🤖 AI Summary
Quantization induces uncontrolled deformations in neural network decision boundaries, compromising model robustness and generalization. This work presents the first systematic characterization of geometric alterations in classifier decision boundaries under finite numerical precision and introduces a boundary-aware quantization strategy. By leveraging geometric and statistical metrics—including local logit-margin radius, boundary displacement, normal vector variation, and sliced Jaccard distance—the method dynamically determines optimal quantization stopping points on a calibration set, integrating PTQ-W with margin-aware rounding optimization. Experiments on CIFAR-10 demonstrate that the approach reduces the prediction flip rate of 6-bit PTQ-W to 5.3% (boundary Jaccard = 0.184); with boundary-aware stopping, the flip rate further drops to 0.0083 at 8 bits (Jaccard = 0.048). Notably, calibration-set boundary metrics exhibit strong correlation with test performance (r = 0.947–0.994).
📝 Abstract
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 \(r=0.947\)--\(0.994\).