We start by providing motivation for the unconstrained Jacobians problem introduced in the main text. We will continue our proof using contradiction. Figure 1: Fully-connected ResNet34 (Type 1 model) trained on MNIST.Figure 2: Fully-connected ResNet34 (Type 1 model) trained on FashionMNIST. Figure 10: Fully-connected ResNet34 (Type 1 model) trained on MNIST. Figure 24: Fully-connected ResNet34 (Type 1 model) trained on MNIST.

The global rise in type 2 diabetes underscores the need for scalable and cost-effective screening methods. Current diagnosis requires biochemical assays, which are invasive and costly. Advances in consumer wearables have enabled early explorations of machine learning-based disease detection, but prior studies were limited to controlled settings. We present SweetDeep, a compact neural network trained on physiological and demographic data from 285 (diabetic and non-diabetic) participants in the EU and MENA regions, collected using Samsung Galaxy Watch 7 devices in free-living conditions over six days. Each participant contributed multiple 2-minute sensor recordings per day, totaling approximately 20 recordings per individual. Despite comprising fewer than 3,000 parameters, SweetDeep achieves 82.5% patient-level accuracy (82.1% macro-F1, 79.7% sensitivity, 84.6% specificity) under three-fold cross-validation, with an expected calibration error of 5.5%. Allowing the model to abstain on less than 10% of low-confidence patient predictions yields an accuracy of 84.5% on the remaining patients. These findings demonstrate that combining engineered features with lightweight architectures can support accurate, rapid, and generalizable detection of type 2 diabetes in real-world wearable settings.

Clinical notes in Electronic Health Records (EHRs) capture rich temporal information on events, clinician reasoning, and lifestyle factors often missing from structured data. Leveraging them for predictive modeling can be impactful for timely identification of chronic diseases. However, they present core natural language processing (NLP) challenges: long text, irregular event distribution, complex temporal dependencies, privacy constraints, and resource limitations. We present two complementary methods for temporally and contextually grounded risk prediction from longitudinal notes. First, we introduce HiTGNN, a hierarchical temporal graph neural network that integrates intra-note temporal event structures, inter-visit dynamics, and medical knowledge to model patient trajectories with fine-grained temporal granularity. Second, we propose ReVeAL, a lightweight, test-time framework that distills the reasoning of large language models into smaller verifier models. Applied to opportunistic screening for Type 2 Diabetes (T2D) using temporally realistic cohorts curated from private and public hospital corpora, HiTGNN achieves the highest predictive accuracy, especially for near-term risk, while preserving privacy and limiting reliance on large proprietary models. ReVeAL enhances sensitivity to true T2D cases and retains explanatory reasoning. Our ablations confirm the value of temporal structure and knowledge augmentation, and fairness analysis shows HiTGNN performs more equitably across subgroups.

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The aim of this work is to address the possible pitfalls to the independence assumption in a social network, as used in the study of influence maximization. The labels on the nodes indicate the "type" of each node.

Clustering is an unsupervised learning technique that aims to identify patterns that consist of similar or interrelated observations within data [39, 87]. Many existing clustering algorithms are often categorised into three primary groups [39, 82]: partitioning algorithms such as K-Means [39] and Spectral Clustering [88], hierarchical algorithms such as Single Linkage [39] and HDBSCAN* [7, 8], and soft (fuzzy or probabilistic) algorithms such as Fuzzy c-Means (FCM) [4] and Expectation Maximisation with Gaussian Mixture Models (EM-GMM) [20]. Partitioning clustering algorithms partition data into a given number of k clusters, while hierarchical clustering algorithms produce a sequence of nested partitions with incrementally varying numbers of clusters. Soft clustering algorithms are similar to partitioning techniques except that each data observation is assigned a degree of membership or probability to each cluster, rather than a full assignment to a single cluster. It is worth mentioning that within the aforementioned categories there are clustering algorithms that may not necessarily assign all observations to clusters, due to outlier trimming or noise detection. Two examples of such algorithms are trimmed K-means [14] and the previously mentioned HDBSCAN*, each of which may produce solutions where not all observations are assigned to clusters. Clustering validation or validity is an important step of the clustering process irrespective of the algorithm used [39, 25], as it is crucial to determine the best produced partition(s) and number of clusters within the data [23].

Type 2 diabetes prevention and treatment can benefit from personalized lifestyle prescriptions. However, the delivery of personalized lifestyle medicine prescriptions is limited by the shortage of trained professionals and the variability in physicians' expertise. We propose an offline contextual bandit approach that learns individualized lifestyle prescriptions from the aggregated NHANES profiles of 119,555 participants by minimizing the Magni glucose risk-reward function. The model encodes patient status and generates lifestyle medicine prescriptions, which are trained using a mixed-action Soft Actor-Critic algorithm. The task is treated as a single-step contextual bandit. The model is validated against lifestyle medicine prescriptions issued by three certified physicians from Xiangya Hospital. These results demonstrate that offline mixed-action SAC can generate risk-aware lifestyle medicine prescriptions from cross-sectional NHANES data, warranting prospective clinical validation.

Objective. Type 2 diabetes mellitus (T2DM) is a highly prevalent non-communicable chronic disease that substantially reduces life expectancy. Accurate estimation of all-cause mortality risk in T2DM patients is crucial for personalizing and optimizing treatment strategies. Research Design and Methods. This study analyzed a cohort of 554 patients (aged 40-87 years) with diagnosed T2DM over a maximum follow-up period of 16.8 years, during which 202 patients (36%) died. Key survival-associated features were identified, and multiple machine learning (ML) models were trained and validated to predict all-cause mortality risk. To improve model interpretability, Shapley additive explanations (SHAP) was applied to the best-performing model. Results. The extra survival trees (EST) model, incorporating ten key features, demonstrated the best predictive performance. The model achieved a C-statistic of 0.776, with the area under the receiver operating characteristic curve (AUC) values of 0.86, 0.80, 0.841, and 0.826 for 5-, 10-, 15-, and 16.8-year all-cause mortality predictions, respectively. The SHAP approach was employed to interpret the model's individual decision-making processes. Conclusions. The developed model exhibited strong predictive performance for mortality risk assessment. Its clinically interpretable outputs enable potential bedside application, improving the identification of high-risk patients and supporting timely treatment optimization.