Boundary-Aware Quantization: Finite-Scale Decision Geometry of Neural Classifiers

We measured quantization-induced decision-boundary changes using local logit-margin radii, first-order boundary displacement, normal variation, slice-boundary Jaccard distance, grid prediction changes, multiclass junction counts, and low-margin boundary-band flips. On the digits benchmark, 8-bit weight quantization preserved all test labels while producing boundary-mask Jaccard $0.428$ on the PCA slice; at 4 bits, accuracy remained $0.9733$, while boundary Jaccard rose to $0.970$ and median local boundary shift reached $0.0290$. Interpolation between adjacent quantization levels localized the visible reconfigurations at multiclass junctions, with 12, 34, and 17 triple-junction cells in the selected transitions. Calibration-to-test stopping reduced the digits held-out flip rate from $0.0094$ to $0.0022$ and boundary Jaccard from $0.825$ to $0.524$; the same stopping rule also reduced flips on MNIST and Fashion-MNIST. On official CIFAR-10 subsets, PTQ-W selected by accuracy gave 6-bit flip $0.0367$ and boundary Jaccard $0.184$, whereas boundary-aware stopping selected 8-bit flip $0.0083$ and boundary Jaccard $0.048$. On full CIFAR-10 with three seeds, 6-bit PTQ-W lost $0.0029$ accuracy relative to float, changed $5.3\%$ of held-out decisions, and changed $24.5\%$ of low-margin boundary-band decisions. A fixed-bit boundary-gap rounding term changed the trade-off at 4 bits by reducing boundary Jaccard from $0.457$ to $0.435$ and boundary-band pair-order flip from $0.3600$ to $0.3558$, with an accuracy trade-off; the 3-bit stress test exposed the tuning limit of this surrogate. Calibration boundary Jaccard predicted held-out boundary Jaccard across PTQ-W and optimized rounding variants with $r=0.947$--$0.994$.