Scaled Outer Product (SOP) is a post-training quantization methodology for large language model weights, designed to deliver near-lossless fidelity at 4.5--6 bits per weight on hardware with per-layer LUT decode. The methodology combines per-layer search of fixed and dynamic codebook pairs selected by a per-block selection bit, signed per-block scales, activation-weighted cosine selection, and multiple-choice knapsack promotion of sensitive layers with outlier and sparse-residual correction. Fixed codebooks include NF4, BOF4, Split87, and SH4; per-layer optimized codebooks (DD4) are hosted in LUT SRAM. A new hardware-efficient LUT output format (HIF) is proposed to improve performance, energy, and cost. Across six open model families, the recommended FP6 operating point (E2M3sUE4M4, 6.5 bpw) achieves lower weight reconstruction error than the conventional per-layer-POT FP8 baseline (E4M3, 8.0 bpw) at 1.5 bpw lower storage cost, demonstrating that block-scaled small atoms with carefully chosen scale precision can replace conventionally-deployed FP8. Full evaluation across the 4.5--6 bpw range, including layer promotion and sparse residual correction, is reported in a companion paper.

翻译：标量外积（SOP）是一种面向大语言模型权重的训练后量化方法，旨在为具有逐层LUT解码能力的硬件实现每权重4.5-6比特的近无损保真度。该方法结合了以下技术：通过逐块选择比特确定的固定与动态码本对的逐层搜索、带符号的逐块缩放因子、激活加权余弦选择、以及针对敏感层的多选背包提升（含异常值与稀疏残差修正）。固定码本包括NF4、BOF4、Split87和SH4；逐层优化码本（DD4）存储于LUT SRAM中。本文提出一种新型硬件高效LUT输出格式（HIF）以提升性能、能效与成本效益。在六个开源模型族中，推荐FP6工作点（E2M3sUE4M4，6.5 bpw）在降低1.5 bpw存储成本的前提下，其权重重建误差优于传统逐层POT FP8基线（E4M3，8.0 bpw），证明采用精心设计的尺度精度的小原子块缩放方案可替代传统部署的FP8。关于4.5-6 bpw范围内的全面评估（包括层提升与稀疏残差修正）将在配套论文中详细报告。