FMCE-Net++: Feature Map Convergence Evaluation and Training

Deep Neural Networks (DNNs) face interpretability challenges due to their opaque internal representations. While Feature Map Convergence Evaluation (FMCE) quantifies module-level convergence via Feature Map Convergence Scores (FMCS), it lacks experimental validation and closed-loop integration. To address this limitation, we propose FMCE-Net++, a novel training framework that integrates a pretrained, frozen FMCE-Net as an auxiliary head. This module generates FMCS predictions, which, combined with task labels, jointly supervise backbone optimization through a Representation Auxiliary Loss. The RAL dynamically balances the primary classification loss and feature convergence optimization via a tunable \Representation Abstraction Factor. Extensive experiments conducted on MNIST, CIFAR-10, FashionMNIST, and CIFAR-100 demonstrate that FMCE-Net++ consistently enhances model performance without architectural modifications or additional data. Key experimental outcomes include accuracy gains of $+1.16$ pp (ResNet-50/CIFAR-10) and $+1.08$ pp (ShuffleNet v2/CIFAR-100), validating that FMCE-Net++ can effectively elevate state-of-the-art performance ceilings.