NLINEX: A Hybrid Loss Function for Artificial Neural Network Optimisation in Neuroimaging

Optimising artificial neural networks for functional magnetic resonance imaging connectivity analysis remains a formidable challenge, particularly in detecting subtle pathological patterns associated with Alzheimer's disease under noisy and imbalanced data conditions. Conventional loss functions—such as Mean Squared Error, Mean Absolute Error, Binary Cross-Entropy, Focal Loss, and LovászSoftmax—often exhibit limited sensitivity to these rare manifestations. This work proposes the Nonlinear Exponential (NLINEX) loss function, a composite penalisation strategy that integrates exponential amplification, quadratic regularisation, and linear calibration to enhance convergence and improve classification fidelity. Implemented within a feedforward neural framework (NeuroNet) and benchmarked on a real-world, 6400-sample MRI dataset preprocessed via principal component analysis, NLINEX achieved superior performance against six baseline losses. The optimal configuration (k = 2.5, c = 0.5) yielded consistent validation metrics across fifty epochs: loss (0.15–0.20), accuracy (0.95–0.96), and area under the receiver operating characteristic curve (0.96–0.98). These findings demonstrate NLINEX's efficacy in capturing nuanced connectivity deviations, establishing it as a scalable and clinically meaningful solution for biomarker discovery and diagnostic modelling in neuroimaging.