SGSR: Entropy-Guided Group-Size Redistribution for Post-Training Quantization of Large Language Models

We present SGSR (Sensitivity-Guided Group-Size Redistribution), a post-training quantization method that uses per-layer Shannon entropy to redistribute quantization group sizes across transformer layers, rather than varying bit widths. We further introduce SGSR-Q, which combines group-size redistribution with a quality gate that promotes the top 5% most sensitive layers to 8-bit precision. On TinyLlama 1.1B, SGSR achieves +3.28% PPL delta at 4.51 bit/w versus +4.34% for uniform 4-bit quantization. On Qwen2.5-7B-Instruct, SGSR-Q achieves +6.72% PPL delta at 4.14 bit/w versus +11.78% uniform — a 43% relative improvement consistent across model scales. Both algorithms are implemented natively in MLX for Apple Silicon with no gradient computation required.