Two-Field Product Bit-Width Allocation for Mixed-Precision LLM Quantization Method, and a Negative Scaling Result on Large Mixture-of-Experts Models

Mixed-precision post-training quantization assigns each group of weights a bit-width so as to minimize task-loss degradation at a fixed average budget. Established methods allocate bits from a single field (weight magnitude/activation scale, AWQ-style) or output sensitivity from second-order information (HAWQ, OBQ, SqueezeLLM). We study two-field product allocation, b_r ∝ √(A_r · B_r), where A_r is a per-row amplitude field and B_r is a measured output-sensitivity field (diagonal empirical Fisher). The product equals, to first order, the per-row contribution to the loss under quantization noise. We introduce a safe-floor, a group-consistent amplitude, and a Fisher-CV statistic CV=std(B)/mean(B) to predict where the method thrives. For small models (under 3B parameters), the equal-budget advantage of A⊗B over the best single field is monotone in Fisher-CV (up to 24 perplexity points on highly heterogeneous models). Conversely, we report a negative scaling result: on a deployable 35B-parameter mixture-of-experts model (Qwen3.6-35B-A3B) with exceptionally high expert heterogeneity (Fisher-CV≈2.12), the two-field advantage does not materialize. We conclude that two-field allocation is highly effective for specialized small-scale edge models, but of limited practical value on production-scale MoEs.