HESREN: A Derivative-Informed Reservoir Framework for Detecting Transient Neural Events and Windowless Estimation of...

Dynamic functional connectivity (dFC) analysis in functional magnetic resonance imaging (fMRI) faces a fundamental challenge: conventional sliding-window methods must trade temporal resolution against statistical reliability, while rare transient neural events risk becoming undetectable when included in training data. We introduce HESREN (Hermite-Enhanced Software Reservoir Network), a novel framework integrating echo state networks with derivative-informed Hermite-type neural operators to enable windowless dFC estimation and leakage-free transient detection. HESREN employs a leaky-integrator reservoir that projects multivariate fMRI time series into high-dimensional state spaces, augmented with Gaussian-smoothed temporal derivatives to form enhanced feature vectors encoding value, velocity, and acceleration. Strict temporal partitioning trains all components exclusively on baseline segments while evaluating on complete time series, preserving transient events as out-of-distribution signals. Teacher-student distillation transfers the temporal precision of micro-window connectivity estimates into stable windowless operators via ridge-regularised linear readout; all hyperparameters and initialisation procedures are fully specified to ensure reproducibility. Validation on the NEBULA101 resting-state fMRI dataset across [Formula: see text] participants demonstrates consistent and substantial improvements over conventional methods. Transient event detection achieves AUC[Formula: see text] and average precision AP[Formula: see text], compared to AUC[Formula: see text] for raw-derivative baselines (Wilcoxon [Formula: see text], [Formula: see text], Cohen's [Formula: see text]), with phase-randomised surrogate testing confirming statistical robustness in all participants ([Formula: see text], [Formula: see text] surrogates). Comparison against mainstream dFC alternatives shows that HESREN statistically significant performance gains Gaussian Hidden Markov Models (AUC[Formula: see text]), temporal convolutional networks (AUC[Formula: see text]), LSTM autoregressive predictors (AUC[Formula: see text]), and conventional sliding-window correlation (AUC[Formula: see text]), with all advantages statistically significant ([Formula: see text]). Windowless dFC trajectories attain lag-corrected correlation [Formula: see text] with micro-window teachers while providing 3-[Formula: see text] finer temporal resolution than 25-TR sliding windows. Network-level analysis reveals that HESREN detects transient events an average of 4.5 TR (9 s) earlier than sliding-window methods, selectively amplifies within-language-network coupling by [Formula: see text] and default-mode-network coupling by [Formula: see text] during detected events, and is the only evaluated method to yield a positive network segregation index ([Formula: see text]), consistent with the known modular organisation of resting-state brain networks. HESREN overcomes fundamental limitations of sliding-window dFC through derivative-aware reservoir dynamics, offering a computationally efficient, mathematically principled framework for capturing transient neural reconfigurations with temporal precision previously improved in fMRI connectivity analysis. The modular architecture facilitates adaptation to diverse neuroimaging applications, from basic neuroscience to real-time clinical monitoring systems.