Regularized statistical feature modeling with graph-constrained optimization for deep image classification

Deep image classification algorithms may suffer from redundant feature responses, unstable class boundaries, and weak robustness when sample differences are subtle and class distributions are complex. To address these issues, this paper proposes the Regularized Statistical Feature Modeling Network (RSFM-Net), a mathematically guided but architecture-specific classification optimization framework. RSFM-Net integrates a reproducible CNN-Transformer encoder, normalized statistical feature screening, mini-batch graph-constrained regularization, supervised contrastive separation, adaptive-margin classification, and a hard-sample bias-corrected AdamW-style update. The novelty is positioned as the coordinated formulation and reproducible implementation of these established ideas rather than as a fundamentally new mathematical theory. In five independent runs on CIFAR-10, CIFAR-100, and Fashion-MNIST, RSFM-Net achieved accuracies of 98.34 +/- 0.11%, 88.61 +/- 0.26%, and 96.63 +/- 0.10%, respectively. The ablation results show that statistical screening and manifold regularization provide the largest gains, while adaptive-margin, contrastive, and bias-correction terms provide smaller complementary improvements. Computational cost, hard-sample selection, margin formulation, component interaction, interpretability scope, and limitations regarding cross-domain generality are further analyzed. Image-level explainability analyses with Grad-CAM and attention heatmaps are also provided, and the sensitivity of the main hyperparameters across the three datasets is analyzed.