LayerShield-QAT: Accuracy-Preserving Integer Quantization for Physics-Grounded Edge Regression

Integer accelerators can make scientific inversion practical at the edge, yet regression models are unusually vulnerable to output discretization: errors that leave a classifier's decision unchanged can invalidate a continuous physical estimate. We present \method, a physics-grounded multi-task regression and quantization workflow for gamma-ray well-logging inversion on 8-bit neural accelerators. The model maps 11 detector-window measurements to five coupled formation and mud properties, using shared representations and task-weighted objectives to prioritize formation density and photoelectric factor. Layer-wise diagnostics identify the input and output transformations as the dominant sources of quantization error; \method therefore quantizes the hidden representation to INT8 while retaining higher precision at the boundary layers. Training additionally injects systematic, random, and count-statistical perturbations to reduce the synthetic-to-field gap. On the reported synthetic benchmark, multi-task learning increases the fraction of predictions within application tolerances from 23.61% to 89.53% for formation density and from 19.82% to 88.15% for photoelectric factor, while reaching 98.18–99.79% on three auxiliary mud targets. Accuracy-preserved quantization and deployment on NPU SoC systems reports 3.5$\times$ CPU and 23$\times$ NPU speedups over a legacy C implementation, with stable field data trends. The results support a broader principle: for high-accuracy edge regression, precision should be allocated according to physical sensitivity and layer-wise error propagation rather than uniformly.