Why nonlinear models matter: unified analysis of cognitive load, stress, and exercise using wearable physiological signals

<i>Objective.</i>Physiological measurements obtained from wearable devices reflect complex autonomic nervous system dynamics that are often assumed to follow simple linear relationships, such as elevated heart rate under stress or reduced stress during exercise. This study investigates whether physiological state recognition from wearable measurements is fundamentally linear or nonlinear by examining stress, cognitive load, and physical exercise detection.<i>Approach.</i>A unified signal-processing and evaluation framework was applied to three publicly available Empatica E4 datasets covering structured stress induction, real-world exam stress, aerobic and anaerobic exercise, and cognitive load tasks. Standardized preprocessing, window-based feature extraction, subject-independent evaluation, leave-one-subject-out (LOSO) validation, multimodal ablation studies, and Shapley Additive Explanations (SHAP)-based interpretability analysis were conducted. Multiple linear models (logistic regression, linear support vector machine (SVM), linear discriminant analysis, and ridge classifier) were compared against nonlinear approaches, including SVM(RBF), random forest, gradient boosting, XGBoost, and LightGBM.<i>Main results.</i>Across all datasets, nonlinear models consistently outperformed linear baselines. Tree-based ensembles achieved 0.89-0.98 accuracy and 0.96-0.99 AUC, whereas linear models remained below 0.70-0.73 AUC. LOSO validation revealed substantial inter-individual variability, yet nonlinear models retained moderate cross-person generalization. Ablation results confirmed the importance of multimodal fusion, particularly electrodermal activity, temperature, and accelerometry. SHAP analysis revealed nonlinear and interaction-driven feature effects consistent with known autonomic mechanisms.<i>Significance.</i>These findings demonstrate that physiological state recognition from wearable measurements is inherently nonlinear, even when individual modalities exhibit monotonic trends. The study establishes a unified benchmark and supports the necessity of nonlinear modeling for robust, real-time wearable health-monitoring systems.