to-verify proofs, creating training data to further improve the verifier. Our resulting model, DeepSeekMath-V2, demonstrates strong theorem-proving capabilities, achieving gold-level scores on IMO 2025 and CMO 2024 and a near-perfect 118/120 on Putnam 2024 with scaled test-time compute.

Large language models (LLMs) are increasingly used both to make decisions in domains such as health, education and law, and to simulate human behavior. Yet how closely LLMs mirror actual human decision-making remains poorly understood. This gap is critical: misalignment could produce harmful outcomes in practical applications, while failure to replicate human behavior renders LLMs ineffective for social simulations. Here, we address this gap by developing a digital twin of game-theoretic experiments and introducing a systematic prompting and probing framework for machine-behavioral evaluation. Testing three open-source models (Llama, Mistral and Qwen), we find that Llama reproduces human cooperation patterns with high fidelity, capturing human deviations from rational choice theory, while Qwen aligns closely with Nash equilibrium predictions. Notably, we achieved population-level behavioral replication without persona-based prompting, simplifying the simulation process. Extending beyond the original human-tested games, we generate and preregister testable hypotheses for novel game configurations outside the original parameter grid. Our findings demonstrate that appropriately calibrated LLMs can replicate aggregate human behavioral patterns and enable systematic exploration of unexplored experimental spaces, offering a complementary approach to traditional research in the social and behavioral sciences that generates new empirical predictions about human social decision-making.