Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to capture nonlinear data manifold structure. More flexible approaches have other problems: autoencoders are generally difficult to interpret, and graph-embedding-based methods can produce pathological distortions in manifold geometry. Motivated by these shortcomings, we propose a variational framework that casts dimensionality reduction algorithms as solutions to an optimal manifold embedding problem. By construction, this framework permits nonlinear embeddings, allowing its solutions to be more flexible than PCA. Moreover, the variational nature of the framework has useful consequences for interpretability: each solution satisfies a set of partial differential equations, and can be shown to reflect symmetries of the embedding objective. We discuss these features in detail and show that solutions can be analytically characterized in some cases. Interestingly, one special case exactly recovers PCA.

MRI-based brain age estimation models aim to assess a subject's biological brain age based on information, such as neuroanatomical features. Various factors, including neurodegenerative diseases, can accelerate brain aging and measuring this phenomena could serve as a potential biomarker for clinical applications. While deep learning (DL)-based regression has recently attracted major attention, existing approaches often fail to capture the continuous nature of neuromorphological changes, potentially resulting in sub-optimal feature representation and results. To address this, we propose to use supervised contrastive learning with the recent Rank-N-Contrast (RNC) loss to estimate brain age based on widely used T1w structural MRI for the first time and leverage Grad-RAM to visually explain regression results. Experiments show that our proposed method achieves a mean absolute error (MAE) of 4.27 years and an $R^2$ of 0.93 with a limited dataset of training samples, significantly outperforming conventional deep regression with the same ResNet backbone while performing better or comparably with the state-of-the-art methods with significantly larger training data. Furthermore, Grad-RAM revealed more nuanced features related to age regression with the RNC loss than conventional deep regression. As an exploratory study, we employed the proposed method to estimate the gap between the biological and chronological brain ages in Alzheimer's Disease and Parkinson's disease patients, and revealed the correlation between the brain age gap and disease severity, demonstrating its potential as a biomarker in neurodegenerative disorders.

Recent efforts in smart manufacturing have enhanced aerospace fuselage assembly processes, particularly by innovating shape adjustment techniques to minimize dimensional gaps between assembled sections. Existing approaches have shown promising results but face the issue of low sample efficiency from the manufacturing systems. It arises from the limitation of the classical Monte Carlo method when uncovering the mean response from a distribution. In contrast, recent work has shown that quantum algorithms can achieve the same level of estimation accuracy with significantly fewer samples than the classical Monte Carlo method from distributions. Therefore, we can adopt the estimation of the quantum algorithm to obtain the estimation from real physical systems (distributions). Motivated by this advantage, we propose a Quantum Bayesian Optimization (QBO) framework for precise shape control during assembly to improve the sample efficiency in manufacturing practice. Specifically, this approach utilizes a quantum oracle, based on finite element analysis (FEA)-based models or surrogate models, to acquire a more accurate estimation of the environment response with fewer queries for a certain input. QBO employs an Upper Confidence Bound (UCB) as the acquisition function to strategically select input values that are most likely to maximize the objective function. It has been theoretically proven to require much fewer samples while maintaining comparable optimization results. In the case study, force-controlled actuators are applied to one fuselage section to adjust its shape and reduce the gap to the adjoining section. Experimental results demonstrate that QBO achieves significantly lower dimensional error and uncertainty compared to classical methods, particularly using the same queries from the simulation.

Score matching has become a central training objective in modern generative modeling, particularly in diffusion models, where it is used to learn high-dimensional data distributions through the estimation of score functions. Despite its empirical success, the theoretical understanding of the optimization behavior of score matching, particularly in over-parameterized regimes, remains limited. In this work, we study gradient descent for training over-parameterized models to learn a single Gaussian distribution. Specifically, we use a student model with $n$ learnable parameters and train it on data generated from a single ground-truth Gaussian using the population score matching objective. We analyze the optimization dynamics under multiple regimes. When the noise scale is sufficiently large, we prove a global convergence result for gradient descent. In the low-noise regime, we identify the existence of a stationary point, highlighting the difficulty of proving global convergence in this case. Nevertheless, we show convergence under certain initialization conditions: when the parameters are initialized to be exponentially small, gradient descent ensures convergence of all parameters to the ground truth. We further prove that without the exponentially small initialization, the parameters may not converge to the ground truth. Finally, we consider the case where parameters are randomly initialized from a Gaussian distribution far from the ground truth. We prove that, with high probability, only one parameter converges while the others diverge, yet the loss still converges to zero with a $1/τ$ rate, where $τ$ is the number of iterations. We also establish a nearly matching lower bound on the convergence rate in this regime. This is the first work to establish global convergence guarantees for Gaussian mixtures with at least three components under the score matching framework.

Abstract--Escalating cyber threats and the high-dimensional complexity of IoT traffic have outpaced classical anomaly detection methods. While deep learning offers improvements, computational bottlenecks limit real-time deployment at scale. We present a quantum autoencoder (QAE) framework that compresses network traffic into discriminative latent representations and employs quantum support vector classification (QSVC) for intrusion detection. Evaluated on three datasets, our approach achieves improved accuracy on ideal simulators and on the IBM Quantum hardware (ibm fez)--demonstrating practical quantum advantage on current NISQ devices. This work establishes quantum machine learning as a viable, hardware-ready solution for real-world cybersecurity challenges.

Deciphering tumor microenvironment from Whole Slide Images (WSIs) is intriguing as it is key to cancer diagnosis, prognosis and treatment response. While these gigapixel images on one hand offer a comprehensive portrait of cancer, on the other hand, the extremely large size, as much as more than 10 billion pixels, make it challenging and time-consuming to navigate to corresponding regions to support diverse clinical inspection. Inspired by pathologists who conducted navigation on WSIs with a combination of sampling, reasoning and self-reflection, we proposed "PathReasoning", a multi-modal reasoning agent that iteratively navigates across WSIs through multiple rounds of reasoning and refinements. Specifically, starting with randomly sampled candidate regions, PathReasoning reviews current selections with self-reflection, reasoning over the correspondence between visual observations and clinical questions, and concludes by proposing new regions to explore. Across rounds, PathReasoning builds a reasoning chain that gradually directs attention to diagnostically relevant areas. PathReasoning turns each whole slide into a sequence of question-guided views, allowing the model to efficiently find informative ROIs within a fixed number of steps, without the need for dense pixel-level annotations. PathReasoning can substantially outperform strong ROI-selection approaches by 6.7% and 3.1% of AUROC on subtyping and longitudinal analysis tasks. The high-quality ROIs further support accurate report generation on breast cancer, significantly outperforming the standard GPT-4o by 10% in accuracy. PathReasoning prioritizes question-specific regions and constructs interpretable reasoning chains, supporting efficient slide review, consistent diagnostic interpretations, comprehensive reporting, and evidence traceability in digital pathology.

Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational Autoencoder (GM-VAE) framework designed to address this by integrating an Expectation-Maximization (EM)-inspired training scheme with a novel spectral interpretability metric. Unlike conventional VAEs that jointly optimize reconstruction and clustering (often leading to training instability), our method utilizes a block-coordinate descent strategy, alternating between expectation and maximization steps. This approach stabilizes training and naturally aligns latent clusters with distinct physical regimes. To objectively evaluate the learned representations, we introduce a quantitative metric based on graph-Laplacian smoothness, which measures the coherence of physical quantities across the latent manifold. We demonstrate the efficacy of this framework on datasets of increasing complexity: surface reaction ODEs, Navier-Stokes wake flows, and experimental laser-induced combustion Schlieren images. The results show that our GM-VAE yields smooth, physically consistent manifolds and accurate regime clustering, offering a robust data-driven tool for interpreting turbulent and reactive flow systems.

This study investigates the effectiveness and efficiency of two variants of the XGBoost regression model, the full-capacity and lightweight (tiny) versions, for predicting the concentrations of carbon monoxide (CO) and nitrogen dioxide (NO2). Using the AirQualityUCI dataset collected over one year in an urban environment, we conducted a comprehensive evaluation based on widely accepted metrics, including Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Bias Error (MBE), and the coefficient of determination (R2). In addition, we assessed resource-oriented metrics such as inference time, model size, and peak RAM usage. The full XGBoost model achieved superior predictive accuracy for both pollutants, while the tiny model, though slightly less precise, offered substantial computational benefits with significantly reduced inference time and model storage requirements. These results demonstrate the feasibility of deploying simplified models in resource-constrained environments without compromising predictive quality. This makes the tiny XGBoost model suitable for real-time air-quality monitoring in IoT and embedded applications.

The rapid expansion of Internet of Things (IoT) deployments across diverse sectors has significantly enhanced operational efficiency, yet concurrently elevated cybersecurity vulnerabilities due to increased exposure to cyber threats. Given the limitations of traditional signature-based Anomaly Detection Systems (ADS) in identifying emerging and zero-day threats, this study investigates the effectiveness of two unsupervised anomaly detection techniques, Isolation Forest (IF) and One-Class Support Vector Machine (OC-SVM), using the TON_IoT thermostat dataset. A comprehensive evaluation was performed based on standard metrics (accuracy, precision, recall, and F1-score) alongside critical resource utilization metrics such as inference time, model size, and peak RAM usage. Experimental results revealed that IF consistently outperformed OC-SVM, achieving higher detection accuracy, superior precision, and recall, along with a significantly better F1-score. Furthermore, Isolation Forest demonstrated a markedly superior computational footprint, making it more suitable for deployment on resource-constrained IoT edge devices. These findings underscore Isolation Forest's robustness in high-dimensional and imbalanced IoT environments and highlight its practical viability for real-time anomaly detection.

Training machine learning models with differential privacy (DP) limits an adversary's ability to infer sensitive information about the training data. It can be interpreted as a bound on adversary's capability to distinguish two adjacent datasets according to chosen adjacency relation. In practice, most DP implementations use the add/remove adjacency relation, where two datasets are adjacent if one can be obtained from the other by adding or removing a single record, thereby protecting membership. In many ML applications, however, the goal is to protect attributes of individual records (e.g., labels used in supervised fine-tuning). We show that privacy accounting under add/remove overstates attribute privacy compared to accounting under the substitute adjacency relation, which permits substituting one record. To demonstrate this gap, we develop novel attacks to audit DP under substitute adjacency, and show empirically that audit results are inconsistent with DP guarantees reported under add/remove, yet remain consistent with the budget accounted under the substitute adjacency relation. Our results highlight that the choice of adjacency when reporting DP guarantees is critical when the protection target is per-record attributes rather than membership.