Low-Dimensional High-Leverage Subspace Optimization: Beyond Full-Parameter Coupled Training for Neural Network Quantization

This paper proposes Normalization Affine Preconditioning (NAP), treating normalization scale and bias parameters as a low-dimensional, high-leverage subspace for quantization robustness. For PTQ, it freezes backbone weights and tunes only affine parameters under the target fake-quantization graph before reconstruction. For QAT, it alternates feature learning with numerical calibration to reduce gradient coupling. The authors report recovery from severe low-bit accuracy collapse and improvements over reconstruction-based PTQ and saturated full-parameter QAT on ImageNet and CIFAR-100, with negligible tuning cost. Exact architectures, bit widths, baselines, and gains require full-paper verification.