An Explainable Deep Learning Framework for Robust Image Classification and Semantic Understanding

Abstract

This paper evaluates a compact, from-scratch convolutional neural network (CNN) on the MNIST handwritten-digit benchmark along four simultaneous axes: classification accuracy against classical baselines, explainability faithfulness, adversarial and random-noise robustness, and feature-space separability. The CNN is implemented on bare metal in NumPy, with handwritten and numerically-verified backpropagation, using three convolution-pooling blocks (≈ 98,400 parameters). Across five independent training seeds, the CNN reaches 97.56% ± 0.13% test accuracy on the full 10,000-image MNIST test set, significantly outperforming logistic regression (89.47%), a hyperparameter-tuned RBF-kernel SVM (95.20%; McNemar’s test, χ² = 143.6, p < 0.001), and a random forest (93.65% ± 0.05% over 5 random states). A controlled experiment isolates how much of this advantage is attributable to input resolution versus network depth: a shallower two-block CNN — architecturally identical to the network used in preliminary work on a lower-resolution benchmark — already reaches 96.29% ± 0.20% at MNIST scale, showing that resolution accounts for most of the advantage over classical baselines, with the additional convolutional block contributing a smaller, secondary gain.
Three explainability methods — gradient-based saliency, Grad-CAM, and occlusion sensitivity — are evaluated quantitatively via deletion/insertion faithfulness curves (pairwise Wilcoxon signed-rank tests confirm occlusion sensitivity is significantly more faithful than either gradient-based method, p < 0.01) and a model-parameter-randomization sanity check repeated across three training seeds. Occlusion sensitivity passes this sanity check cleanly (correlation 0.025 ± 0.020); Grad-CAM is borderline (0.272 ± 0.017); gradient-based saliency shows the least favorable result (0.643 ± 0.058), indicating its attributions are driven substantially by network architecture rather than by learned weights alone. Robustness is characterized here, not claimed as solved: accuracy degrades gracefully under Gaussian noise (97.6% to 80.9% as noise increases, full test set) but collapses more sharply under FGSM adversarial perturbation (97.6% to 17.6% at the largest tested budget); no adversarial defense is proposed or evaluated. The learned penultimate-layer representation shows strong class-discriminative structure: a 5-fold cross-validated nearest-centroid classifier recovers 97.33% ± 1.33% accuracy from the raw feature space alone, nearly matching the network’s own classification accuracy.